local_mass_matrix := array(0..n_functions-1, 0..n_functions-1);
for i from 0 to n_functions-1 do
- # note that the interp function wants vector indexed from
+ # note that the interp function wants vectors indexed from
# one and not from zero.
values := array(1..n_functions);
for j from 1 to n_functions do
perl -pi -e 's/phi_polynom\[(\d)\] =/case $1: return/g;' shape_value_1d
perl -pi -e 's/grad_phi_polynom\[(\d)\] = (.*);/case $1: return Point<1>($2);/g;' shape_grad_1d
- perl -pi -e 's/\[(\d)\]\[(\d)\]/($1,$2)/g;' massmatrix_1d
- perl -pi -e 's/\[(\d)\]\[(\d)\]\[(\d)\]/[$1]($2,$3)/g;' prolongation_1d
- perl -pi~ -e 's/(t\d)/const double $1/g;' massmatrix_1d
+ perl -pi -e 's/\[(\d+)\]\[(\d)\]/($1,$2)/g;' massmatrix_1d
+ perl -pi -e 's/\[(\d+)\]\[(\d)\]\[(\d)\]/[$1]($2,$3)/g;' prolongation_1d
+ perl -pi -e 's/(t\d+) =/const double $1/g;' massmatrix_1d
*/
-- You should only have to change the very first lines for polynomials
-- of higher order.
--------------------------------------------------------------------------
- n_functions := 16;
+ n_functions := 16:
+ n_face_functions := 4:
ansatz_function := (a1 + a2*xi + a3*xi*xi + a4*xi*xi*xi) +
(b1 + b2*xi + b3*xi*xi + b4*xi*xi*xi)*eta +
(c1 + c2*xi + c3*xi*xi + c4*xi*xi*xi)*eta*eta +
- (d1 + d2*xi + d3*xi*xi + d4*xi*xi*xi)*eta*eta*eta;
- ansatz_points := array(0..n_functions-1);
+ (d1 + d2*xi + d3*xi*xi + d4*xi*xi*xi)*eta*eta*eta:
+ face_ansatz_function := a + b*xi + c*xi*xi + d*xi*xi*xi:
# note: ansatz_points[i] is a vector which is indexed from
# one and not from zero!
- ansatz_points[0] := [0,0];
- ansatz_points[1] := [1,0];
- ansatz_points[2] := [1,1];
- ansatz_points[3] := [0,1];
- ansatz_points[4] := [1/3,0];
- ansatz_points[5] := [2/3,0];
- ansatz_points[6] := [1,1/3];
- ansatz_points[7] := [1,2/3];
- ansatz_points[8] := [1/3,1];
- ansatz_points[9] := [2/3,1];
- ansatz_points[10]:= [0,1/3];
- ansatz_points[11]:= [0,2/3];
- ansatz_points[12]:= [1/3,1/3];
- ansatz_points[13]:= [2/3,1/3];
- ansatz_points[14]:= [2/3,2/3];
- ansatz_points[15]:= [1/3,2/3];
-
+ ansatz_points := array(0..n_functions-1):
+ ansatz_points[0] := [0,0]:
+ ansatz_points[1] := [1,0]:
+ ansatz_points[2] := [1,1]:
+ ansatz_points[3] := [0,1]:
+ ansatz_points[4] := [1/3,0]:
+ ansatz_points[5] := [2/3,0]:
+ ansatz_points[6] := [1,1/3]:
+ ansatz_points[7] := [1,2/3]:
+ ansatz_points[8] := [1/3,1]:
+ ansatz_points[9] := [2/3,1]:
+ ansatz_points[10]:= [0,1/3]:
+ ansatz_points[11]:= [0,2/3]:
+ ansatz_points[12]:= [1/3,1/3]:
+ ansatz_points[13]:= [2/3,1/3]:
+ ansatz_points[14]:= [2/3,2/3]:
+ ansatz_points[15]:= [1/3,2/3]:
+
+ face_ansatz_points := array(0..n_face_functions-1):
+ face_ansatz_points[0] := 0:
+ face_ansatz_points[1] := 1:
+ face_ansatz_points[2] := 1/3:
+ face_ansatz_points[3] := 2/3:
+ constrained_face_ansatz_points := array(0..2*(n_face_functions-2)+1-1):
+ constrained_face_ansatz_points[0] := 1/2:
+ constrained_face_ansatz_points[1] := 1/6:
+ constrained_face_ansatz_points[2] := 2/6:
+ constrained_face_ansatz_points[3] := 4/6:
+ constrained_face_ansatz_points[4] := 5/6:
- phi_polynom := array(0..n_functions-1);
- grad_phi_polynom := array(0..n_functions-1,0..1);
- local_mass_matrix := array(0..n_functions-1, 0..n_functions-1);
- prolongation := array(0..3,0..n_functions-1, 0..n_functions-1);
-
-
+ phi_polynom := array(0..n_functions-1):
+ grad_phi_polynom := array(0..n_functions-1,0..1):
+ local_mass_matrix := array(0..n_functions-1, 0..n_functions-1):
+ prolongation := array(0..3,0..n_functions-1, 0..n_functions-1):
+ interface_constraints := array(0..2*(n_face_functions-2)+1-1,
+ 0..n_face_functions-1):
+ real_points := array(0..n_functions-1, 0..1);
+
+ print ("Computing basis functions"):
for i from 0 to n_functions-1 do
- values := array(1..n_functions);
+ print (i):
+ values := array(1..n_functions):
for j from 1 to n_functions do
- values[j] := 0;
- od;
- values[i+1] := 1;
+ values[j] := 0:
+ od:
+ values[i+1] := 1:
- equation_system := {};
+ equation_system := {}:
for j from 0 to n_functions-1 do
poly := subs(xi=ansatz_points[j][1],
eta=ansatz_points[j][2],
- ansatz_function);
+ ansatz_function):
if (i=j) then
- equation_system := equation_system union {poly = 1};
+ equation_system := equation_system union {poly = 1}:
else
- equation_system := equation_system union {poly = 0};
- fi;
- od;
+ equation_system := equation_system union {poly = 0}:
+ fi:
+ od:
- phi_polynom[i] := subs(solve(equation_system), ansatz_function);
- grad_phi_polynom[i,0] := diff(phi_polynom[i], xi);
- grad_phi_polynom[i,1] := diff(phi_polynom[i], eta);
- od;
+ phi_polynom[i] := subs(solve(equation_system), ansatz_function):
+ grad_phi_polynom[i,0] := diff(phi_polynom[i], xi):
+ grad_phi_polynom[i,1] := diff(phi_polynom[i], eta):
+ od:
- phi:= proc(i,x,y) subs(xi=x, eta=y, phi_polynom[i]); end;
+ phi:= proc(i,x,y) subs(xi=x, eta=y, phi_polynom[i]): end:
- #points on children; let them be indexed one-based, as are
+
+ #points on children: let them be indexed one-based, as are
#the ansatz_points
- points[0] := array(0..n_functions-1, 1..2);
- points[1] := array(0..n_functions-1, 1..2);
- points[2] := array(0..n_functions-1, 1..2);
- points[3] := array(0..n_functions-1, 1..2);
+ points[0] := array(0..n_functions-1, 1..2):
+ points[1] := array(0..n_functions-1, 1..2):
+ points[2] := array(0..n_functions-1, 1..2):
+ points[3] := array(0..n_functions-1, 1..2):
for i from 0 to n_functions-1 do
- points[0][i,1] := ansatz_points[i][1]/2;
- points[0][i,2] := ansatz_points[i][2]/2;
+ points[0][i,1] := ansatz_points[i][1]/2:
+ points[0][i,2] := ansatz_points[i][2]/2:
- points[1][i,1] := ansatz_points[i][1]/2+1/2;
- points[1][i,2] := ansatz_points[i][2]/2;
+ points[1][i,1] := ansatz_points[i][1]/2+1/2:
+ points[1][i,2] := ansatz_points[i][2]/2:
- points[2][i,1] := ansatz_points[i][1]/2+1/2;
- points[2][i,2] := ansatz_points[i][2]/2+1/2;
+ points[2][i,1] := ansatz_points[i][1]/2+1/2:
+ points[2][i,2] := ansatz_points[i][2]/2+1/2:
- points[3][i,1] := ansatz_points[i][1]/2;
- points[3][i,2] := ansatz_points[i][2]/2+1/2;
- od;
+ points[3][i,1] := ansatz_points[i][1]/2:
+ points[3][i,2] := ansatz_points[i][2]/2+1/2:
+ od:
+ print ("Computing prolongation matrices"):
for i from 0 to 3 do
+ print ("child", i):
for j from 0 to n_functions-1 do
for k from 0 to n_functions-1 do
- prolongation[i,j,k] := phi(k, points[i][j,1], points[i][j,2]);
- od;
- od;
- od;
+ prolongation[i,j,k] := phi(k, points[i][j,1], points[i][j,2]):
+ od:
+ od:
+ od:
+ print ("Computing local mass matrix"):
# tphi are the basis functions of the linear element. These functions
# are used for the computation of the subparametric transformation from
# unit cell to real cell.
- tphi[0] := (1-xi)*(1-eta);
- tphi[1] := xi*(1-eta);
- tphi[2] := xi*eta;
- tphi[3] := (1-xi)*eta;
- x_real := sum(x[s]*tphi[s], s=0..3);
- y_real := sum(y[s]*tphi[s], s=0..3);
- detJ := diff(x_real,xi)*diff(y_real,eta) - diff(x_real,eta)*diff(y_real,xi);
+ # x and y are arrays holding the x- and y-values of the four vertices
+ # of this cell in real space.
+ x := array(0..3);
+ y := array(0..3);
+ tphi[0] := (1-xi)*(1-eta):
+ tphi[1] := xi*(1-eta):
+ tphi[2] := xi*eta:
+ tphi[3] := (1-xi)*eta:
+ x_real := sum(x[s]*tphi[s], s=0..3):
+ y_real := sum(y[s]*tphi[s], s=0..3):
+ detJ := diff(x_real,xi)*diff(y_real,eta) - diff(x_real,eta)*diff(y_real,xi):
for i from 0 to n_functions-1 do
+ print ("line", i):
for j from 0 to n_functions-1 do
local_mass_matrix[i,j] := int(int(phi_polynom[i] * phi_polynom[j] * detJ,
- xi=0..1), eta=0..1);
- od;
- od;
-
- readlib(C);
- C(phi_polynom, filename=shape_value_2d);
- C(grad_phi_polynom, filename=shape_grad_2d);
- C(prolongation, filename=prolongation_2d);
- C(local_mass_matrix, optimized, filename=massmatrix_2d);
+ xi=0..1), eta=0..1):
+ od:
+ od:
+
+ print ("computing ansatz points in real space"):
+ for i from 0 to n_functions-1 do
+ real_points[i,0] := subs(xi=ansatz_points[i][1],
+ eta=ansatz_points[i][2], x_real);
+ real_points[i,1] := subs(xi=ansatz_points[i][1],
+ eta=ansatz_points[i][2], y_real);
+ od:
+
+ print ("computing interface constraint matrices"):
+ # compute the interface constraint matrices. these are the values of the
+ # basis functions on the coarse cell's face at the points of the child
+ # cell's basis functions on the child faces
+ face_phi_polynom := array(0..n_face_functions-1):
+ for i from 0 to n_face_functions-1 do
+ # note that the interp function wants vectors indexed from
+ # one and not from zero.
+ values := array(1..n_face_functions):
+ for j from 1 to n_face_functions do
+ values[j] := 0:
+ od:
+ values[i+1] := 1:
+
+ shifted_face_ansatz_points := array (1..n_face_functions):
+ for j from 1 to n_face_functions do
+ shifted_face_ansatz_points[j] := face_ansatz_points[j-1]:
+ od:
+
+ face_phi_polynom[i] := interp (shifted_face_ansatz_points, values, xi):
+ od:
+
+ for i from 0 to 2*(n_face_functions-2)+1-1 do
+ for j from 0 to n_face_functions-1 do
+ interface_constraints[i,j] := subs(xi=constrained_face_ansatz_points[i],
+ face_phi_polynom[j]);
+ od:
+ od:
+
+
+ print ("writing data to files"):
+ readlib(C):
+ C(phi_polynom, filename=shape_value_2d):
+ C(grad_phi_polynom, filename=shape_grad_2d):
+ C(prolongation, filename=prolongation_2d):
+ C(local_mass_matrix, optimized, filename=massmatrix_2d):
+ C(interface_constraints, filename=constraints_2d):
+ C(real_points, optimized, filename=real_points_2d);
-----------------------------------------------------------------------
Use the following perl scripts to convert the output into a
perl -pi -e 's/grad_phi_polynom\[(\d+)\]\[0\] = (.*);/case $1: return Point<2>($2,/g;' shape_grad_2d
perl -pi -e 's/grad_phi_polynom\[(\d+)\]\[1\] = (.*);/$2);/g;' shape_grad_2d
perl -pi -e 's/\[(\d+)\]\[(\d+)\]/($1,$2)/g;' massmatrix_2d
+ perl -pi -e 's/(t\d+) =/const double $1 =/g;' massmatrix_2d
perl -pi -e 's/\[(\d+)\]\[(\d+)\]\[(\d+)\]/[$1]($2,$3)/g;' prolongation_2d
- perl -pi~ -e 's/(t\d+) =/const double $1 =/g;' massmatrix_2d
+ perl -pi -e 's/.*= 0.0;\n//g;' prolongation_2d
+ perl -pi -e 's/\[(\d+)\]\[(\d+)\]/($1,$2)/g;' constraints_2d
*/
const double h = cell->vertex(1)(0) - cell->vertex(0)(0);
Assert (h>0, ExcJacobiDeterminantHasWrongSign());
- const double t1 = 8.0/105.0*h;
- const double t2 = 19.0/1680.0*h;
- const double t3 = 33.0/560.0*h;
- const double t4 = 3.0/140.0*h;
- const double t5 = 27.0/70.0*h;
- const double t6 = 27.0/560.0*h;
- local_mass_matrix(0,0) = const double t1;
- local_mass_matrix(0,1) = const double t2;
- local_mass_matrix(0,2) = const double t3;
- local_mass_matrix(0,3) = - const double t4;
- local_mass_matrix(1,0) = const double t2;
- local_mass_matrix(1,1) = const double t1;
- local_mass_matrix(1,2) = - const double t4;
- local_mass_matrix(1,3) = const double t3;
- local_mass_matrix(2,0) = const double t3;
- local_mass_matrix(2,1) = - const double t4;
- local_mass_matrix(2,2) = const double t5;
- local_mass_matrix(2,3) = - const double t6;
- local_mass_matrix(3,0) = - const double t4;
- local_mass_matrix(3,1) = const double t3;
- local_mass_matrix(3,2) = - const double t6;
- local_mass_matrix(3,3) = const double t5;
+ const double t1 8.0/105.0*h;
+ const double t2 19.0/1680.0*h;
+ const double t3 33.0/560.0*h;
+ const double t4 3.0/140.0*h;
+ const double t5 27.0/70.0*h;
+ const double t6 27.0/560.0*h;
+ local_mass_matrix(0,0) = t1;
+ local_mass_matrix(0,1) = t2;
+ local_mass_matrix(0,2) = t3;
+ local_mass_matrix(0,3) = -t4;
+ local_mass_matrix(1,0) = t2;
+ local_mass_matrix(1,1) = t1;
+ local_mass_matrix(1,2) = -t4;
+ local_mass_matrix(1,3) = t3;
+ local_mass_matrix(2,0) = t3;
+ local_mass_matrix(2,1) = -t4;
+ local_mass_matrix(2,2) = t5;
+ local_mass_matrix(2,3) = -t6;
+ local_mass_matrix(3,0) = -t4;
+ local_mass_matrix(3,1) = t3;
+ local_mass_matrix(3,2) = -t6;
+ local_mass_matrix(3,3) = t5;
};
#endif
FECubicSub<2>::FECubicSub () :
FiniteElement<2> (1, 1, 1)
{
- interface_constraints(0,2) = 1.0;
- interface_constraints(1,0) = 3./8.;
- interface_constraints(1,1) = -1./8.;
- interface_constraints(1,2) = 3./4.;
- interface_constraints(2,0) = -1./8.;
- interface_constraints(2,1) = 3./8.;
- interface_constraints(2,2) = 3./4.;
-
-/*
- Get the prolongation matrices by the following little maple script:
-
- phi[0] := proc(xi,eta) (1-xi)*( 2*xi-1) * (1-eta)*( 2*eta-1); end;
- phi[1] := proc(xi,eta) xi *(-2*xi+1) * (1-eta)*( 2*eta-1); end;
- phi[2] := proc(xi,eta) xi *(-2*xi+1) * eta *(-2*eta+1); end;
- phi[3] := proc(xi,eta) (1-xi)*( 2*xi-1) * eta *(-2*eta+1); end;
- phi[4] := proc(xi,eta) 4 * (1-xi)*xi * (1-eta)*(1-2*eta); end;
- phi[5] := proc(xi,eta) 4 * xi *(-1+2*xi) * (1-eta)*eta; end;
- phi[6] := proc(xi,eta) 4 * (1-xi)*xi * eta *(-1+2*eta);end;
- phi[7] := proc(xi,eta) 4 * (1-xi)*(1-2*xi) * (1-eta)*eta; end;
- phi[8] := proc(xi,eta) 16 * xi*(1-xi) * eta*(1-eta); end;
-
- points_x[0] := array(0..8, [0, 1/2, 1/2, 0, 1/4, 1/2, 1/4, 0, 1/4]);
- points_y[0] := array(0..8, [0, 0, 1/2, 1/2, 0, 1/4, 1/2, 1/4, 1/4]);
-
- points_x[1] := array(0..8, [1/2, 1, 1, 1/2, 3/4, 1, 3/4, 1/2, 3/4]);
- points_y[1] := array(0..8, [0, 0, 1/2, 1/2, 0, 1/4, 1/2, 1/4, 1/4]);
-
- points_x[2] := array(0..8, [1/2, 1, 1, 1/2, 3/4, 1, 3/4, 1/2, 3/4]);
- points_y[2] := array(0..8, [1/2, 1/2, 1, 1, 1/2, 3/4, 1, 3/4, 3/4]);
-
- points_x[3] := array(0..8, [0, 1/2, 1/2, 0, 1/4, 1/2, 1/4, 0, 1/4]);
- points_y[3] := array(0..8, [1/2, 1/2, 1, 1, 1/2, 3/4, 1, 3/4, 3/4]);
-
- prolongation := array(0..3,0..8, 0..8);
-
- for i from 0 to 3 do
- for j from 0 to 8 do
- for k from 0 to 8 do
- prolongation[i,j,k] := phi[k](points_x[i][j], points_y[i][j]);
- od;
- od;
- od;
-
- readlib(C);
- C(prolongation);
-*/
+ interface_constraints(0,0) = -1.0/16.0;
+ interface_constraints(0,1) = -1.0/16.0;
+ interface_constraints(0,2) = 9.0/16.0;
+ interface_constraints(0,3) = 9.0/16.0;
+ interface_constraints(1,0) = 5.0/16.0;
+ interface_constraints(1,1) = 1.0/16.0;
+ interface_constraints(1,2) = 15.0/16.0;
+ interface_constraints(1,3) = -5.0/16.0;
+ interface_constraints(2,2) = 1.0;
+ interface_constraints(3,3) = 1.0;
+ interface_constraints(4,0) = 1.0/16.0;
+ interface_constraints(4,1) = 5.0/16.0;
+ interface_constraints(4,2) = -5.0/16.0;
+ interface_constraints(4,3) = 15.0/16.0;
prolongation[0](0,0) = 1.0;
- prolongation[0](0,1) = 0.0;
- prolongation[0](0,2) = 0.0;
- prolongation[0](0,3) = 0.0;
- prolongation[0](0,4) = 0.0;
- prolongation[0](0,5) = 0.0;
- prolongation[0](0,6) = 0.0;
- prolongation[0](0,7) = 0.0;
- prolongation[0](0,8) = 0.0;
- prolongation[0](1,0) = 0.0;
- prolongation[0](1,1) = 0.0;
- prolongation[0](1,2) = 0.0;
- prolongation[0](1,3) = 0.0;
- prolongation[0](1,4) = 1.0;
- prolongation[0](1,5) = 0.0;
- prolongation[0](1,6) = 0.0;
- prolongation[0](1,7) = 0.0;
- prolongation[0](1,8) = 0.0;
- prolongation[0](2,0) = 0.0;
- prolongation[0](2,1) = 0.0;
- prolongation[0](2,2) = 0.0;
- prolongation[0](2,3) = 0.0;
- prolongation[0](2,4) = 0.0;
- prolongation[0](2,5) = 0.0;
- prolongation[0](2,6) = 0.0;
- prolongation[0](2,7) = 0.0;
- prolongation[0](2,8) = 1.0;
- prolongation[0](3,0) = 0.0;
- prolongation[0](3,1) = 0.0;
- prolongation[0](3,2) = 0.0;
- prolongation[0](3,3) = 0.0;
- prolongation[0](3,4) = 0.0;
- prolongation[0](3,5) = 0.0;
- prolongation[0](3,6) = 0.0;
- prolongation[0](3,7) = 1.0;
- prolongation[0](3,8) = 0.0;
- prolongation[0](4,0) = 3.0/8.0;
- prolongation[0](4,1) = -1.0/8.0;
- prolongation[0](4,2) = 0.0;
- prolongation[0](4,3) = 0.0;
- prolongation[0](4,4) = 3.0/4.0;
- prolongation[0](4,5) = 0.0;
- prolongation[0](4,6) = 0.0;
- prolongation[0](4,7) = 0.0;
- prolongation[0](4,8) = 0.0;
- prolongation[0](5,0) = 0.0;
- prolongation[0](5,1) = 0.0;
- prolongation[0](5,2) = 0.0;
- prolongation[0](5,3) = 0.0;
- prolongation[0](5,4) = 3.0/8.0;
- prolongation[0](5,5) = 0.0;
- prolongation[0](5,6) = -1.0/8.0;
- prolongation[0](5,7) = 0.0;
- prolongation[0](5,8) = 3.0/4.0;
- prolongation[0](6,0) = 0.0;
- prolongation[0](6,1) = 0.0;
- prolongation[0](6,2) = 0.0;
- prolongation[0](6,3) = 0.0;
- prolongation[0](6,4) = 0.0;
- prolongation[0](6,5) = -1.0/8.0;
- prolongation[0](6,6) = 0.0;
- prolongation[0](6,7) = 3.0/8.0;
- prolongation[0](6,8) = 3.0/4.0;
- prolongation[0](7,0) = 3.0/8.0;
- prolongation[0](7,1) = 0.0;
- prolongation[0](7,2) = 0.0;
- prolongation[0](7,3) = -1.0/8.0;
- prolongation[0](7,4) = 0.0;
- prolongation[0](7,5) = 0.0;
- prolongation[0](7,6) = 0.0;
- prolongation[0](7,7) = 3.0/4.0;
- prolongation[0](7,8) = 0.0;
- prolongation[0](8,0) = 9.0/64.0;
- prolongation[0](8,1) = -3.0/64.0;
- prolongation[0](8,2) = 1.0/64.0;
- prolongation[0](8,3) = -3.0/64.0;
- prolongation[0](8,4) = 9.0/32.0;
- prolongation[0](8,5) = -3.0/32.0;
- prolongation[0](8,6) = -3.0/32.0;
- prolongation[0](8,7) = 9.0/32.0;
- prolongation[0](8,8) = 9.0/16.0;
- prolongation[1](0,0) = 0.0;
- prolongation[1](0,1) = 0.0;
- prolongation[1](0,2) = 0.0;
- prolongation[1](0,3) = 0.0;
- prolongation[1](0,4) = 1.0;
- prolongation[1](0,5) = 0.0;
- prolongation[1](0,6) = 0.0;
- prolongation[1](0,7) = 0.0;
- prolongation[1](0,8) = 0.0;
- prolongation[1](1,0) = 0.0;
+ prolongation[0](1,0) = -1.0/16.0;
+ prolongation[0](1,1) = -1.0/16.0;
+ prolongation[0](1,4) = 9.0/16.0;
+ prolongation[0](1,5) = 9.0/16.0;
+ prolongation[0](2,0) = 1.0/256.0;
+ prolongation[0](2,1) = 1.0/256.0;
+ prolongation[0](2,2) = 1.0/256.0;
+ prolongation[0](2,3) = 1.0/256.0;
+ prolongation[0](2,4) = -9.0/256.0;
+ prolongation[0](2,5) = -9.0/256.0;
+ prolongation[0](2,6) = -9.0/256.0;
+ prolongation[0](2,7) = -9.0/256.0;
+ prolongation[0](2,8) = -9.0/256.0;
+ prolongation[0](2,9) = -9.0/256.0;
+ prolongation[0](2,10) = -9.0/256.0;
+ prolongation[0](2,11) = -9.0/256.0;
+ prolongation[0](2,12) = 81.0/256.0;
+ prolongation[0](2,13) = 81.0/256.0;
+ prolongation[0](2,14) = 81.0/256.0;
+ prolongation[0](2,15) = 81.0/256.0;
+ prolongation[0](3,0) = -1.0/16.0;
+ prolongation[0](3,3) = -1.0/16.0;
+ prolongation[0](3,10) = 9.0/16.0;
+ prolongation[0](3,11) = 9.0/16.0;
+ prolongation[0](4,0) = 5.0/16.0;
+ prolongation[0](4,1) = 1.0/16.0;
+ prolongation[0](4,4) = 15.0/16.0;
+ prolongation[0](4,5) = -5.0/16.0;
+ prolongation[0](5,4) = 1.0;
+ prolongation[0](6,0) = -5.0/256.0;
+ prolongation[0](6,1) = -5.0/256.0;
+ prolongation[0](6,2) = -1.0/256.0;
+ prolongation[0](6,3) = -1.0/256.0;
+ prolongation[0](6,4) = 45.0/256.0;
+ prolongation[0](6,5) = 45.0/256.0;
+ prolongation[0](6,6) = -15.0/256.0;
+ prolongation[0](6,7) = 5.0/256.0;
+ prolongation[0](6,8) = 9.0/256.0;
+ prolongation[0](6,9) = 9.0/256.0;
+ prolongation[0](6,10) = -15.0/256.0;
+ prolongation[0](6,11) = 5.0/256.0;
+ prolongation[0](6,12) = 135.0/256.0;
+ prolongation[0](6,13) = 135.0/256.0;
+ prolongation[0](6,14) = -45.0/256.0;
+ prolongation[0](6,15) = -45.0/256.0;
+ prolongation[0](7,6) = -1.0/16.0;
+ prolongation[0](7,10) = -1.0/16.0;
+ prolongation[0](7,12) = 9.0/16.0;
+ prolongation[0](7,13) = 9.0/16.0;
+ prolongation[0](8,0) = -5.0/256.0;
+ prolongation[0](8,1) = -1.0/256.0;
+ prolongation[0](8,2) = -1.0/256.0;
+ prolongation[0](8,3) = -5.0/256.0;
+ prolongation[0](8,4) = -15.0/256.0;
+ prolongation[0](8,5) = 5.0/256.0;
+ prolongation[0](8,6) = 9.0/256.0;
+ prolongation[0](8,7) = 9.0/256.0;
+ prolongation[0](8,8) = -15.0/256.0;
+ prolongation[0](8,9) = 5.0/256.0;
+ prolongation[0](8,10) = 45.0/256.0;
+ prolongation[0](8,11) = 45.0/256.0;
+ prolongation[0](8,12) = 135.0/256.0;
+ prolongation[0](8,13) = -45.0/256.0;
+ prolongation[0](8,14) = -45.0/256.0;
+ prolongation[0](8,15) = 135.0/256.0;
+ prolongation[0](9,4) = -1.0/16.0;
+ prolongation[0](9,8) = -1.0/16.0;
+ prolongation[0](9,12) = 9.0/16.0;
+ prolongation[0](9,15) = 9.0/16.0;
+ prolongation[0](10,0) = 5.0/16.0;
+ prolongation[0](10,3) = 1.0/16.0;
+ prolongation[0](10,10) = 15.0/16.0;
+ prolongation[0](10,11) = -5.0/16.0;
+ prolongation[0](11,10) = 1.0;
+ prolongation[0](12,0) = 25.0/256.0;
+ prolongation[0](12,1) = 5.0/256.0;
+ prolongation[0](12,2) = 1.0/256.0;
+ prolongation[0](12,3) = 5.0/256.0;
+ prolongation[0](12,4) = 75.0/256.0;
+ prolongation[0](12,5) = -25.0/256.0;
+ prolongation[0](12,6) = 15.0/256.0;
+ prolongation[0](12,7) = -5.0/256.0;
+ prolongation[0](12,8) = 15.0/256.0;
+ prolongation[0](12,9) = -5.0/256.0;
+ prolongation[0](12,10) = 75.0/256.0;
+ prolongation[0](12,11) = -25.0/256.0;
+ prolongation[0](12,12) = 225.0/256.0;
+ prolongation[0](12,13) = -75.0/256.0;
+ prolongation[0](12,14) = 25.0/256.0;
+ prolongation[0](12,15) = -75.0/256.0;
+ prolongation[0](13,4) = 5.0/16.0;
+ prolongation[0](13,8) = 1.0/16.0;
+ prolongation[0](13,12) = 15.0/16.0;
+ prolongation[0](13,15) = -5.0/16.0;
+ prolongation[0](14,12) = 1.0;
+ prolongation[0](15,6) = 1.0/16.0;
+ prolongation[0](15,10) = 5.0/16.0;
+ prolongation[0](15,12) = 15.0/16.0;
+ prolongation[0](15,13) = -5.0/16.0;
+ prolongation[1](0,0) = -1.0/16.0;
+ prolongation[1](0,1) = -1.0/16.0;
+ prolongation[1](0,4) = 9.0/16.0;
+ prolongation[1](0,5) = 9.0/16.0;
prolongation[1](1,1) = 1.0;
- prolongation[1](1,2) = 0.0;
- prolongation[1](1,3) = 0.0;
- prolongation[1](1,4) = 0.0;
- prolongation[1](1,5) = 0.0;
- prolongation[1](1,6) = 0.0;
- prolongation[1](1,7) = 0.0;
- prolongation[1](1,8) = 0.0;
- prolongation[1](2,0) = 0.0;
- prolongation[1](2,1) = 0.0;
- prolongation[1](2,2) = 0.0;
- prolongation[1](2,3) = 0.0;
- prolongation[1](2,4) = 0.0;
- prolongation[1](2,5) = 1.0;
- prolongation[1](2,6) = 0.0;
- prolongation[1](2,7) = 0.0;
- prolongation[1](2,8) = 0.0;
- prolongation[1](3,0) = 0.0;
- prolongation[1](3,1) = 0.0;
- prolongation[1](3,2) = 0.0;
- prolongation[1](3,3) = 0.0;
- prolongation[1](3,4) = 0.0;
- prolongation[1](3,5) = 0.0;
- prolongation[1](3,6) = 0.0;
- prolongation[1](3,7) = 0.0;
- prolongation[1](3,8) = 1.0;
- prolongation[1](4,0) = -1.0/8.0;
- prolongation[1](4,1) = 3.0/8.0;
- prolongation[1](4,2) = 0.0;
- prolongation[1](4,3) = 0.0;
- prolongation[1](4,4) = 3.0/4.0;
- prolongation[1](4,5) = 0.0;
- prolongation[1](4,6) = 0.0;
- prolongation[1](4,7) = 0.0;
- prolongation[1](4,8) = 0.0;
- prolongation[1](5,0) = 0.0;
- prolongation[1](5,1) = 3.0/8.0;
- prolongation[1](5,2) = -1.0/8.0;
- prolongation[1](5,3) = 0.0;
- prolongation[1](5,4) = 0.0;
- prolongation[1](5,5) = 3.0/4.0;
- prolongation[1](5,6) = 0.0;
- prolongation[1](5,7) = 0.0;
- prolongation[1](5,8) = 0.0;
- prolongation[1](6,0) = 0.0;
- prolongation[1](6,1) = 0.0;
- prolongation[1](6,2) = 0.0;
- prolongation[1](6,3) = 0.0;
- prolongation[1](6,4) = 0.0;
- prolongation[1](6,5) = 3.0/8.0;
- prolongation[1](6,6) = 0.0;
- prolongation[1](6,7) = -1.0/8.0;
- prolongation[1](6,8) = 3.0/4.0;
- prolongation[1](7,0) = 0.0;
- prolongation[1](7,1) = 0.0;
- prolongation[1](7,2) = 0.0;
- prolongation[1](7,3) = 0.0;
- prolongation[1](7,4) = 3.0/8.0;
- prolongation[1](7,5) = 0.0;
- prolongation[1](7,6) = -1.0/8.0;
- prolongation[1](7,7) = 0.0;
- prolongation[1](7,8) = 3.0/4.0;
- prolongation[1](8,0) = -3.0/64.0;
- prolongation[1](8,1) = 9.0/64.0;
- prolongation[1](8,2) = -3.0/64.0;
- prolongation[1](8,3) = 1.0/64.0;
- prolongation[1](8,4) = 9.0/32.0;
- prolongation[1](8,5) = 9.0/32.0;
- prolongation[1](8,6) = -3.0/32.0;
- prolongation[1](8,7) = -3.0/32.0;
- prolongation[1](8,8) = 9.0/16.0;
- prolongation[2](0,0) = 0.0;
- prolongation[2](0,1) = 0.0;
- prolongation[2](0,2) = 0.0;
- prolongation[2](0,3) = 0.0;
- prolongation[2](0,4) = 0.0;
- prolongation[2](0,5) = 0.0;
- prolongation[2](0,6) = 0.0;
- prolongation[2](0,7) = 0.0;
- prolongation[2](0,8) = 1.0;
- prolongation[2](1,0) = 0.0;
- prolongation[2](1,1) = 0.0;
- prolongation[2](1,2) = 0.0;
- prolongation[2](1,3) = 0.0;
- prolongation[2](1,4) = 0.0;
- prolongation[2](1,5) = 1.0;
- prolongation[2](1,6) = 0.0;
- prolongation[2](1,7) = 0.0;
- prolongation[2](1,8) = 0.0;
- prolongation[2](2,0) = 0.0;
- prolongation[2](2,1) = 0.0;
+ prolongation[1](2,1) = -1.0/16.0;
+ prolongation[1](2,2) = -1.0/16.0;
+ prolongation[1](2,6) = 9.0/16.0;
+ prolongation[1](2,7) = 9.0/16.0;
+ prolongation[1](3,0) = 1.0/256.0;
+ prolongation[1](3,1) = 1.0/256.0;
+ prolongation[1](3,2) = 1.0/256.0;
+ prolongation[1](3,3) = 1.0/256.0;
+ prolongation[1](3,4) = -9.0/256.0;
+ prolongation[1](3,5) = -9.0/256.0;
+ prolongation[1](3,6) = -9.0/256.0;
+ prolongation[1](3,7) = -9.0/256.0;
+ prolongation[1](3,8) = -9.0/256.0;
+ prolongation[1](3,9) = -9.0/256.0;
+ prolongation[1](3,10) = -9.0/256.0;
+ prolongation[1](3,11) = -9.0/256.0;
+ prolongation[1](3,12) = 81.0/256.0;
+ prolongation[1](3,13) = 81.0/256.0;
+ prolongation[1](3,14) = 81.0/256.0;
+ prolongation[1](3,15) = 81.0/256.0;
+ prolongation[1](4,5) = 1.0;
+ prolongation[1](5,0) = 1.0/16.0;
+ prolongation[1](5,1) = 5.0/16.0;
+ prolongation[1](5,4) = -5.0/16.0;
+ prolongation[1](5,5) = 15.0/16.0;
+ prolongation[1](6,1) = 5.0/16.0;
+ prolongation[1](6,2) = 1.0/16.0;
+ prolongation[1](6,6) = 15.0/16.0;
+ prolongation[1](6,7) = -5.0/16.0;
+ prolongation[1](7,6) = 1.0;
+ prolongation[1](8,5) = -1.0/16.0;
+ prolongation[1](8,9) = -1.0/16.0;
+ prolongation[1](8,13) = 9.0/16.0;
+ prolongation[1](8,14) = 9.0/16.0;
+ prolongation[1](9,0) = -1.0/256.0;
+ prolongation[1](9,1) = -5.0/256.0;
+ prolongation[1](9,2) = -5.0/256.0;
+ prolongation[1](9,3) = -1.0/256.0;
+ prolongation[1](9,4) = 5.0/256.0;
+ prolongation[1](9,5) = -15.0/256.0;
+ prolongation[1](9,6) = 45.0/256.0;
+ prolongation[1](9,7) = 45.0/256.0;
+ prolongation[1](9,8) = 5.0/256.0;
+ prolongation[1](9,9) = -15.0/256.0;
+ prolongation[1](9,10) = 9.0/256.0;
+ prolongation[1](9,11) = 9.0/256.0;
+ prolongation[1](9,12) = -45.0/256.0;
+ prolongation[1](9,13) = 135.0/256.0;
+ prolongation[1](9,14) = 135.0/256.0;
+ prolongation[1](9,15) = -45.0/256.0;
+ prolongation[1](10,0) = -5.0/256.0;
+ prolongation[1](10,1) = -5.0/256.0;
+ prolongation[1](10,2) = -1.0/256.0;
+ prolongation[1](10,3) = -1.0/256.0;
+ prolongation[1](10,4) = 45.0/256.0;
+ prolongation[1](10,5) = 45.0/256.0;
+ prolongation[1](10,6) = -15.0/256.0;
+ prolongation[1](10,7) = 5.0/256.0;
+ prolongation[1](10,8) = 9.0/256.0;
+ prolongation[1](10,9) = 9.0/256.0;
+ prolongation[1](10,10) = -15.0/256.0;
+ prolongation[1](10,11) = 5.0/256.0;
+ prolongation[1](10,12) = 135.0/256.0;
+ prolongation[1](10,13) = 135.0/256.0;
+ prolongation[1](10,14) = -45.0/256.0;
+ prolongation[1](10,15) = -45.0/256.0;
+ prolongation[1](11,6) = -1.0/16.0;
+ prolongation[1](11,10) = -1.0/16.0;
+ prolongation[1](11,12) = 9.0/16.0;
+ prolongation[1](11,13) = 9.0/16.0;
+ prolongation[1](12,5) = 5.0/16.0;
+ prolongation[1](12,9) = 1.0/16.0;
+ prolongation[1](12,13) = 15.0/16.0;
+ prolongation[1](12,14) = -5.0/16.0;
+ prolongation[1](13,0) = 5.0/256.0;
+ prolongation[1](13,1) = 25.0/256.0;
+ prolongation[1](13,2) = 5.0/256.0;
+ prolongation[1](13,3) = 1.0/256.0;
+ prolongation[1](13,4) = -25.0/256.0;
+ prolongation[1](13,5) = 75.0/256.0;
+ prolongation[1](13,6) = 75.0/256.0;
+ prolongation[1](13,7) = -25.0/256.0;
+ prolongation[1](13,8) = -5.0/256.0;
+ prolongation[1](13,9) = 15.0/256.0;
+ prolongation[1](13,10) = 15.0/256.0;
+ prolongation[1](13,11) = -5.0/256.0;
+ prolongation[1](13,12) = -75.0/256.0;
+ prolongation[1](13,13) = 225.0/256.0;
+ prolongation[1](13,14) = -75.0/256.0;
+ prolongation[1](13,15) = 25.0/256.0;
+ prolongation[1](14,6) = 5.0/16.0;
+ prolongation[1](14,10) = 1.0/16.0;
+ prolongation[1](14,12) = -5.0/16.0;
+ prolongation[1](14,13) = 15.0/16.0;
+ prolongation[1](15,13) = 1.0;
+ prolongation[2](0,0) = 1.0/256.0;
+ prolongation[2](0,1) = 1.0/256.0;
+ prolongation[2](0,2) = 1.0/256.0;
+ prolongation[2](0,3) = 1.0/256.0;
+ prolongation[2](0,4) = -9.0/256.0;
+ prolongation[2](0,5) = -9.0/256.0;
+ prolongation[2](0,6) = -9.0/256.0;
+ prolongation[2](0,7) = -9.0/256.0;
+ prolongation[2](0,8) = -9.0/256.0;
+ prolongation[2](0,9) = -9.0/256.0;
+ prolongation[2](0,10) = -9.0/256.0;
+ prolongation[2](0,11) = -9.0/256.0;
+ prolongation[2](0,12) = 81.0/256.0;
+ prolongation[2](0,13) = 81.0/256.0;
+ prolongation[2](0,14) = 81.0/256.0;
+ prolongation[2](0,15) = 81.0/256.0;
+ prolongation[2](1,1) = -1.0/16.0;
+ prolongation[2](1,2) = -1.0/16.0;
+ prolongation[2](1,6) = 9.0/16.0;
+ prolongation[2](1,7) = 9.0/16.0;
prolongation[2](2,2) = 1.0;
- prolongation[2](2,3) = 0.0;
- prolongation[2](2,4) = 0.0;
- prolongation[2](2,5) = 0.0;
- prolongation[2](2,6) = 0.0;
- prolongation[2](2,7) = 0.0;
- prolongation[2](2,8) = 0.0;
- prolongation[2](3,0) = 0.0;
- prolongation[2](3,1) = 0.0;
- prolongation[2](3,2) = 0.0;
- prolongation[2](3,3) = 0.0;
- prolongation[2](3,4) = 0.0;
- prolongation[2](3,5) = 0.0;
- prolongation[2](3,6) = 1.0;
- prolongation[2](3,7) = 0.0;
- prolongation[2](3,8) = 0.0;
- prolongation[2](4,0) = 0.0;
- prolongation[2](4,1) = 0.0;
- prolongation[2](4,2) = 0.0;
- prolongation[2](4,3) = 0.0;
- prolongation[2](4,4) = 0.0;
- prolongation[2](4,5) = 3.0/8.0;
- prolongation[2](4,6) = 0.0;
- prolongation[2](4,7) = -1.0/8.0;
- prolongation[2](4,8) = 3.0/4.0;
- prolongation[2](5,0) = 0.0;
- prolongation[2](5,1) = -1.0/8.0;
- prolongation[2](5,2) = 3.0/8.0;
- prolongation[2](5,3) = 0.0;
- prolongation[2](5,4) = 0.0;
- prolongation[2](5,5) = 3.0/4.0;
- prolongation[2](5,6) = 0.0;
- prolongation[2](5,7) = 0.0;
- prolongation[2](5,8) = 0.0;
- prolongation[2](6,0) = 0.0;
- prolongation[2](6,1) = 0.0;
- prolongation[2](6,2) = 3.0/8.0;
- prolongation[2](6,3) = -1.0/8.0;
- prolongation[2](6,4) = 0.0;
- prolongation[2](6,5) = 0.0;
- prolongation[2](6,6) = 3.0/4.0;
- prolongation[2](6,7) = 0.0;
- prolongation[2](6,8) = 0.0;
- prolongation[2](7,0) = 0.0;
- prolongation[2](7,1) = 0.0;
- prolongation[2](7,2) = 0.0;
- prolongation[2](7,3) = 0.0;
- prolongation[2](7,4) = -1.0/8.0;
- prolongation[2](7,5) = 0.0;
- prolongation[2](7,6) = 3.0/8.0;
- prolongation[2](7,7) = 0.0;
- prolongation[2](7,8) = 3.0/4.0;
- prolongation[2](8,0) = 1.0/64.0;
- prolongation[2](8,1) = -3.0/64.0;
- prolongation[2](8,2) = 9.0/64.0;
- prolongation[2](8,3) = -3.0/64.0;
- prolongation[2](8,4) = -3.0/32.0;
- prolongation[2](8,5) = 9.0/32.0;
- prolongation[2](8,6) = 9.0/32.0;
- prolongation[2](8,7) = -3.0/32.0;
- prolongation[2](8,8) = 9.0/16.0;
- prolongation[3](0,0) = 0.0;
- prolongation[3](0,1) = 0.0;
- prolongation[3](0,2) = 0.0;
- prolongation[3](0,3) = 0.0;
- prolongation[3](0,4) = 0.0;
- prolongation[3](0,5) = 0.0;
- prolongation[3](0,6) = 0.0;
- prolongation[3](0,7) = 1.0;
- prolongation[3](0,8) = 0.0;
- prolongation[3](1,0) = 0.0;
- prolongation[3](1,1) = 0.0;
- prolongation[3](1,2) = 0.0;
- prolongation[3](1,3) = 0.0;
- prolongation[3](1,4) = 0.0;
- prolongation[3](1,5) = 0.0;
- prolongation[3](1,6) = 0.0;
- prolongation[3](1,7) = 0.0;
- prolongation[3](1,8) = 1.0;
- prolongation[3](2,0) = 0.0;
- prolongation[3](2,1) = 0.0;
- prolongation[3](2,2) = 0.0;
- prolongation[3](2,3) = 0.0;
- prolongation[3](2,4) = 0.0;
- prolongation[3](2,5) = 0.0;
- prolongation[3](2,6) = 1.0;
- prolongation[3](2,7) = 0.0;
- prolongation[3](2,8) = 0.0;
- prolongation[3](3,0) = 0.0;
- prolongation[3](3,1) = 0.0;
- prolongation[3](3,2) = 0.0;
+ prolongation[2](3,2) = -1.0/16.0;
+ prolongation[2](3,3) = -1.0/16.0;
+ prolongation[2](3,8) = 9.0/16.0;
+ prolongation[2](3,9) = 9.0/16.0;
+ prolongation[2](4,5) = -1.0/16.0;
+ prolongation[2](4,9) = -1.0/16.0;
+ prolongation[2](4,13) = 9.0/16.0;
+ prolongation[2](4,14) = 9.0/16.0;
+ prolongation[2](5,0) = -1.0/256.0;
+ prolongation[2](5,1) = -5.0/256.0;
+ prolongation[2](5,2) = -5.0/256.0;
+ prolongation[2](5,3) = -1.0/256.0;
+ prolongation[2](5,4) = 5.0/256.0;
+ prolongation[2](5,5) = -15.0/256.0;
+ prolongation[2](5,6) = 45.0/256.0;
+ prolongation[2](5,7) = 45.0/256.0;
+ prolongation[2](5,8) = 5.0/256.0;
+ prolongation[2](5,9) = -15.0/256.0;
+ prolongation[2](5,10) = 9.0/256.0;
+ prolongation[2](5,11) = 9.0/256.0;
+ prolongation[2](5,12) = -45.0/256.0;
+ prolongation[2](5,13) = 135.0/256.0;
+ prolongation[2](5,14) = 135.0/256.0;
+ prolongation[2](5,15) = -45.0/256.0;
+ prolongation[2](6,7) = 1.0;
+ prolongation[2](7,1) = 1.0/16.0;
+ prolongation[2](7,2) = 5.0/16.0;
+ prolongation[2](7,6) = -5.0/16.0;
+ prolongation[2](7,7) = 15.0/16.0;
+ prolongation[2](8,9) = 1.0;
+ prolongation[2](9,2) = 5.0/16.0;
+ prolongation[2](9,3) = 1.0/16.0;
+ prolongation[2](9,8) = -5.0/16.0;
+ prolongation[2](9,9) = 15.0/16.0;
+ prolongation[2](10,7) = -1.0/16.0;
+ prolongation[2](10,11) = -1.0/16.0;
+ prolongation[2](10,14) = 9.0/16.0;
+ prolongation[2](10,15) = 9.0/16.0;
+ prolongation[2](11,0) = -1.0/256.0;
+ prolongation[2](11,1) = -1.0/256.0;
+ prolongation[2](11,2) = -5.0/256.0;
+ prolongation[2](11,3) = -5.0/256.0;
+ prolongation[2](11,4) = 9.0/256.0;
+ prolongation[2](11,5) = 9.0/256.0;
+ prolongation[2](11,6) = 5.0/256.0;
+ prolongation[2](11,7) = -15.0/256.0;
+ prolongation[2](11,8) = 45.0/256.0;
+ prolongation[2](11,9) = 45.0/256.0;
+ prolongation[2](11,10) = 5.0/256.0;
+ prolongation[2](11,11) = -15.0/256.0;
+ prolongation[2](11,12) = -45.0/256.0;
+ prolongation[2](11,13) = -45.0/256.0;
+ prolongation[2](11,14) = 135.0/256.0;
+ prolongation[2](11,15) = 135.0/256.0;
+ prolongation[2](12,14) = 1.0;
+ prolongation[2](13,7) = 5.0/16.0;
+ prolongation[2](13,11) = 1.0/16.0;
+ prolongation[2](13,14) = 15.0/16.0;
+ prolongation[2](13,15) = -5.0/16.0;
+ prolongation[2](14,0) = 1.0/256.0;
+ prolongation[2](14,1) = 5.0/256.0;
+ prolongation[2](14,2) = 25.0/256.0;
+ prolongation[2](14,3) = 5.0/256.0;
+ prolongation[2](14,4) = -5.0/256.0;
+ prolongation[2](14,5) = 15.0/256.0;
+ prolongation[2](14,6) = -25.0/256.0;
+ prolongation[2](14,7) = 75.0/256.0;
+ prolongation[2](14,8) = -25.0/256.0;
+ prolongation[2](14,9) = 75.0/256.0;
+ prolongation[2](14,10) = -5.0/256.0;
+ prolongation[2](14,11) = 15.0/256.0;
+ prolongation[2](14,12) = 25.0/256.0;
+ prolongation[2](14,13) = -75.0/256.0;
+ prolongation[2](14,14) = 225.0/256.0;
+ prolongation[2](14,15) = -75.0/256.0;
+ prolongation[2](15,5) = 1.0/16.0;
+ prolongation[2](15,9) = 5.0/16.0;
+ prolongation[2](15,13) = -5.0/16.0;
+ prolongation[2](15,14) = 15.0/16.0;
+ prolongation[3](0,0) = -1.0/16.0;
+ prolongation[3](0,3) = -1.0/16.0;
+ prolongation[3](0,10) = 9.0/16.0;
+ prolongation[3](0,11) = 9.0/16.0;
+ prolongation[3](1,0) = 1.0/256.0;
+ prolongation[3](1,1) = 1.0/256.0;
+ prolongation[3](1,2) = 1.0/256.0;
+ prolongation[3](1,3) = 1.0/256.0;
+ prolongation[3](1,4) = -9.0/256.0;
+ prolongation[3](1,5) = -9.0/256.0;
+ prolongation[3](1,6) = -9.0/256.0;
+ prolongation[3](1,7) = -9.0/256.0;
+ prolongation[3](1,8) = -9.0/256.0;
+ prolongation[3](1,9) = -9.0/256.0;
+ prolongation[3](1,10) = -9.0/256.0;
+ prolongation[3](1,11) = -9.0/256.0;
+ prolongation[3](1,12) = 81.0/256.0;
+ prolongation[3](1,13) = 81.0/256.0;
+ prolongation[3](1,14) = 81.0/256.0;
+ prolongation[3](1,15) = 81.0/256.0;
+ prolongation[3](2,2) = -1.0/16.0;
+ prolongation[3](2,3) = -1.0/16.0;
+ prolongation[3](2,8) = 9.0/16.0;
+ prolongation[3](2,9) = 9.0/16.0;
prolongation[3](3,3) = 1.0;
- prolongation[3](3,4) = 0.0;
- prolongation[3](3,5) = 0.0;
- prolongation[3](3,6) = 0.0;
- prolongation[3](3,7) = 0.0;
- prolongation[3](3,8) = 0.0;
- prolongation[3](4,0) = 0.0;
- prolongation[3](4,1) = 0.0;
- prolongation[3](4,2) = 0.0;
- prolongation[3](4,3) = 0.0;
- prolongation[3](4,4) = 0.0;
- prolongation[3](4,5) = -1.0/8.0;
- prolongation[3](4,6) = 0.0;
- prolongation[3](4,7) = 3.0/8.0;
- prolongation[3](4,8) = 3.0/4.0;
- prolongation[3](5,0) = 0.0;
- prolongation[3](5,1) = 0.0;
- prolongation[3](5,2) = 0.0;
- prolongation[3](5,3) = 0.0;
- prolongation[3](5,4) = -1.0/8.0;
- prolongation[3](5,5) = 0.0;
- prolongation[3](5,6) = 3.0/8.0;
- prolongation[3](5,7) = 0.0;
- prolongation[3](5,8) = 3.0/4.0;
- prolongation[3](6,0) = 0.0;
- prolongation[3](6,1) = 0.0;
- prolongation[3](6,2) = -1.0/8.0;
- prolongation[3](6,3) = 3.0/8.0;
- prolongation[3](6,4) = 0.0;
- prolongation[3](6,5) = 0.0;
- prolongation[3](6,6) = 3.0/4.0;
- prolongation[3](6,7) = 0.0;
- prolongation[3](6,8) = 0.0;
- prolongation[3](7,0) = -1.0/8.0;
- prolongation[3](7,1) = 0.0;
- prolongation[3](7,2) = 0.0;
- prolongation[3](7,3) = 3.0/8.0;
- prolongation[3](7,4) = 0.0;
- prolongation[3](7,5) = 0.0;
- prolongation[3](7,6) = 0.0;
- prolongation[3](7,7) = 3.0/4.0;
- prolongation[3](7,8) = 0.0;
- prolongation[3](8,0) = -3.0/64.0;
- prolongation[3](8,1) = 1.0/64.0;
- prolongation[3](8,2) = -3.0/64.0;
- prolongation[3](8,3) = 9.0/64.0;
- prolongation[3](8,4) = -3.0/32.0;
- prolongation[3](8,5) = -3.0/32.0;
- prolongation[3](8,6) = 9.0/32.0;
- prolongation[3](8,7) = 9.0/32.0;
- prolongation[3](8,8) = 9.0/16.0;
+ prolongation[3](4,0) = -5.0/256.0;
+ prolongation[3](4,1) = -1.0/256.0;
+ prolongation[3](4,2) = -1.0/256.0;
+ prolongation[3](4,3) = -5.0/256.0;
+ prolongation[3](4,4) = -15.0/256.0;
+ prolongation[3](4,5) = 5.0/256.0;
+ prolongation[3](4,6) = 9.0/256.0;
+ prolongation[3](4,7) = 9.0/256.0;
+ prolongation[3](4,8) = -15.0/256.0;
+ prolongation[3](4,9) = 5.0/256.0;
+ prolongation[3](4,10) = 45.0/256.0;
+ prolongation[3](4,11) = 45.0/256.0;
+ prolongation[3](4,12) = 135.0/256.0;
+ prolongation[3](4,13) = -45.0/256.0;
+ prolongation[3](4,14) = -45.0/256.0;
+ prolongation[3](4,15) = 135.0/256.0;
+ prolongation[3](5,4) = -1.0/16.0;
+ prolongation[3](5,8) = -1.0/16.0;
+ prolongation[3](5,12) = 9.0/16.0;
+ prolongation[3](5,15) = 9.0/16.0;
+ prolongation[3](6,7) = -1.0/16.0;
+ prolongation[3](6,11) = -1.0/16.0;
+ prolongation[3](6,14) = 9.0/16.0;
+ prolongation[3](6,15) = 9.0/16.0;
+ prolongation[3](7,0) = -1.0/256.0;
+ prolongation[3](7,1) = -1.0/256.0;
+ prolongation[3](7,2) = -5.0/256.0;
+ prolongation[3](7,3) = -5.0/256.0;
+ prolongation[3](7,4) = 9.0/256.0;
+ prolongation[3](7,5) = 9.0/256.0;
+ prolongation[3](7,6) = 5.0/256.0;
+ prolongation[3](7,7) = -15.0/256.0;
+ prolongation[3](7,8) = 45.0/256.0;
+ prolongation[3](7,9) = 45.0/256.0;
+ prolongation[3](7,10) = 5.0/256.0;
+ prolongation[3](7,11) = -15.0/256.0;
+ prolongation[3](7,12) = -45.0/256.0;
+ prolongation[3](7,13) = -45.0/256.0;
+ prolongation[3](7,14) = 135.0/256.0;
+ prolongation[3](7,15) = 135.0/256.0;
+ prolongation[3](8,2) = 1.0/16.0;
+ prolongation[3](8,3) = 5.0/16.0;
+ prolongation[3](8,8) = 15.0/16.0;
+ prolongation[3](8,9) = -5.0/16.0;
+ prolongation[3](9,8) = 1.0;
+ prolongation[3](10,11) = 1.0;
+ prolongation[3](11,0) = 1.0/16.0;
+ prolongation[3](11,3) = 5.0/16.0;
+ prolongation[3](11,10) = -5.0/16.0;
+ prolongation[3](11,11) = 15.0/16.0;
+ prolongation[3](12,7) = 1.0/16.0;
+ prolongation[3](12,11) = 5.0/16.0;
+ prolongation[3](12,14) = -5.0/16.0;
+ prolongation[3](12,15) = 15.0/16.0;
+ prolongation[3](13,15) = 1.0;
+ prolongation[3](14,4) = 1.0/16.0;
+ prolongation[3](14,8) = 5.0/16.0;
+ prolongation[3](14,12) = -5.0/16.0;
+ prolongation[3](14,15) = 15.0/16.0;
+ prolongation[3](15,0) = 5.0/256.0;
+ prolongation[3](15,1) = 1.0/256.0;
+ prolongation[3](15,2) = 5.0/256.0;
+ prolongation[3](15,3) = 25.0/256.0;
+ prolongation[3](15,4) = 15.0/256.0;
+ prolongation[3](15,5) = -5.0/256.0;
+ prolongation[3](15,6) = -5.0/256.0;
+ prolongation[3](15,7) = 15.0/256.0;
+ prolongation[3](15,8) = 75.0/256.0;
+ prolongation[3](15,9) = -25.0/256.0;
+ prolongation[3](15,10) = -25.0/256.0;
+ prolongation[3](15,11) = 75.0/256.0;
+ prolongation[3](15,12) = -75.0/256.0;
+ prolongation[3](15,13) = 25.0/256.0;
+ prolongation[3](15,14) = -75.0/256.0;
+ prolongation[3](15,15) = 225.0/256.0;
};
eta= p(1);
switch (i)
{
- case 0: return (1-xi)*( 2*xi-1) * (1-eta)*( 2*eta-1);
- case 1: return xi *(-2*xi+1) * (1-eta)*( 2*eta-1);
- case 2: return xi *(-2*xi+1) * eta *(-2*eta+1);
- case 3: return (1-xi)*( 2*xi-1) * eta *(-2*eta+1);
- case 4: return 4 * (1-xi)*xi * (1-eta)*(1-2*eta);
- case 5: return 4 * xi *(-1+2*xi) * (1-eta)*eta;
- case 6: return 4 * (1-xi)*xi * eta *(-1+2*eta);
- case 7: return 4 * (1-xi)*(1-2*xi) * (1-eta)*eta;
- case 8: return 16 * xi*(1-xi) * eta*(1-eta);
+ case 0: return 1.0-11.0/2.0*xi+9.0*xi*xi-9.0/2.0*xi*xi*xi+(-11.0/2.0+
+121.0/4.0*xi-99.0/2.0*xi*xi+99.0/4.0*xi*xi*xi)*eta+(9.0-99.0/2.0*xi+81.0*xi*xi
+-81.0/2.0*xi*xi*xi)*eta*eta+(-9.0/2.0+99.0/4.0*xi-81.0/2.0*xi*xi+81.0/4.0*xi*xi
+*xi)*eta*eta*eta;
+ case 1: return xi-9.0/2.0*xi*xi+9.0/2.0*xi*xi*xi+(-11.0/2.0*xi+99.0/4.0
+*xi*xi-99.0/4.0*xi*xi*xi)*eta+(9.0*xi-81.0/2.0*xi*xi+81.0/2.0*xi*xi*xi)*eta*eta
++(-9.0/2.0*xi+81.0/4.0*xi*xi-81.0/4.0*xi*xi*xi)*eta*eta*eta;
+ case 2: return (xi-9.0/2.0*xi*xi+9.0/2.0*xi*xi*xi)*eta+(-9.0/2.0*xi+
+81.0/4.0*xi*xi-81.0/4.0*xi*xi*xi)*eta*eta+(9.0/2.0*xi-81.0/4.0*xi*xi+81.0/4.0*
+xi*xi*xi)*eta*eta*eta;
+ case 3: return (1.0-11.0/2.0*xi+9.0*xi*xi-9.0/2.0*xi*xi*xi)*eta+(-9.0/
+2.0+99.0/4.0*xi-81.0/2.0*xi*xi+81.0/4.0*xi*xi*xi)*eta*eta+(9.0/2.0-99.0/4.0*xi+
+81.0/2.0*xi*xi-81.0/4.0*xi*xi*xi)*eta*eta*eta;
+ case 4: return 9.0*xi-45.0/2.0*xi*xi+27.0/2.0*xi*xi*xi+(-99.0/2.0*xi+
+495.0/4.0*xi*xi-297.0/4.0*xi*xi*xi)*eta+(81.0*xi-405.0/2.0*xi*xi+243.0/2.0*xi*
+xi*xi)*eta*eta+(-81.0/2.0*xi+405.0/4.0*xi*xi-243.0/4.0*xi*xi*xi)*eta*eta*eta;
+ case 5: return -9.0/2.0*xi+18.0*xi*xi-27.0/2.0*xi*xi*xi+(99.0/4.0*xi
+-99.0*xi*xi+297.0/4.0*xi*xi*xi)*eta+(-81.0/2.0*xi+162.0*xi*xi-243.0/2.0*xi*xi*
+xi)*eta*eta+(81.0/4.0*xi-81.0*xi*xi+243.0/4.0*xi*xi*xi)*eta*eta*eta;
+ case 6: return (9.0*xi-81.0/2.0*xi*xi+81.0/2.0*xi*xi*xi)*eta+(-45.0/2.0
+*xi+405.0/4.0*xi*xi-405.0/4.0*xi*xi*xi)*eta*eta+(27.0/2.0*xi-243.0/4.0*xi*xi+
+243.0/4.0*xi*xi*xi)*eta*eta*eta;
+ case 7: return (-9.0/2.0*xi+81.0/4.0*xi*xi-81.0/4.0*xi*xi*xi)*eta+(18.0
+*xi-81.0*xi*xi+81.0*xi*xi*xi)*eta*eta+(-27.0/2.0*xi+243.0/4.0*xi*xi-243.0/4.0*
+xi*xi*xi)*eta*eta*eta;
+ case 8: return (9.0*xi-45.0/2.0*xi*xi+27.0/2.0*xi*xi*xi)*eta+(-81.0/2.0
+*xi+405.0/4.0*xi*xi-243.0/4.0*xi*xi*xi)*eta*eta+(81.0/2.0*xi-405.0/4.0*xi*xi+
+243.0/4.0*xi*xi*xi)*eta*eta*eta;
+ case 9: return (-9.0/2.0*xi+18.0*xi*xi-27.0/2.0*xi*xi*xi)*eta+(81.0/4.0
+*xi-81.0*xi*xi+243.0/4.0*xi*xi*xi)*eta*eta+(-81.0/4.0*xi+81.0*xi*xi-243.0/4.0*
+xi*xi*xi)*eta*eta*eta;
+ case 10: return (9.0-99.0/2.0*xi+81.0*xi*xi-81.0/2.0*xi*xi*xi)*eta+(
+-45.0/2.0+495.0/4.0*xi-405.0/2.0*xi*xi+405.0/4.0*xi*xi*xi)*eta*eta+(27.0/2.0
+-297.0/4.0*xi+243.0/2.0*xi*xi-243.0/4.0*xi*xi*xi)*eta*eta*eta;
+ case 11: return (-9.0/2.0+99.0/4.0*xi-81.0/2.0*xi*xi+81.0/4.0*xi*xi*xi)
+*eta+(18.0-99.0*xi+162.0*xi*xi-81.0*xi*xi*xi)*eta*eta+(-27.0/2.0+297.0/4.0*xi
+-243.0/2.0*xi*xi+243.0/4.0*xi*xi*xi)*eta*eta*eta;
+ case 12: return (81.0*xi-405.0/2.0*xi*xi+243.0/2.0*xi*xi*xi)*eta+(
+-405.0/2.0*xi+2025.0/4.0*xi*xi-1215.0/4.0*xi*xi*xi)*eta*eta+(243.0/2.0*xi
+-1215.0/4.0*xi*xi+729.0/4.0*xi*xi*xi)*eta*eta*eta;
+ case 13: return (-81.0/2.0*xi+162.0*xi*xi-243.0/2.0*xi*xi*xi)*eta+(
+405.0/4.0*xi-405.0*xi*xi+1215.0/4.0*xi*xi*xi)*eta*eta+(-243.0/4.0*xi+243.0*xi*
+xi-729.0/4.0*xi*xi*xi)*eta*eta*eta;
+ case 14: return (81.0/4.0*xi-81.0*xi*xi+243.0/4.0*xi*xi*xi)*eta+(-81.0*
+xi+324.0*xi*xi-243.0*xi*xi*xi)*eta*eta+(243.0/4.0*xi-243.0*xi*xi+729.0/4.0*xi*
+xi*xi)*eta*eta*eta;
+ case 15: return (-81.0/2.0*xi+405.0/4.0*xi*xi-243.0/4.0*xi*xi*xi)*eta+(
+162.0*xi-405.0*xi*xi+243.0*xi*xi*xi)*eta*eta+(-243.0/2.0*xi+1215.0/4.0*xi*xi
+-729.0/4.0*xi*xi*xi)*eta*eta*eta;
};
return 0;
};
eta= p(1);
switch (i)
{
- case 0: return Point<2>(-(2*xi-1)*(1-eta)*(2*eta-1)+2*(1-xi)*(1-eta)*(2*eta-1),
- -(1-xi)*(2*xi-1)*(2*eta-1)+2*(1-xi)*(2*xi-1)*(1-eta));
- case 1: return Point<2>((-2*xi+1)*(1-eta)*(2*eta-1)-2*xi*(1-eta)*(2*eta-1),
- -xi*(-2*xi+1)*(2*eta-1)+2*xi*(-2*xi+1)*(1-eta));
- case 2: return Point<2>((-2*xi+1)*eta*(-2*eta+1)-2*xi*eta*(-2*eta+1),
- xi*(-2*xi+1)*(-2*eta+1)-2*xi*(-2*xi+1)*eta);
- case 3: return Point<2>(-(2*xi-1)*eta*(-2*eta+1)+2*(1-xi)*eta*(-2*eta+1),
- (1-xi)*(2*xi-1)*(-2*eta+1)-2*(1-xi)*(2*xi-1)*eta);
- case 4: return Point<2>(-4*xi*(1-eta)*(-2*eta+1)+4*(1-xi)*(1-eta)*(-2*eta+1),
- -4*(1-xi)*xi*(-2*eta+1)-8*(1-xi)*xi*(1-eta));
- case 5: return Point<2>(4*(2*xi-1)*(1-eta)*eta+8*xi*(1-eta)*eta,
- -4*xi*(2*xi-1)*eta+4*xi*(2*xi-1)*(1-eta));
- case 6: return Point<2>(-4*xi*eta*(2*eta-1)+4*(1-xi)*eta*(2*eta-1),
- 4*(1-xi)*xi*(2*eta-1)+8*(1-xi)*xi*eta);
- case 7: return Point<2>(-4*(-2*xi+1)*(1-eta)*eta-8*(1-xi)*(1-eta)*eta,
- -4*(1-xi)*(-2*xi+1)*eta+4*(1-xi)*(-2*xi+1)*(1-eta));
- case 8: return Point<2>(16*(1-xi)*(1-eta)*eta-16*xi*eta*(1-eta),
- 16*xi*(1-xi)*(1-eta)-16*(1-xi)*xi*eta);
+ case 0: return Point<2>(-11.0/2.0+18.0*xi-27.0/2.0*xi*xi+(121.0/4.0-99.0*xi+297.0/4.0*xi*xi)*eta+(-99.0/2.0+162.0*xi-243.0/2.0*xi*xi)*eta*eta+(99.0/4.0-81.0*xi+243.0/4.0*xi*xi)*eta*eta*eta,
+ -11.0/2.0+121.0/4.0*xi-99.0/2.0*xi*xi+99.0/4.0*xi*xi*xi+2.0*(9.0-99.0/2.0*xi+81.0*xi*xi-81.0/2.0*xi*xi*xi)*eta+3.0*(-9.0/2.0+99.0/4.0*xi-81.0/2.0*xi*xi+81.0/4.0*xi*xi*xi)*eta*eta);
+ case 1: return Point<2>(1.0-9.0*xi+27.0/2.0*xi*xi+(-11.0/2.0+99.0/2.0*xi-297.0/4.0*xi*xi)*eta+(9.0-81.0*xi+243.0/2.0*xi*xi)*eta*eta+(-9.0/2.0+81.0/2.0*xi-243.0/4.0*xi*xi)*eta*eta*eta,
+ -11.0/2.0*xi+99.0/4.0*xi*xi-99.0/4.0*xi*xi*xi+2.0*(9.0*xi-81.0/2.0*xi*xi+81.0/2.0*xi*xi*xi)*eta+3.0*(-9.0/2.0*xi+81.0/4.0*xi*xi-81.0/4.0*xi*xi*xi)*eta*eta);
+ case 2: return Point<2>((1.0-9.0*xi+27.0/2.0*xi*xi)*eta+(-9.0/2.0+81.0/2.0*xi-243.0/4.0*xi*xi)*eta*eta+(9.0/2.0-81.0/2.0*xi+243.0/4.0*xi*xi)*eta*eta*eta,
+ xi-9.0/2.0*xi*xi+9.0/2.0*xi*xi*xi+2.0*(-9.0/2.0*xi+81.0/4.0*xi*xi-81.0/4.0*xi*xi*xi)*eta+3.0*(9.0/2.0*xi-81.0/4.0*xi*xi+81.0/4.0*xi*xi*xi)*eta*eta);
+ case 3: return Point<2>((-11.0/2.0+18.0*xi-27.0/2.0*xi*xi)*eta+(99.0/4.0-81.0*xi+243.0/4.0*xi*xi)*eta*eta+(-99.0/4.0+81.0*xi-243.0/4.0*xi*xi)*eta*eta*eta,
+ 1.0-11.0/2.0*xi+9.0*xi*xi-9.0/2.0*xi*xi*xi+2.0*(-9.0/2.0+99.0/4.0*xi-81.0/2.0*xi*xi+81.0/4.0*xi*xi*xi)*eta+3.0*(9.0/2.0-99.0/4.0*xi+81.0/2.0*xi*xi-81.0/4.0*xi*xi*xi)*eta*eta);
+ case 4: return Point<2>(9.0-45.0*xi+81.0/2.0*xi*xi+(-99.0/2.0+495.0/2.0*xi-891.0/4.0*xi*xi)*eta+(81.0-405.0*xi+729.0/2.0*xi*xi)*eta*eta+(-81.0/2.0+405.0/2.0*xi-729.0/4.0*xi*xi)*eta*eta*eta,
+ -99.0/2.0*xi+495.0/4.0*xi*xi-297.0/4.0*xi*xi*xi+2.0*(81.0*xi-405.0/2.0*xi*xi+243.0/2.0*xi*xi*xi)*eta+3.0*(-81.0/2.0*xi+405.0/4.0*xi*xi-243.0/4.0*xi*xi*xi)*eta*eta);
+ case 5: return Point<2>(-9.0/2.0+36.0*xi-81.0/2.0*xi*xi+(99.0/4.0-198.0*xi+891.0/4.0*xi*xi)*eta+(-81.0/2.0+324.0*xi-729.0/2.0*xi*xi)*eta*eta+(81.0/4.0-162.0*xi+729.0/4.0*xi*xi)*eta*eta*eta,
+ 99.0/4.0*xi-99.0*xi*xi+297.0/4.0*xi*xi*xi+2.0*(-81.0/2.0*xi+162.0*xi*xi-243.0/2.0*xi*xi*xi)*eta+3.0*(81.0/4.0*xi-81.0*xi*xi+243.0/4.0*xi*xi*xi)*eta*eta);
+ case 6: return Point<2>((9.0-81.0*xi+243.0/2.0*xi*xi)*eta+(-45.0/2.0+405.0/2.0*xi-1215.0/4.0*xi*xi)*eta*eta+(27.0/2.0-243.0/2.0*xi+729.0/4.0*xi*xi)*eta*eta*eta,
+ 9.0*xi-81.0/2.0*xi*xi+81.0/2.0*xi*xi*xi+2.0*(-45.0/2.0*xi+405.0/4.0*xi*xi-405.0/4.0*xi*xi*xi)*eta+3.0*(27.0/2.0*xi-243.0/4.0*xi*xi+243.0/4.0*xi*xi*xi)*eta*eta);
+ case 7: return Point<2>((-9.0/2.0+81.0/2.0*xi-243.0/4.0*xi*xi)*eta+(18.0-162.0*xi+243.0*xi*xi)*eta*eta+(-27.0/2.0+243.0/2.0*xi-729.0/4.0*xi*xi)*eta*eta*eta,
+ -9.0/2.0*xi+81.0/4.0*xi*xi-81.0/4.0*xi*xi*xi+2.0*(18.0*xi-81.0*xi*xi+81.0*xi*xi*xi)*eta+3.0*(-27.0/2.0*xi+243.0/4.0*xi*xi-243.0/4.0*xi*xi*xi)*eta*eta);
+ case 8: return Point<2>((9.0-45.0*xi+81.0/2.0*xi*xi)*eta+(-81.0/2.0+405.0/2.0*xi-729.0/4.0*xi*xi)*eta*eta+(81.0/2.0-405.0/2.0*xi+729.0/4.0*xi*xi)*eta*eta*eta,
+ 9.0*xi-45.0/2.0*xi*xi+27.0/2.0*xi*xi*xi+2.0*(-81.0/2.0*xi+405.0/4.0*xi*xi-243.0/4.0*xi*xi*xi)*eta+3.0*(81.0/2.0*xi-405.0/4.0*xi*xi+243.0/4.0*xi*xi*xi)*eta*eta);
+ case 9: return Point<2>((-9.0/2.0+36.0*xi-81.0/2.0*xi*xi)*eta+(81.0/4.0-162.0*xi+729.0/4.0*xi*xi)*eta*eta+(-81.0/4.0+162.0*xi-729.0/4.0*xi*xi)*eta*eta*eta,
+ -9.0/2.0*xi+18.0*xi*xi-27.0/2.0*xi*xi*xi+2.0*(81.0/4.0*xi-81.0*xi*xi+243.0/4.0*xi*xi*xi)*eta+3.0*(-81.0/4.0*xi+81.0*xi*xi-243.0/4.0*xi*xi*xi)*eta*eta);
+ case 10: return Point<2>((-99.0/2.0+162.0*xi-243.0/2.0*xi*xi)*eta+(495.0/4.0-405.0*xi+1215.0/4.0*xi*xi)*eta*eta+(-297.0/4.0+243.0*xi-729.0/4.0*xi*xi)*eta*eta*eta,
+ 9.0-99.0/2.0*xi+81.0*xi*xi-81.0/2.0*xi*xi*xi+2.0*(-45.0/2.0+495.0/4.0*xi-405.0/2.0*xi*xi+405.0/4.0*xi*xi*xi)*eta+3.0*(27.0/2.0-297.0/4.0*xi+243.0/2.0*xi*xi-243.0/4.0*xi*xi*xi)*eta*eta);
+ case 11: return Point<2>((99.0/4.0-81.0*xi+243.0/4.0*xi*xi)*eta+(-99.0+324.0*xi-243.0*xi*xi)*eta*eta+(297.0/4.0-243.0*xi+729.0/4.0*xi*xi)*eta*eta*eta,
+ -9.0/2.0+99.0/4.0*xi-81.0/2.0*xi*xi+81.0/4.0*xi*xi*xi+2.0*(18.0-99.0*xi+162.0*xi*xi-81.0*xi*xi*xi)*eta+3.0*(-27.0/2.0+297.0/4.0*xi-243.0/2.0*xi*xi+243.0/4.0*xi*xi*xi)*eta*eta);
+ case 12: return Point<2>((81.0-405.0*xi+729.0/2.0*xi*xi)*eta+(-405.0/2.0+2025.0/2.0*xi-3645.0/4.0*xi*xi)*eta*eta+(243.0/2.0-1215.0/2.0*xi+2187.0/4.0*xi*xi)*eta*eta*eta,
+ 81.0*xi-405.0/2.0*xi*xi+243.0/2.0*xi*xi*xi+2.0*(-405.0/2.0*xi+2025.0/4.0*xi*xi-1215.0/4.0*xi*xi*xi)*eta+3.0*(243.0/2.0*xi-1215.0/4.0*xi*xi+729.0/4.0*xi*xi*xi)*eta*eta);
+ case 13: return Point<2>((-81.0/2.0+324.0*xi-729.0/2.0*xi*xi)*eta+(405.0/4.0-810.0*xi+3645.0/4.0*xi*xi)*eta*eta+(-243.0/4.0+486.0*xi-2187.0/4.0*xi*xi)*eta*eta*eta,
+ -81.0/2.0*xi+162.0*xi*xi-243.0/2.0*xi*xi*xi+2.0*(405.0/4.0*xi-405.0*xi*xi+1215.0/4.0*xi*xi*xi)*eta+3.0*(-243.0/4.0*xi+243.0*xi*xi-729.0/4.0*xi*xi*xi)*eta*eta);
+ case 14: return Point<2>((81.0/4.0-162.0*xi+729.0/4.0*xi*xi)*eta+(-81.0+648.0*xi-729.0*xi*xi)*eta*eta+(243.0/4.0-486.0*xi+2187.0/4.0*xi*xi)*eta*eta*eta,
+ 81.0/4.0*xi-81.0*xi*xi+243.0/4.0*xi*xi*xi+2.0*(-81.0*xi+324.0*xi*xi-243.0*xi*xi*xi)*eta+3.0*(243.0/4.0*xi-243.0*xi*xi+729.0/4.0*xi*xi*xi)*eta*eta);
+ case 15: return Point<2>((-81.0/2.0+405.0/2.0*xi-729.0/4.0*xi*xi)*eta+(162.0-810.0*xi+729.0*xi*xi)*eta*eta+(-243.0/2.0+1215.0/2.0*xi-2187.0/4.0*xi*xi)*eta*eta*eta,
+ -81.0/2.0*xi+405.0/4.0*xi*xi-243.0/4.0*xi*xi*xi+2.0*(162.0*xi-405.0*xi*xi+243.0*xi*xi*xi)*eta+3.0*(-243.0/2.0*xi+1215.0/4.0*xi*xi-729.0/4.0*xi*xi*xi)*eta*eta);
};
return Point<2> ();
};
Assert (local_mass_matrix.m() == total_dofs,
ExcWrongFieldDimension(local_mass_matrix.m(),total_dofs));
-/* Get the computation of the local mass matrix by these lines in maple. Note
- that tphi[i] are the basis function of the linear finite element, which
- are used by the transformation (therefore >t<phi), while the phi[i]
- are the basis functions of the biquadratic element.
-
- x_real := sum(x[i]*tphi[i], i=0..3);
- y_real := sum(y[i]*tphi[i], i=0..3);
- tphi[0] := (1-xi)*(1-eta);
- tphi[1] := xi*(1-eta);
- tphi[2] := xi*eta;
- tphi[3] := (1-xi)*eta;
- detJ := diff(x_real,xi)*diff(y_real,eta) - diff(x_real,eta)*diff(y_real,xi);
-
- phi[0] := (1-xi)*( 2*xi-1) * (1-eta)*( 2*eta-1);
- phi[1] := xi *(-2*xi+1) * (1-eta)*( 2*eta-1);
- phi[2] := xi *(-2*xi+1) * eta *(-2*eta+1);
- phi[3] := (1-xi)*( 2*xi-1) * eta *(-2*eta+1);
- phi[4] := 4 * (1-xi)*xi * (1-eta)*(1-2*eta);
- phi[5] := 4 * xi *(-1+2*xi) * (1-eta)*eta;
- phi[6] := 4 * (1-xi)*xi * eta *(-1+2*eta);
- phi[7] := 4 * (1-xi)*(1-2*xi) * (1-eta)*eta;
- phi[8] := 16 * xi*(1-xi) * eta*(1-eta);
- m := proc (i,j) int( int(phi[i]*phi[j]*detJ, xi=0..1), eta=0..1); end;
-
- M := array(0..8,0..8);
- for i from 0 to 8 do
- for j from 0 to 8 do
- M[i,j] := m(i,j);
- od;
- od;
-
- readlib(C);
- C(M, optimized);
-*/
-
const double x[4] = { cell->vertex(0)(0),
cell->vertex(1)(0),
cell->vertex(2)(0),
Assert ((-x[0]+x[1])*(-y[1]+y[2])-(-x[1]+x[2])*(-y[0]+y[1]), // xi=1, eta=0
ExcJacobiDeterminantHasWrongSign());
- const double t1 = (x[1]*y[0]);
- const double t2 = (x[1]*y[2]);
- const double t3 = (x[0]*y[3]);
- const double t4 = (x[3]*y[2]);
- const double t5 = (x[2]*y[3]);
- const double t6 = (x[0]*y[1]);
- const double t7 = (x[3]*y[1]);
- const double t8 = (x[3]*y[0]);
- const double t9 = (x[2]*y[1]);
- const double t10 = (x[1]*y[3]);
- const double t12 = (x[0]*y[2]);
- const double t13 = (x[2]*y[0]);
- const double t14 = (7.0/1800.0*t1-t2/450+t3/450+t4/1800-t5/1800-
- 7.0/1800.0*t6+t12/600+
- t7/600-t8/450-t13/600+t9/450-t10/600);
- const double t15 = (-t1/1800+t2/1800-t3/1800-t4/1800+t5/1800+
- t6/1800+t8/1800-t9/1800);
- const double t16 = (t1/450-t2/1800+7.0/1800.0*t3+t4/450-
- t5/450-t6/450-t12/600+t7/600
- -7.0/1800.0*t8+t13/600+t9/1800-t10/600);
- const double t17 = (-7.0/900.0*t1-2.0/225.0*t3-t4/900+t5/900
- +7.0/900.0*t6+t12/900-7.0/
- 900.0*t7+2.0/225.0*t8-t13/900+7.0/900.0*t10);
- const double t18 = (t1/450-t2/900+t3/900-t6/450+t12/900+
- t7/900-t8/900-t13/900+t9/900-
- t10/900);
- const double t19 = (t1/900+t3/450+t4/900-t5/900-t6/900
- -t12/900+t7/900-t8/450+t13/900-
- t10/900);
- const double t20 = (-2.0/225.0*t1+t2/900-7.0/900.0*t3+
- 2.0/225.0*t6-t12/900-7.0/900.0*t7
- +7.0/900.0*t8+t13/900-t9/900+7.0/900.0*t10);
- const double t21 = (-t1/225-t3/225+t6/225-t7/225+t8/225+t10/225);
- const double t23 = (t1/450-7.0/1800.0*t2+t3/1800+t4/450
- -t5/450-t6/450+t12/600-t7/600-t8
- /1800-t13/600+7.0/1800.0*t9+t10/600);
- const double t24 = (-7.0/900.0*t1+2.0/225.0*t2-t4/900+t5/900
- +7.0/900.0*t6-7.0/900.0*t12
- +t7/900+7.0/900.0*t13-2.0/225.0*t9-t10/900);
- const double t25 = (-2.0/225.0*t1+7.0/900.0*t2-t3/900+2.0/225.0*t6
- -7.0/900.0*t12-t7/900
- +t8/900+7.0/900.0*t13-7.0/900.0*t9+t10/900);
- const double t26 = (t1/900-t2/450+t4/900-t5/900-t6/900+t12/900
- -t7/900-t13/900+t9/450+
- t10/900);
- const double t27 = (-t1/225+t2/225+t6/225-t12/225+t13/225-t9/225);
- const double t29 = (t1/1800-t2/450+t3/450+7.0/1800.0*t4-7.0/1800.0*t5
- -t6/1800-t12/600-
- t7/600-t8/450+t13/600+t9/450+t10/600);
- const double t30 = (7.0/900.0*t2-t3/900-2.0/225.0*t4+2.0/225.0*t5
- +t12/900+7.0/900.0*t7+
- t8/900-t13/900-7.0/900.0*t9-7.0/900.0*t10);
- const double t31 = (-t1/900+2.0/225.0*t2-7.0/900.0*t4+7.0/900.0*t5
- +t6/900-t12/900+7.0/
- 900.0*t7+t13/900-2.0/225.0*t9-7.0/900.0*t10);
- const double t32 = (-t2/900+t3/900+t4/450-t5/450-t12/900-t7/900
- -t8/900+t13/900+t9/900+
- t10/900);
- const double t33 = (t2/225-t4/225+t5/225+t7/225-t9/225-t10/225);
- const double t35 = (-t1/900-2.0/225.0*t3-7.0/900.0*t4+7.0/900.0*t5
- +t6/900+7.0/900.0*t12
- -t7/900+2.0/225.0*t8-7.0/900.0*t13+t10/900);
- const double t36 = (t2/900-7.0/900.0*t3-2.0/225.0*t4+2.0/225.0*t5
- +7.0/900.0*t12+t7/900+
- 7.0/900.0*t8-7.0/900.0*t13-t9/900-t10/900);
- const double t37 = (-t3/225-t4/225+t5/225+t12/225+t8/225-t13/225);
- const double t38 = (-14.0/225.0*t1+8.0/225.0*t2-8.0/225.0*t3
- -2.0/225.0*t4+2.0/225.0*t5+
- 14.0/225.0*t6-2.0/75.0*t12-2.0/75.0*t7
- +8.0/225.0*t8+2.0/75.0*t13-8.0/225.0*t9+
- 2.0/75.0*t10);
- const double t39 = (2.0/225.0*t1-2.0/225.0*t2+2.0/225.0*t3
- +2.0/225.0*t4-2.0/225.0*t5
- -2.0/225.0*t6-2.0/225.0*t8+2.0/225.0*t9);
- const double t40 = (-8.0/225.0*t1+4.0/225.0*t2-4.0/225.0*t3
- +8.0/225.0*t6-4.0/225.0*t12
- -4.0/225.0*t7+4.0/225.0*t8+4.0/225.0*t13
- -4.0/225.0*t9+4.0/225.0*t10);
- const double t41 = (-8.0/225.0*t1+14.0/225.0*t2-2.0/225.0*t3
- -8.0/225.0*t4+8.0/225.0*t5+
- 8.0/225.0*t6-2.0/75.0*t12+2.0/75.0*t7
- +2.0/225.0*t8+2.0/75.0*t13-14.0/225.0*t9
- -2.0/75.0*t10);
- const double t42 = (-4.0/225.0*t1+8.0/225.0*t2-4.0/225.0*t4
- +4.0/225.0*t5+4.0/225.0*t6
- -4.0/225.0*t12+4.0/225.0*t7+4.0/225.0*t13
- -8.0/225.0*t9-4.0/225.0*t10);
- const double t43 = (-2.0/225.0*t1+8.0/225.0*t2-8.0/225.0*t3
- -14.0/225.0*t4+14.0/225.0*t5
- +2.0/225.0*t6+2.0/75.0*t12+2.0/75.0*t7
- +8.0/225.0*t8-2.0/75.0*t13-8.0/225.0*t9
- -2.0/75.0*t10);
- const double t44 = (4.0/225.0*t2-4.0/225.0*t3-8.0/225.0*t4
- +8.0/225.0*t5+4.0/225.0*t12+
- 4.0/225.0*t7+4.0/225.0*t8-4.0/225.0*t13
- -4.0/225.0*t9-4.0/225.0*t10);
- const double t45 = (-8.0/225.0*t1+2.0/225.0*t2-14.0/225.0*t3
- -8.0/225.0*t4+8.0/225.0*t5+
- 8.0/225.0*t6+2.0/75.0*t12-2.0/75.0*t7
- +14.0/225.0*t8-2.0/75.0*t13-2.0/225.0*t9+
- 2.0/75.0*t10);
- const double t46 = (-4.0/225.0*t1-8.0/225.0*t3-4.0/225.0*t4
- +4.0/225.0*t5+4.0/225.0*t6+
- 4.0/225.0*t12-4.0/225.0*t7+8.0/225.0*t8
- -4.0/225.0*t13+4.0/225.0*t10);
-
- local_mass_matrix(0,0) = (-7.0/450.0*t1+t2/450-7.0/450.0*t3
- -t4/450+t5/450+7.0/450.0*t6-t7/75
- +7.0/450.0*t8-t9/450+t10/75);
- local_mass_matrix(0,1) = (t14);
- local_mass_matrix(0,2) = (t15);
- local_mass_matrix(0,3) = (t16);
- local_mass_matrix(0,4) = (t17);
- local_mass_matrix(0,5) = (t18);
- local_mass_matrix(0,6) = (t19);
- local_mass_matrix(0,7) = (t20);
- local_mass_matrix(0,8) = (t21);
- local_mass_matrix(1,0) = (t14);
- local_mass_matrix(1,1) = (-7.0/450.0*t1+7.0/450.0*t2-t3/450
- -t4/450+t5/450+7.0/450.0*t6-
- t12/75+t8/450+t13/75-7.0/450.0*t9);
- local_mass_matrix(1,2) = (t23);
- local_mass_matrix(1,3) = (t15);
- local_mass_matrix(1,4) = (t24);
- local_mass_matrix(1,5) = (t25);
- local_mass_matrix(1,6) = (t26);
- local_mass_matrix(1,7) = (t18);
- local_mass_matrix(1,8) = (t27);
- local_mass_matrix(2,0) = (t15);
- local_mass_matrix(2,1) = (t23);
- local_mass_matrix(2,2) = (-t1/450+7.0/450.0*t2-t3/450-7.0/450.0*t4
- +7.0/450.0*t5+t6/450+t7/75
- +t8/450-7.0/450.0*t9-t10/75);
- local_mass_matrix(2,3) = (t29);
- local_mass_matrix(2,4) = (t26);
- local_mass_matrix(2,5) = (t30);
- local_mass_matrix(2,6) = (t31);
- local_mass_matrix(2,7) = (t32);
- local_mass_matrix(2,8) = (t33);
- local_mass_matrix(3,0) = (t16);
- local_mass_matrix(3,1) = (t15);
- local_mass_matrix(3,2) = (t29);
- local_mass_matrix(3,3) = (-t1/450+t2/450-7.0/450.0*t3-7.0/450.0*t4
- +7.0/450.0*t5+t6/450+
- t12/75+7.0/450.0*t8-t13/75-t9/450);
- local_mass_matrix(3,4) = (t19);
- local_mass_matrix(3,5) = (t32);
- local_mass_matrix(3,6) = (t35);
- local_mass_matrix(3,7) = (t36);
- local_mass_matrix(3,8) = (t37);
- local_mass_matrix(4,0) = (t17);
- local_mass_matrix(4,1) = (t24);
- local_mass_matrix(4,2) = (t26);
- local_mass_matrix(4,3) = (t19);
- local_mass_matrix(4,4) = (t38);
- local_mass_matrix(4,5) = (t27);
- local_mass_matrix(4,6) = (t39);
- local_mass_matrix(4,7) = (t21);
- local_mass_matrix(4,8) = (t40);
- local_mass_matrix(5,0) = (t18);
- local_mass_matrix(5,1) = (t25);
- local_mass_matrix(5,2) = (t30);
- local_mass_matrix(5,3) = (t32);
- local_mass_matrix(5,4) = (t27);
- local_mass_matrix(5,5) = (t41);
- local_mass_matrix(5,6) = (t33);
- local_mass_matrix(5,7) = (t39);
- local_mass_matrix(5,8) = (t42);
- local_mass_matrix(6,0) = (t19);
- local_mass_matrix(6,1) = (t26);
- local_mass_matrix(6,2) = (t31);
- local_mass_matrix(6,3) = (t35);
- local_mass_matrix(6,4) = (t39);
- local_mass_matrix(6,5) = (t33);
- local_mass_matrix(6,6) = (t43);
- local_mass_matrix(6,7) = (t37);
- local_mass_matrix(6,8) = (t44);
- local_mass_matrix(7,0) = (t20);
- local_mass_matrix(7,1) = (t18);
- local_mass_matrix(7,2) = (t32);
- local_mass_matrix(7,3) = (t36);
- local_mass_matrix(7,4) = (t21);
- local_mass_matrix(7,5) = (t39);
- local_mass_matrix(7,6) = (t37);
- local_mass_matrix(7,7) = (t45);
- local_mass_matrix(7,8) = (t46);
- local_mass_matrix(8,0) = (t21);
- local_mass_matrix(8,1) = (t27);
- local_mass_matrix(8,2) = (t33);
- local_mass_matrix(8,3) = (t37);
- local_mass_matrix(8,4) = (t40);
- local_mass_matrix(8,5) = (t42);
- local_mass_matrix(8,6) = (t44);
- local_mass_matrix(8,7) = (t46);
- local_mass_matrix(8,8) = (-32.0/225.0*t1+32.0/225.0*t2-32.0/225.0*t3
- -32.0/225.0*t4+32.0/225.0*t5+32.0/225.0*t6
- +32.0/225.0*t8-32.0/225.0*t9);
+ const double t1 = x[0]-x[1]+x[2]-x[3];
+ const double t2 = -y[0]+y[1];
+ const double t3 = t1*t2;
+ const double t4 = 19.0/44100.0*t3;
+ const double t5 = -x[0]+x[1];
+ const double t6 = y[0]-y[1]+y[2]-y[3];
+ const double t7 = t5*t6;
+ const double t8 = 19.0/44100.0*t7;
+ const double t9 = -x[0]+x[3];
+ const double t10 = t9*t6;
+ const double t11 = 19.0/44100.0*t10;
+ const double t12 = t9*t2;
+ const double t13 = 64.0/11025.0*t12;
+ const double t14 = -y[0]+y[3];
+ const double t15 = t1*t14;
+ const double t16 = 19.0/44100.0*t15;
+ const double t17 = t5*t14;
+ const double t18 = 64.0/11025.0*t17;
+ const double t20 = 361.0/5644800.0*t10;
+ const double t21 = 19.0/22050.0*t12;
+ const double t22 = 361.0/5644800.0*t15;
+ const double t23 = 19.0/22050.0*t17;
+ const double t24 = -t4+t8-t20-t21+t22+t23;
+ const double t25 = 361.0/5644800.0*t3;
+ const double t26 = 361.0/5644800.0*t7;
+ const double t29 = -t25+t26-t20-361.0/2822400.0*t12+t22+361.0/2822400.0*t17;
+ const double t30 = -t25+t26-t11-t21+t16+t23;
+ const double t31 = t3/4900.0;
+ const double t32 = t7/4900.0;
+ const double t33 = 209.0/627200.0*t10;
+ const double t34 = 11.0/2450.0*t12;
+ const double t35 = 209.0/627200.0*t15;
+ const double t36 = 11.0/2450.0*t17;
+ const double t37 = -t31+t32-t33-t34+t35+t36;
+ const double t38 = 19.0/156800.0*t10;
+ const double t39 = 2.0/1225.0*t12;
+ const double t40 = 19.0/156800.0*t15;
+ const double t41 = 2.0/1225.0*t17;
+ const double t42 = -t31+t32+t38+t39-t40-t41;
+ const double t43 = 209.0/627200.0*t3;
+ const double t44 = 209.0/627200.0*t7;
+ const double t45 = 19.0/627200.0*t10;
+ const double t46 = 209.0/313600.0*t12;
+ const double t47 = 19.0/627200.0*t15;
+ const double t48 = 209.0/313600.0*t17;
+ const double t49 = -t43+t44-t45-t46+t47+t48;
+ const double t50 = 19.0/156800.0*t3;
+ const double t51 = 19.0/156800.0*t7;
+ const double t52 = 19.0/78400.0*t12;
+ const double t53 = 19.0/78400.0*t17;
+ const double t54 = t50-t51-t45+t52+t47-t53;
+ const double t55 = 19.0/627200.0*t3;
+ const double t56 = 19.0/627200.0*t7;
+ const double t57 = -t55+t56-t33-t46+t35+t48;
+ const double t58 = -t55+t56+t38+t52-t40-t53;
+ const double t59 = t10/4900.0;
+ const double t60 = t15/4900.0;
+ const double t61 = -t43+t44-t59-t34+t60+t36;
+ const double t62 = t50-t51-t59+t39+t60-t41;
+ const double t63 = 99.0/627200.0*t3;
+ const double t64 = 99.0/627200.0*t7;
+ const double t65 = 99.0/627200.0*t10;
+ const double t66 = 1089.0/313600.0*t12;
+ const double t67 = 99.0/627200.0*t15;
+ const double t68 = 1089.0/313600.0*t17;
+ const double t69 = -t63+t64-t65-t66+t67+t68;
+ const double t70 = 9.0/156800.0*t10;
+ const double t71 = 99.0/78400.0*t12;
+ const double t72 = 9.0/156800.0*t15;
+ const double t73 = 99.0/78400.0*t17;
+ const double t74 = -t63+t64+t70+t71-t72-t73;
+ const double t75 = 9.0/156800.0*t3;
+ const double t76 = 9.0/156800.0*t7;
+ const double t77 = 9.0/19600.0*t12;
+ const double t78 = 9.0/19600.0*t17;
+ const double t79 = t75-t76+t70-t77-t72+t78;
+ const double t80 = t75-t76-t65+t71+t67-t73;
+ const double t81 = 79.0/14700.0*t3;
+ const double t82 = 79.0/14700.0*t7;
+ const double t86 = -1501.0/1881600.0*t3+1501.0/1881600.0*t7-t11-t21+t16+t23;
+ const double t87 = 9.0/4900.0*t3;
+ const double t88 = 9.0/4900.0*t7;
+ const double t89 = t87-t88+t38+t39-t40-t41;
+ const double t90 = 3.0/700.0*t3;
+ const double t91 = 3.0/700.0*t7;
+ const double t92 = -t90+t91-t33-t34+t35+t36;
+ const double t93 = 2607.0/627200.0*t3;
+ const double t94 = 2607.0/627200.0*t7;
+ const double t95 = -t93+t94-t59-t34+t60+t36;
+ const double t96 = 237.0/156800.0*t3;
+ const double t97 = 237.0/156800.0*t7;
+ const double t98 = t96-t97-t59+t39+t60-t41;
+ const double t99 = 171.0/627200.0*t3;
+ const double t100 = 171.0/627200.0*t7;
+ const double t101 = t99-t100+t38+t52-t40-t53;
+ const double t104 = -57.0/89600.0*t3+57.0/89600.0*t7-t33-t46+t35+t48;
+ const double t105 = 891.0/627200.0*t3;
+ const double t106 = 891.0/627200.0*t7;
+ const double t107 = t105-t106+t70+t71-t72-t73;
+ const double t108 = 297.0/89600.0*t3;
+ const double t109 = 297.0/89600.0*t7;
+ const double t110 = -t108+t109-t65-t66+t67+t68;
+ const double t111 = 27.0/22400.0*t3;
+ const double t112 = 27.0/22400.0*t7;
+ const double t113 = t111-t112-t65+t71+t67-t73;
+ const double t114 = 81.0/156800.0*t3;
+ const double t115 = 81.0/156800.0*t7;
+ const double t116 = -t114+t115+t70-t77-t72+t78;
+ const double t117 = 79.0/14700.0*t10;
+ const double t118 = 79.0/14700.0*t15;
+ const double t122 = -t4+t8-1501.0/1881600.0*t10-t21+1501.0/1881600.0*t15+t23;
+ const double t123 = 9.0/4900.0*t10;
+ const double t124 = 9.0/4900.0*t15;
+ const double t125 = t96-t97+t123+t39-t124-t41;
+ const double t126 = 3.0/700.0*t10;
+ const double t127 = 3.0/700.0*t15;
+ const double t128 = -t93+t94-t126-t34+t127+t36;
+ const double t129 = 237.0/156800.0*t10;
+ const double t130 = 237.0/156800.0*t15;
+ const double t131 = t87-t88+t129+t39-t130-t41;
+ const double t132 = 2607.0/627200.0*t10;
+ const double t133 = 2607.0/627200.0*t15;
+ const double t134 = -t90+t91-t132-t34+t133+t36;
+ const double t135 = 171.0/627200.0*t10;
+ const double t136 = 171.0/627200.0*t15;
+ const double t137 = t50-t51+t135+t52-t136-t53;
+ const double t140 = -t43+t44-57.0/89600.0*t10-t46+57.0/89600.0*t15+t48;
+ const double t141 = 81.0/156800.0*t10;
+ const double t142 = 81.0/156800.0*t15;
+ const double t143 = -t114+t115-t141-t77+t142+t78;
+ const double t144 = 891.0/627200.0*t10;
+ const double t145 = 891.0/627200.0*t15;
+ const double t146 = t111-t112+t144+t71-t145-t73;
+ const double t147 = 297.0/89600.0*t10;
+ const double t148 = 297.0/89600.0*t15;
+ const double t149 = -t108+t109-t147-t66+t148+t68;
+ const double t150 = 27.0/22400.0*t10;
+ const double t151 = 27.0/22400.0*t15;
+ const double t152 = t105-t106+t150+t71-t151-t73;
+ const double t154 = -t31+t32-t132-t34+t133+t36;
+ const double t155 = -t31+t32+t129+t39-t130-t41;
+ const double t156 = t50-t51+t123+t39-t124-t41;
+ const double t157 = -t43+t44-t126-t34+t127+t36;
+ const double t158 = t75-t76+t144+t71-t145-t73;
+ const double t159 = t75-t76-t141-t77+t142+t78;
+ const double t160 = -t63+t64+t150+t71-t151-t73;
+ const double t161 = -t63+t64-t147-t66+t148+t68;
+ const double t162 = 9.0/980.0*t3;
+ const double t163 = 9.0/980.0*t7;
+ const double t164 = 171.0/78400.0*t10;
+ const double t165 = 36.0/1225.0*t12;
+ const double t166 = 171.0/78400.0*t15;
+ const double t167 = 36.0/1225.0*t17;
+ const double t169 = 9.0/2450.0*t12;
+ const double t170 = 9.0/2450.0*t17;
+ const double t171 = t87-t88+t135+t169-t136-t170;
+ const double t174 = 171.0/39200.0*t12;
+ const double t175 = 171.0/39200.0*t17;
+ const double t176 = -171.0/125440.0*t3+171.0/125440.0*t7-t164-t174+t166+t175;
+ const double t179 = t99-t100+t135+171.0/313600.0*t12-t136-171.0/313600.0*t17;
+ const double t180 = 891.0/125440.0*t3;
+ const double t181 = 891.0/125440.0*t7;
+ const double t182 = 81.0/78400.0*t10;
+ const double t183 = 891.0/39200.0*t12;
+ const double t184 = 81.0/78400.0*t15;
+ const double t185 = 891.0/39200.0*t17;
+ const double t186 = -t180+t181-t182-t183+t184+t185;
+ const double t187 = 81.0/627200.0*t10;
+ const double t188 = 891.0/313600.0*t12;
+ const double t189 = 81.0/627200.0*t15;
+ const double t190 = 891.0/313600.0*t17;
+ const double t191 = t105-t106+t187+t188-t189-t190;
+ const double t192 = 81.0/78400.0*t12;
+ const double t193 = 81.0/78400.0*t17;
+ const double t194 = -t114+t115+t187-t192-t189+t193;
+ const double t195 = 81.0/31360.0*t3;
+ const double t196 = 81.0/31360.0*t7;
+ const double t197 = 81.0/9800.0*t12;
+ const double t198 = 81.0/9800.0*t17;
+ const double t199 = t195-t196-t182+t197+t184-t198;
+ const double t200 = 99.0/4900.0*t3;
+ const double t201 = 99.0/4900.0*t7;
+ const double t205 = -1881.0/627200.0*t3+1881.0/627200.0*t7-t164-t174+t166+t175;
+ const double t206 = 9801.0/627200.0*t3;
+ const double t207 = 9801.0/627200.0*t7;
+ const double t208 = -t206+t207-t182-t183+t184+t185;
+ const double t209 = 891.0/156800.0*t3;
+ const double t210 = 891.0/156800.0*t7;
+ const double t211 = t209-t210-t182+t197+t184-t198;
+ const double t212 = 2133.0/78400.0*t3;
+ const double t213 = 2133.0/78400.0*t7;
+ const double t214 = 9.0/980.0*t10;
+ const double t215 = 9.0/980.0*t15;
+ const double t219 = 2133.0/627200.0*t3-2133.0/627200.0*t7+t123+t169-t124-t170;
+ const double t220 = 171.0/78400.0*t3;
+ const double t221 = 171.0/78400.0*t7;
+ const double t224 = -t220+t221-171.0/125440.0*t10-t174+171.0/125440.0*t15+t175;
+ const double t225 = 729.0/78400.0*t3;
+ const double t226 = 729.0/78400.0*t7;
+ const double t227 = 81.0/31360.0*t10;
+ const double t228 = 81.0/31360.0*t15;
+ const double t229 = t225-t226+t227+t197-t228-t198;
+ const double t230 = 243.0/11200.0*t3;
+ const double t231 = 243.0/11200.0*t7;
+ const double t232 = 891.0/125440.0*t10;
+ const double t233 = 891.0/125440.0*t15;
+ const double t234 = -t230+t231-t232-t183+t233+t185;
+ const double t237 = 243.0/89600.0*t3-243.0/89600.0*t7+t144+t188-t145-t190;
+ const double t238 = 729.0/627200.0*t3;
+ const double t239 = 729.0/627200.0*t7;
+ const double t240 = -t238+t239-t141-t192+t142+t193;
+ const double t241 = 99.0/4900.0*t10;
+ const double t242 = 99.0/4900.0*t15;
+ const double t246 = -t220+t221-1881.0/627200.0*t10-t174+1881.0/627200.0*t15+t175;
+ const double t247 = 9801.0/627200.0*t10;
+ const double t248 = 9801.0/627200.0*t15;
+ const double t249 = -t230+t231-t247-t183+t248+t185;
+ const double t250 = 891.0/156800.0*t10;
+ const double t251 = 891.0/156800.0*t15;
+ const double t252 = t225-t226+t250+t197-t251-t198;
+ const double t253 = 2133.0/78400.0*t10;
+ const double t254 = 2133.0/78400.0*t15;
+ const double t258 = t87-t88+2133.0/627200.0*t10+t169-2133.0/627200.0*t15-t170;
+ const double t259 = 729.0/78400.0*t10;
+ const double t260 = 729.0/78400.0*t15;
+ const double t261 = t195-t196+t259+t197-t260-t198;
+ const double t262 = 729.0/627200.0*t10;
+ const double t263 = 729.0/627200.0*t15;
+ const double t264 = -t114+t115-t262-t192+t263+t193;
+ const double t267 = t105-t106+243.0/89600.0*t10+t188-243.0/89600.0*t15-t190;
+ const double t268 = 243.0/11200.0*t10;
+ const double t269 = 243.0/11200.0*t15;
+ const double t270 = -t180+t181-t268-t183+t269+t185;
+ const double t272 = t209-t210+t259+t197-t260-t198;
+ const double t273 = -t206+t207-t268-t183+t269+t185;
+ const double t275 = t99-t100+t123+t169-t124-t170;
+ const double t276 = 81.0/78400.0*t3;
+ const double t277 = 81.0/78400.0*t7;
+ const double t278 = -t276+t277-t232-t183+t233+t185;
+ const double t279 = -t276+t277+t227+t197-t228-t198;
+ const double t280 = 81.0/627200.0*t3;
+ const double t281 = 81.0/627200.0*t7;
+ const double t282 = t280-t281-t141-t192+t142+t193;
+ const double t283 = t280-t281+t144+t188-t145-t190;
+ const double t285 = -t276+t277+t250+t197-t251-t198;
+ const double t286 = -t276+t277-t247-t183+t248+t185;
+ const double t287 = 729.0/15680.0*t3;
+ const double t288 = 729.0/15680.0*t7;
+ const double t289 = 729.0/15680.0*t10;
+ const double t290 = 729.0/4900.0*t12;
+ const double t291 = 729.0/15680.0*t15;
+ const double t292 = 729.0/4900.0*t17;
+ const double t295 = 729.0/39200.0*t12;
+ const double t297 = 729.0/39200.0*t17;
+ const double t298 = t225-t226+729.0/125440.0*t10+t295-729.0/125440.0*t15-t297;
+ const double t301 = -t238+t239-t262-729.0/313600.0*t12+t263+729.0/313600.0*t17;
+ const double t304 = 729.0/125440.0*t3-729.0/125440.0*t7+t259+t295-t260-t297;
+ const double t305 = 8019.0/78400.0*t3;
+ const double t306 = 8019.0/78400.0*t7;
+ const double t310 = 8019.0/627200.0*t3-8019.0/627200.0*t7+t259+t295-t260-t297;
+ const double t311 = 8019.0/78400.0*t10;
+ const double t312 = 8019.0/78400.0*t15;
+ const double t316 = t225-t226+8019.0/627200.0*t10+t295-8019.0/627200.0*t15-t297;
+ local_mass_matrix(0,0) = -t4+t8-t11-t13+t16+t18;
+ local_mass_matrix(0,1) = t24;
+ local_mass_matrix(0,2) = t29;
+ local_mass_matrix(0,3) = t30;
+ local_mass_matrix(0,4) = t37;
+ local_mass_matrix(0,5) = t42;
+ local_mass_matrix(0,6) = t49;
+ local_mass_matrix(0,7) = t54;
+ local_mass_matrix(0,8) = t57;
+ local_mass_matrix(0,9) = t58;
+ local_mass_matrix(0,10) = t61;
+ local_mass_matrix(0,11) = t62;
+ local_mass_matrix(0,12) = t69;
+ local_mass_matrix(0,13) = t74;
+ local_mass_matrix(0,14) = t79;
+ local_mass_matrix(0,15) = t80;
+ local_mass_matrix(1,0) = t24;
+ local_mass_matrix(1,1) = -t81+t82-t11-t13+t16+t18;
+ local_mass_matrix(1,2) = t86;
+ local_mass_matrix(1,3) = t29;
+ local_mass_matrix(1,4) = t89;
+ local_mass_matrix(1,5) = t92;
+ local_mass_matrix(1,6) = t95;
+ local_mass_matrix(1,7) = t98;
+ local_mass_matrix(1,8) = t101;
+ local_mass_matrix(1,9) = t104;
+ local_mass_matrix(1,10) = t49;
+ local_mass_matrix(1,11) = t54;
+ local_mass_matrix(1,12) = t107;
+ local_mass_matrix(1,13) = t110;
+ local_mass_matrix(1,14) = t113;
+ local_mass_matrix(1,15) = t116;
+ local_mass_matrix(2,0) = t29;
+ local_mass_matrix(2,1) = t86;
+ local_mass_matrix(2,2) = -t81+t82-t117-t13+t118+t18;
+ local_mass_matrix(2,3) = t122;
+ local_mass_matrix(2,4) = t101;
+ local_mass_matrix(2,5) = t104;
+ local_mass_matrix(2,6) = t125;
+ local_mass_matrix(2,7) = t128;
+ local_mass_matrix(2,8) = t131;
+ local_mass_matrix(2,9) = t134;
+ local_mass_matrix(2,10) = t137;
+ local_mass_matrix(2,11) = t140;
+ local_mass_matrix(2,12) = t143;
+ local_mass_matrix(2,13) = t146;
+ local_mass_matrix(2,14) = t149;
+ local_mass_matrix(2,15) = t152;
+ local_mass_matrix(3,0) = t30;
+ local_mass_matrix(3,1) = t29;
+ local_mass_matrix(3,2) = t122;
+ local_mass_matrix(3,3) = -t4+t8-t117-t13+t118+t18;
+ local_mass_matrix(3,4) = t57;
+ local_mass_matrix(3,5) = t58;
+ local_mass_matrix(3,6) = t137;
+ local_mass_matrix(3,7) = t140;
+ local_mass_matrix(3,8) = t154;
+ local_mass_matrix(3,9) = t155;
+ local_mass_matrix(3,10) = t156;
+ local_mass_matrix(3,11) = t157;
+ local_mass_matrix(3,12) = t158;
+ local_mass_matrix(3,13) = t159;
+ local_mass_matrix(3,14) = t160;
+ local_mass_matrix(3,15) = t161;
+ local_mass_matrix(4,0) = t37;
+ local_mass_matrix(4,1) = t89;
+ local_mass_matrix(4,2) = t101;
+ local_mass_matrix(4,3) = t57;
+ local_mass_matrix(4,4) = -t162+t163-t164-t165+t166+t167;
+ local_mass_matrix(4,5) = t171;
+ local_mass_matrix(4,6) = t107;
+ local_mass_matrix(4,7) = t116;
+ local_mass_matrix(4,8) = t176;
+ local_mass_matrix(4,9) = t179;
+ local_mass_matrix(4,10) = t69;
+ local_mass_matrix(4,11) = t80;
+ local_mass_matrix(4,12) = t186;
+ local_mass_matrix(4,13) = t191;
+ local_mass_matrix(4,14) = t194;
+ local_mass_matrix(4,15) = t199;
+ local_mass_matrix(5,0) = t42;
+ local_mass_matrix(5,1) = t92;
+ local_mass_matrix(5,2) = t104;
+ local_mass_matrix(5,3) = t58;
+ local_mass_matrix(5,4) = t171;
+ local_mass_matrix(5,5) = -t200+t201-t164-t165+t166+t167;
+ local_mass_matrix(5,6) = t110;
+ local_mass_matrix(5,7) = t113;
+ local_mass_matrix(5,8) = t179;
+ local_mass_matrix(5,9) = t205;
+ local_mass_matrix(5,10) = t74;
+ local_mass_matrix(5,11) = t79;
+ local_mass_matrix(5,12) = t191;
+ local_mass_matrix(5,13) = t208;
+ local_mass_matrix(5,14) = t211;
+ local_mass_matrix(5,15) = t194;
+ local_mass_matrix(6,0) = t49;
+ local_mass_matrix(6,1) = t95;
+ local_mass_matrix(6,2) = t125;
+ local_mass_matrix(6,3) = t137;
+ local_mass_matrix(6,4) = t107;
+ local_mass_matrix(6,5) = t110;
+ local_mass_matrix(6,6) = -t212+t213-t214-t165+t215+t167;
+ local_mass_matrix(6,7) = t219;
+ local_mass_matrix(6,8) = t143;
+ local_mass_matrix(6,9) = t146;
+ local_mass_matrix(6,10) = t224;
+ local_mass_matrix(6,11) = t179;
+ local_mass_matrix(6,12) = t229;
+ local_mass_matrix(6,13) = t234;
+ local_mass_matrix(6,14) = t237;
+ local_mass_matrix(6,15) = t240;
+ local_mass_matrix(7,0) = t54;
+ local_mass_matrix(7,1) = t98;
+ local_mass_matrix(7,2) = t128;
+ local_mass_matrix(7,3) = t140;
+ local_mass_matrix(7,4) = t116;
+ local_mass_matrix(7,5) = t113;
+ local_mass_matrix(7,6) = t219;
+ local_mass_matrix(7,7) = -t212+t213-t241-t165+t242+t167;
+ local_mass_matrix(7,8) = t152;
+ local_mass_matrix(7,9) = t149;
+ local_mass_matrix(7,10) = t179;
+ local_mass_matrix(7,11) = t246;
+ local_mass_matrix(7,12) = t240;
+ local_mass_matrix(7,13) = t237;
+ local_mass_matrix(7,14) = t249;
+ local_mass_matrix(7,15) = t252;
+ local_mass_matrix(8,0) = t57;
+ local_mass_matrix(8,1) = t101;
+ local_mass_matrix(8,2) = t131;
+ local_mass_matrix(8,3) = t154;
+ local_mass_matrix(8,4) = t176;
+ local_mass_matrix(8,5) = t179;
+ local_mass_matrix(8,6) = t143;
+ local_mass_matrix(8,7) = t152;
+ local_mass_matrix(8,8) = -t162+t163-t253-t165+t254+t167;
+ local_mass_matrix(8,9) = t258;
+ local_mass_matrix(8,10) = t158;
+ local_mass_matrix(8,11) = t161;
+ local_mass_matrix(8,12) = t261;
+ local_mass_matrix(8,13) = t264;
+ local_mass_matrix(8,14) = t267;
+ local_mass_matrix(8,15) = t270;
+ local_mass_matrix(9,0) = t58;
+ local_mass_matrix(9,1) = t104;
+ local_mass_matrix(9,2) = t134;
+ local_mass_matrix(9,3) = t155;
+ local_mass_matrix(9,4) = t179;
+ local_mass_matrix(9,5) = t205;
+ local_mass_matrix(9,6) = t146;
+ local_mass_matrix(9,7) = t149;
+ local_mass_matrix(9,8) = t258;
+ local_mass_matrix(9,9) = -t200+t201-t253-t165+t254+t167;
+ local_mass_matrix(9,10) = t159;
+ local_mass_matrix(9,11) = t160;
+ local_mass_matrix(9,12) = t264;
+ local_mass_matrix(9,13) = t272;
+ local_mass_matrix(9,14) = t273;
+ local_mass_matrix(9,15) = t267;
+ local_mass_matrix(10,0) = t61;
+ local_mass_matrix(10,1) = t49;
+ local_mass_matrix(10,2) = t137;
+ local_mass_matrix(10,3) = t156;
+ local_mass_matrix(10,4) = t69;
+ local_mass_matrix(10,5) = t74;
+ local_mass_matrix(10,6) = t224;
+ local_mass_matrix(10,7) = t179;
+ local_mass_matrix(10,8) = t158;
+ local_mass_matrix(10,9) = t159;
+ local_mass_matrix(10,10) = -t220+t221-t214-t165+t215+t167;
+ local_mass_matrix(10,11) = t275;
+ local_mass_matrix(10,12) = t278;
+ local_mass_matrix(10,13) = t279;
+ local_mass_matrix(10,14) = t282;
+ local_mass_matrix(10,15) = t283;
+ local_mass_matrix(11,0) = t62;
+ local_mass_matrix(11,1) = t54;
+ local_mass_matrix(11,2) = t140;
+ local_mass_matrix(11,3) = t157;
+ local_mass_matrix(11,4) = t80;
+ local_mass_matrix(11,5) = t79;
+ local_mass_matrix(11,6) = t179;
+ local_mass_matrix(11,7) = t246;
+ local_mass_matrix(11,8) = t161;
+ local_mass_matrix(11,9) = t160;
+ local_mass_matrix(11,10) = t275;
+ local_mass_matrix(11,11) = -t220+t221-t241-t165+t242+t167;
+ local_mass_matrix(11,12) = t283;
+ local_mass_matrix(11,13) = t282;
+ local_mass_matrix(11,14) = t285;
+ local_mass_matrix(11,15) = t286;
+ local_mass_matrix(12,0) = t69;
+ local_mass_matrix(12,1) = t107;
+ local_mass_matrix(12,2) = t143;
+ local_mass_matrix(12,3) = t158;
+ local_mass_matrix(12,4) = t186;
+ local_mass_matrix(12,5) = t191;
+ local_mass_matrix(12,6) = t229;
+ local_mass_matrix(12,7) = t240;
+ local_mass_matrix(12,8) = t261;
+ local_mass_matrix(12,9) = t264;
+ local_mass_matrix(12,10) = t278;
+ local_mass_matrix(12,11) = t283;
+ local_mass_matrix(12,12) = -t287+t288-t289-t290+t291+t292;
+ local_mass_matrix(12,13) = t298;
+ local_mass_matrix(12,14) = t301;
+ local_mass_matrix(12,15) = t304;
+ local_mass_matrix(13,0) = t74;
+ local_mass_matrix(13,1) = t110;
+ local_mass_matrix(13,2) = t146;
+ local_mass_matrix(13,3) = t159;
+ local_mass_matrix(13,4) = t191;
+ local_mass_matrix(13,5) = t208;
+ local_mass_matrix(13,6) = t234;
+ local_mass_matrix(13,7) = t237;
+ local_mass_matrix(13,8) = t264;
+ local_mass_matrix(13,9) = t272;
+ local_mass_matrix(13,10) = t279;
+ local_mass_matrix(13,11) = t282;
+ local_mass_matrix(13,12) = t298;
+ local_mass_matrix(13,13) = -t305+t306-t289-t290+t291+t292;
+ local_mass_matrix(13,14) = t310;
+ local_mass_matrix(13,15) = t301;
+ local_mass_matrix(14,0) = t79;
+ local_mass_matrix(14,1) = t113;
+ local_mass_matrix(14,2) = t149;
+ local_mass_matrix(14,3) = t160;
+ local_mass_matrix(14,4) = t194;
+ local_mass_matrix(14,5) = t211;
+ local_mass_matrix(14,6) = t237;
+ local_mass_matrix(14,7) = t249;
+ local_mass_matrix(14,8) = t267;
+ local_mass_matrix(14,9) = t273;
+ local_mass_matrix(14,10) = t282;
+ local_mass_matrix(14,11) = t285;
+ local_mass_matrix(14,12) = t301;
+ local_mass_matrix(14,13) = t310;
+ local_mass_matrix(14,14) = -t305+t306-t311-t290+t312+t292;
+ local_mass_matrix(14,15) = t316;
+ local_mass_matrix(15,0) = t80;
+ local_mass_matrix(15,1) = t116;
+ local_mass_matrix(15,2) = t152;
+ local_mass_matrix(15,3) = t161;
+ local_mass_matrix(15,4) = t199;
+ local_mass_matrix(15,5) = t194;
+ local_mass_matrix(15,6) = t240;
+ local_mass_matrix(15,7) = t252;
+ local_mass_matrix(15,8) = t270;
+ local_mass_matrix(15,9) = t267;
+ local_mass_matrix(15,10) = t283;
+ local_mass_matrix(15,11) = t286;
+ local_mass_matrix(15,12) = t304;
+ local_mass_matrix(15,13) = t301;
+ local_mass_matrix(15,14) = t316;
+ local_mass_matrix(15,15) = -t287+t288-t311-t290+t312+t292;
};
vector<Point<2> > &ansatz_points) const {
Assert (ansatz_points.size() == total_dofs,
ExcWrongFieldDimension (ansatz_points.size(), total_dofs));
-
- for (unsigned int vertex=0; vertex<4; ++vertex)
- ansatz_points[vertex] = cell->vertex(vertex);
-
- // for the bilinear mapping, the centers
- // of the face on the unit cell are mapped
- // to the mean coordinates of the vertices
- for (unsigned int line=0; line<4; ++line)
- ansatz_points[4+line] = (cell->line(line)->vertex(0) +
- cell->line(line)->vertex(1)) / 2;
- // same for the center of the square:
- // since all four linear basis functions
- // take on the value 1/4 at the center,
- // the center is mapped to the mean
- // coordinates of the four vertices
- ansatz_points[8] = (ansatz_points[0] +
- ansatz_points[1] +
- ansatz_points[2] +
- ansatz_points[3]) / 4;
+
+ const double x[4] = { cell->vertex(0)(0),
+ cell->vertex(1)(0),
+ cell->vertex(2)(0),
+ cell->vertex(3)(0) };
+ const double y[4] = { cell->vertex(0)(1),
+ cell->vertex(1)(1),
+ cell->vertex(2)(1),
+ cell->vertex(3)(1) };
+ const double t1 = 2.0/3.0*x[0];
+ const double t2 = x[1]/3.0;
+ const double t4 = 2.0/3.0*y[0];
+ const double t5 = y[1]/3.0;
+ const double t7 = x[0]/3.0;
+ const double t8 = 2.0/3.0*x[1];
+ const double t10 = y[0]/3.0;
+ const double t11 = 2.0/3.0*y[1];
+ const double t13 = x[2]/3.0;
+ const double t15 = y[2]/3.0;
+ const double t17 = 2.0/3.0*x[2];
+ const double t19 = 2.0/3.0*y[2];
+ const double t21 = 2.0/3.0*x[3];
+ const double t23 = 2.0/3.0*y[3];
+ const double t25 = x[3]/3.0;
+ const double t27 = y[3]/3.0;
+ const double t34 = 2.0/9.0*x[1];
+ const double t36 = 2.0/9.0*x[3];
+ const double t39 = 2.0/9.0*y[1];
+ const double t41 = 2.0/9.0*y[3];
+ const double t43 = 2.0/9.0*x[0];
+ const double t45 = 2.0/9.0*x[2];
+ const double t48 = 2.0/9.0*y[0];
+ const double t50 = 2.0/9.0*y[2];
+ ansatz_points[0](0) = x[0];
+ ansatz_points[0](1) = y[0];
+ ansatz_points[1](0) = x[1];
+ ansatz_points[1](1) = y[1];
+ ansatz_points[2](0) = x[2];
+ ansatz_points[2](1) = y[2];
+ ansatz_points[3](0) = x[3];
+ ansatz_points[3](1) = y[3];
+ ansatz_points[4](0) = t1+t2;
+ ansatz_points[4](1) = t4+t5;
+ ansatz_points[5](0) = t7+t8;
+ ansatz_points[5](1) = t10+t11;
+ ansatz_points[6](0) = t8+t13;
+ ansatz_points[6](1) = t11+t15;
+ ansatz_points[7](0) = t2+t17;
+ ansatz_points[7](1) = t5+t19;
+ ansatz_points[8](0) = t13+t21;
+ ansatz_points[8](1) = t15+t23;
+ ansatz_points[9](0) = t17+t25;
+ ansatz_points[9](1) = t19+t27;
+ ansatz_points[10](0) = t1+t25;
+ ansatz_points[10](1) = t4+t27;
+ ansatz_points[11](0) = t7+t21;
+ ansatz_points[11](1) = t10+t23;
+ ansatz_points[12](0) = 4.0/9.0*x[0]+t34+x[2]/9.0+t36;
+ ansatz_points[12](1) = 4.0/9.0*y[0]+t39+y[2]/9.0+t41;
+ ansatz_points[13](0) = t43+4.0/9.0*x[1]+t45+x[3]/9.0;
+ ansatz_points[13](1) = t48+4.0/9.0*y[1]+t50+y[3]/9.0;
+ ansatz_points[14](0) = x[0]/9.0+t34+4.0/9.0*x[2]+t36;
+ ansatz_points[14](1) = y[0]/9.0+t39+4.0/9.0*y[2]+t41;
+ ansatz_points[15](0) = t43+x[1]/9.0+t45+4.0/9.0*x[3];
+ ansatz_points[15](1) = t48+y[1]/9.0+t50+4.0/9.0*y[3];
};
for (unsigned int vertex=0; vertex<2; ++vertex)
ansatz_points[vertex] = face->vertex(vertex);
- ansatz_points[2] = (ansatz_points[0] + ansatz_points[1]) / 2;
+ ansatz_points[2] = (2*ansatz_points[0] + ansatz_points[1]) / 3;
+ ansatz_points[3] = (ansatz_points[0] + 2*ansatz_points[1]) / 3;
};
M_{ij}(l) = sum_s p_i(s) d(N_s(l))/d(xi_j)
where p_i(s) is the i-th coordinate of the s-th vertex vector,
N_s(l) is the value of the s-th vertex shape function at the
- quadrature point l.
+ quadrature point l (linear shape functions implied, as these
+ are used for the mapping).
We could therefore write:
l=0..n_points-1
--- /dev/null
+/* $Id$ */
+
+#include <fe/fe_lib.h>
+#include <grid/tria_iterator.h>
+#include <grid/dof_accessor.h>
+#include <grid/geometry_info.h>
+#include <algorithm>
+
+
+/*--------------------------------- For 1d ---------------------------------
+ -- Use the following maple script to generate the basis functions,
+ -- gradients and prolongation matrices as well as the mass matrix.
+ -- Make sure that the files do not exists beforehand, since output
+ -- is appended instead of overwriting previous contents.
+ --
+ -- You should only have to change the very first lines for polynomials
+ -- of higher order.
+ --------------------------------------------------------------------------
+ n_functions := 4;
+
+ ansatz_points := array(0..n_functions-1);
+ ansatz_points[0] := 0;
+ ansatz_points[1] := 1;
+ ansatz_points[2] := 1/3;
+ ansatz_points[3] := 2/3;
+
+ phi_polynom := array(0..n_functions-1);
+ grad_phi_polynom := array(0..n_functions-1);
+ local_mass_matrix := array(0..n_functions-1, 0..n_functions-1);
+
+ for i from 0 to n_functions-1 do
+ # note that the interp function wants vectors indexed from
+ # one and not from zero.
+ values := array(1..n_functions);
+ for j from 1 to n_functions do
+ values[j] := 0;
+ od;
+ values[i+1] := 1;
+
+ shifted_ansatz_points := array (1..n_functions);
+ for j from 1 to n_functions do
+ shifted_ansatz_points[j] := ansatz_points[j-1];
+ od;
+
+ phi_polynom[i] := interp (shifted_ansatz_points, values, xi);
+ grad_phi_polynom[i] := diff(phi_polynom[i], xi);
+ od;
+
+ phi:= proc(i,x) subs(xi=x, phi_polynom[i]); end;
+
+
+ points[0] := array(0..n_functions-1);
+ points[1] := array(0..n_functions-1);
+ for i from 0 to n_functions-1 do
+ points[0][i] := ansatz_points[i]/2;
+ points[1][i] := ansatz_points[i]/2+1/2;
+ od;
+
+ prolongation := array(0..1,0..n_functions-1, 0..n_functions-1);
+
+ for i from 0 to 1 do
+ for j from 0 to n_functions-1 do
+ for k from 0 to n_functions-1 do
+ prolongation[i,j,k] := phi(k, points[i][j]);
+ od;
+ od;
+ od;
+
+ for i from 0 to n_functions-1 do
+ for j from 0 to n_functions-1 do
+ local_mass_matrix[i,j] := int(phi_polynom[i] * phi_polynom[j] * h,
+ xi=0..1);
+ od;
+ od;
+
+ readlib(C);
+ C(phi_polynom, filename=shape_value_1d);
+ C(grad_phi_polynom, filename=shape_grad_1d);
+ C(prolongation, filename=prolongation_1d);
+ C(local_mass_matrix, optimized, filename=massmatrix_1d);
+
+ -----------------------------------------------------------------------
+ Use the following perl scripts to convert the output into a
+ suitable format:
+
+ perl -pi -e 's/phi_polynom\[(\d)\] =/case $1: return/g;' shape_value_1d
+ perl -pi -e 's/grad_phi_polynom\[(\d)\] = (.*);/case $1: return Point<1>($2);/g;' shape_grad_1d
+ perl -pi -e 's/\[(\d+)\]\[(\d)\]/($1,$2)/g;' massmatrix_1d
+ perl -pi -e 's/\[(\d+)\]\[(\d)\]\[(\d)\]/[$1]($2,$3)/g;' prolongation_1d
+ perl -pi -e 's/(t\d+) =/const double $1/g;' massmatrix_1d
+*/
+
+
+
+
+/*--------------------------------- For 2d ---------------------------------
+ -- Use the following maple script to generate the basis functions,
+ -- gradients and prolongation matrices as well as the mass matrix.
+ -- Make sure that the files do not exists beforehand, since output
+ -- is appended instead of overwriting previous contents.
+ --
+ -- You should only have to change the very first lines for polynomials
+ -- of higher order.
+ --------------------------------------------------------------------------
+ n_functions := 25:
+ n_face_functions := 5:
+
+ ansatz_function := (a1 + a2*xi + a3*xi*xi + a4*xi**3 + a5*xi**4) +
+ (b1 + b2*xi + b3*xi*xi + b4*xi**3 + b5*xi**4)*eta +
+ (c1 + c2*xi + c3*xi*xi + c4*xi**3 + c5*xi**4)*eta*eta +
+ (d1 + d2*xi + d3*xi*xi + d4*xi**3 + d5*xi**4)*eta**3 +
+ (e1 + e2*xi + e3*xi*xi + e4*xi**3 + e5*xi**4)*eta**4:
+ face_ansatz_function := a + b*xi + c*xi*xi + d*xi**3 + e*xi**4:
+ # note: ansatz_points[i] is a vector which is indexed from
+ # one and not from zero!
+ ansatz_points := array(0..n_functions-1):
+ ansatz_points[0] := [0,0]:
+ ansatz_points[1] := [1,0]:
+ ansatz_points[2] := [1,1]:
+ ansatz_points[3] := [0,1]:
+ ansatz_points[4] := [1/4,0]:
+ ansatz_points[5] := [2/4,0]:
+ ansatz_points[6] := [3/4,0]:
+ ansatz_points[7] := [1,1/4]:
+ ansatz_points[8] := [1,2/4]:
+ ansatz_points[9] := [1,3/4]:
+ ansatz_points[10] := [1/4,1]:
+ ansatz_points[11] := [2/4,1]:
+ ansatz_points[12] := [3/4,1]:
+ ansatz_points[13] := [0,1/4]:
+ ansatz_points[14] := [0,2/4]:
+ ansatz_points[15] := [0,3/4]:
+ ansatz_points[16] := [1/4,1/4]:
+ ansatz_points[17] := [3/4,1/4]:
+ ansatz_points[18] := [3/4,3/4]:
+ ansatz_points[19] := [1/4,3/4]:
+ ansatz_points[20] := [1/2,1/4]:
+ ansatz_points[21] := [3/4,1/2]:
+ ansatz_points[22] := [1/2,3/4]:
+ ansatz_points[23] := [1/4,1/2]:
+ ansatz_points[24] := [1/2,1/2]:
+
+ face_ansatz_points := array(0..n_face_functions-1):
+ face_ansatz_points[0] := 0:
+ face_ansatz_points[1] := 1:
+ face_ansatz_points[2] := 1/4:
+ face_ansatz_points[3] := 2/4:
+ face_ansatz_points[4] := 3/4:
+ constrained_face_ansatz_points := array(0..2*(n_face_functions-2)+1-1):
+ constrained_face_ansatz_points[0] := 1/2:
+ constrained_face_ansatz_points[1] := 1/8:
+ constrained_face_ansatz_points[2] := 2/8:
+ constrained_face_ansatz_points[3] := 3/8:
+ constrained_face_ansatz_points[4] := 5/8:
+ constrained_face_ansatz_points[5] := 6/8:
+ constrained_face_ansatz_points[6] := 7/8:
+
+ phi_polynom := array(0..n_functions-1):
+ grad_phi_polynom := array(0..n_functions-1,0..1):
+ local_mass_matrix := array(0..n_functions-1, 0..n_functions-1):
+ prolongation := array(0..3,0..n_functions-1, 0..n_functions-1):
+ interface_constraints := array(0..2*(n_face_functions-2)+1-1,
+ 0..n_face_functions-1):
+ real_points := array(0..n_functions-1, 0..1);
+
+ print ("Computing basis functions"):
+ for i from 0 to n_functions-1 do
+ print (i):
+ values := array(1..n_functions):
+ for j from 1 to n_functions do
+ values[j] := 0:
+ od:
+ values[i+1] := 1:
+
+ equation_system := {}:
+ for j from 0 to n_functions-1 do
+ poly := subs(xi=ansatz_points[j][1],
+ eta=ansatz_points[j][2],
+ ansatz_function):
+ if (i=j) then
+ equation_system := equation_system union {poly = 1}:
+ else
+ equation_system := equation_system union {poly = 0}:
+ fi:
+ od:
+
+ phi_polynom[i] := subs(solve(equation_system), ansatz_function):
+ grad_phi_polynom[i,0] := diff(phi_polynom[i], xi):
+ grad_phi_polynom[i,1] := diff(phi_polynom[i], eta):
+ od:
+
+ phi:= proc(i,x,y) subs(xi=x, eta=y, phi_polynom[i]): end:
+
+
+ #points on children: let them be indexed one-based, as are
+ #the ansatz_points
+ points[0] := array(0..n_functions-1, 1..2):
+ points[1] := array(0..n_functions-1, 1..2):
+ points[2] := array(0..n_functions-1, 1..2):
+ points[3] := array(0..n_functions-1, 1..2):
+ for i from 0 to n_functions-1 do
+ points[0][i,1] := ansatz_points[i][1]/2:
+ points[0][i,2] := ansatz_points[i][2]/2:
+
+ points[1][i,1] := ansatz_points[i][1]/2+1/2:
+ points[1][i,2] := ansatz_points[i][2]/2:
+
+ points[2][i,1] := ansatz_points[i][1]/2+1/2:
+ points[2][i,2] := ansatz_points[i][2]/2+1/2:
+
+ points[3][i,1] := ansatz_points[i][1]/2:
+ points[3][i,2] := ansatz_points[i][2]/2+1/2:
+ od:
+
+ print ("Computing prolongation matrices"):
+ for i from 0 to 3 do
+ print ("child", i):
+ for j from 0 to n_functions-1 do
+ for k from 0 to n_functions-1 do
+ prolongation[i,j,k] := phi(k, points[i][j,1], points[i][j,2]):
+ od:
+ od:
+ od:
+
+ print ("Computing local mass matrix"):
+ # tphi are the basis functions of the linear element. These functions
+ # are used for the computation of the subparametric transformation from
+ # unit cell to real cell.
+ # x and y are arrays holding the x- and y-values of the four vertices
+ # of this cell in real space.
+ x := array(0..3);
+ y := array(0..3);
+ tphi[0] := (1-xi)*(1-eta):
+ tphi[1] := xi*(1-eta):
+ tphi[2] := xi*eta:
+ tphi[3] := (1-xi)*eta:
+ x_real := sum(x[s]*tphi[s], s=0..3):
+ y_real := sum(y[s]*tphi[s], s=0..3):
+ detJ := diff(x_real,xi)*diff(y_real,eta) - diff(x_real,eta)*diff(y_real,xi):
+ for i from 0 to n_functions-1 do
+ print ("line", i):
+ for j from 0 to n_functions-1 do
+ local_mass_matrix[i,j] := int(int(phi_polynom[i] * phi_polynom[j] * detJ,
+ xi=0..1), eta=0..1):
+ od:
+ od:
+
+ print ("computing ansatz points in real space"):
+ for i from 0 to n_functions-1 do
+ real_points[i,0] := subs(xi=ansatz_points[i][1],
+ eta=ansatz_points[i][2], x_real);
+ real_points[i,1] := subs(xi=ansatz_points[i][1],
+ eta=ansatz_points[i][2], y_real);
+ od:
+
+ print ("computing interface constraint matrices"):
+ # compute the interface constraint matrices. these are the values of the
+ # basis functions on the coarse cell's face at the points of the child
+ # cell's basis functions on the child faces
+ face_phi_polynom := array(0..n_face_functions-1):
+ for i from 0 to n_face_functions-1 do
+ # note that the interp function wants vectors indexed from
+ # one and not from zero.
+ values := array(1..n_face_functions):
+ for j from 1 to n_face_functions do
+ values[j] := 0:
+ od:
+ values[i+1] := 1:
+
+ shifted_face_ansatz_points := array (1..n_face_functions):
+ for j from 1 to n_face_functions do
+ shifted_face_ansatz_points[j] := face_ansatz_points[j-1]:
+ od:
+
+ face_phi_polynom[i] := interp (shifted_face_ansatz_points, values, xi):
+ od:
+
+ for i from 0 to 2*(n_face_functions-2)+1-1 do
+ for j from 0 to n_face_functions-1 do
+ interface_constraints[i,j] := subs(xi=constrained_face_ansatz_points[i],
+ face_phi_polynom[j]);
+ od:
+ od:
+
+ print ("writing data to files"):
+ readlib(C):
+ C(phi_polynom, filename=shape_value_2d):
+ C(grad_phi_polynom, filename=shape_grad_2d):
+ C(prolongation, filename=prolongation_2d):
+ C(local_mass_matrix, optimized, filename=massmatrix_2d):
+ C(interface_constraints, filename=constraints_2d):
+ C(real_points, optimized, filename=real_points_2d);
+
+
+ -----------------------------------------------------------------------
+ Use the following perl scripts to convert the output into a
+ suitable format.
+
+ perl -pi -e 's/phi_polynom\[(\d+)\] =/case $1: return/g;' shape_value_2d
+ perl -pi -e 's/([^;])\n/$1/g;' shape_grad_2d
+ perl -pi -e 's/grad_phi_polynom\[(\d+)\]\[0\] = (.*);/case $1: return Point<2>($2,/g;' shape_grad_2d
+ perl -pi -e 's/grad_phi_polynom\[(\d+)\]\[1\] = (.*);/$2);/g;' shape_grad_2d
+ perl -pi -e 's/\[(\d+)\]\[(\d+)\]/($1,$2)/g;' massmatrix_2d
+ perl -pi -e 's/(t\d+) =/const double $1 =/g;' massmatrix_2d
+ perl -pi -e 's/\[(\d+)\]\[(\d+)\]\[(\d+)\]/[$1]($2,$3)/g;' prolongation_2d
+ perl -pi -e 's/.*= 0.0;\n//g;' prolongation_2d
+ perl -pi -e 's/\[(\d+)\]\[(\d+)\]/($1,$2)/g;' constraints_2d
+*/
+
+
+
+
+
+
+#if deal_II_dimension == 1
+
+template <>
+FEQuarticSub<1>::FEQuarticSub () :
+ FiniteElement<1> (1, 2) {
+ prolongation[0](0,0) = 1.0;
+ prolongation[0](0,1) = 0.0;
+ prolongation[0](0,2) = 0.0;
+ prolongation[0](0,3) = 0.0;
+ prolongation[0](1,0) = -1.0/16.0;
+ prolongation[0](1,1) = -1.0/16.0;
+ prolongation[0](1,2) = 9.0/16.0;
+ prolongation[0](1,3) = 9.0/16.0;
+ prolongation[0](2,0) = 5.0/16.0;
+ prolongation[0](2,1) = 1.0/16.0;
+ prolongation[0](2,2) = 15.0/16.0;
+ prolongation[0](2,3) = -5.0/16.0;
+ prolongation[0](3,0) = 0.0;
+ prolongation[0](3,1) = 0.0;
+ prolongation[0](3,2) = 1.0;
+ prolongation[0](3,3) = 0.0;
+ prolongation[1](0,0) = -1.0/16.0;
+ prolongation[1](0,1) = -1.0/16.0;
+ prolongation[1](0,2) = 9.0/16.0;
+ prolongation[1](0,3) = 9.0/16.0;
+ prolongation[1](1,0) = 0.0;
+ prolongation[1](1,1) = 1.0;
+ prolongation[1](1,2) = 0.0;
+ prolongation[1](1,3) = 0.0;
+ prolongation[1](2,0) = 0.0;
+ prolongation[1](2,1) = 0.0;
+ prolongation[1](2,2) = 0.0;
+ prolongation[1](2,3) = 1.0;
+ prolongation[1](3,0) = 1.0/16.0;
+ prolongation[1](3,1) = 5.0/16.0;
+ prolongation[1](3,2) = -5.0/16.0;
+ prolongation[1](3,3) = 15.0/16.0;
+};
+
+
+
+template <>
+void FEQuarticSub<1>::fill_fe_values (const DoFHandler<1>::cell_iterator &cell,
+ const vector<Point<1> > &unit_points,
+ vector<dFMatrix> &jacobians,
+ const bool compute_jacobians,
+ vector<Point<1> > &ansatz_points,
+ const bool compute_ansatz_points,
+ vector<Point<1> > &q_points,
+ const bool compute_q_points,
+ const Boundary<1> &boundary) const {
+ // simply pass down
+ FiniteElement<1>::fill_fe_values (cell, unit_points,
+ jacobians, compute_jacobians,
+ ansatz_points, compute_ansatz_points,
+ q_points, compute_q_points, boundary);
+};
+
+
+
+template <>
+double
+FEQuarticSub<1>::shape_value(const unsigned int i,
+ const Point<1> &p) const
+{
+ Assert((i<total_dofs), ExcInvalidIndex(i));
+ const double xi = p(0);
+ switch (i)
+ {
+ case 0: return -9.0/2.0*xi*xi*xi+9.0*xi*xi-11.0/2.0*xi+1.0;
+ case 1: return 9.0/2.0*xi*xi*xi-9.0/2.0*xi*xi+xi;
+ case 2: return 27.0/2.0*xi*xi*xi-45.0/2.0*xi*xi+9.0*xi;
+ case 3: return -27.0/2.0*xi*xi*xi+18.0*xi*xi-9.0/2.0*xi;
+ }
+ return 0.;
+};
+
+
+
+template <>
+inline
+double
+FEQuarticSub<1>::linear_shape_value(const unsigned int i,
+ const Point<1> &p) const
+{
+ Assert((i<2), ExcInvalidIndex(i));
+ const double xi = p(0);
+ switch (i)
+ {
+ case 0: return 1.-xi;
+ case 1: return xi;
+ }
+ return 0.;
+};
+
+
+
+template <>
+Point<1>
+FEQuarticSub<1>::shape_grad(const unsigned int i,
+ const Point<1> &p) const
+{
+ Assert((i<total_dofs), ExcInvalidIndex(i));
+ const double xi = p(0);
+ switch (i)
+ {
+ case 0: return Point<1>(-27.0/2.0*xi*xi+18.0*xi-11.0/2.0);
+ case 1: return Point<1>(27.0/2.0*xi*xi-9.0*xi+1.0);
+ case 2: return Point<1>(81.0/2.0*xi*xi-45.0*xi+9.0);
+ case 3: return Point<1>(-81.0/2.0*xi*xi+36.0*xi-9.0/2.0);
+ }
+ return Point<1>();
+};
+
+
+
+template <>
+inline
+Point<1>
+FEQuarticSub<1>::linear_shape_grad(const unsigned int i,
+ const Point<1>&) const
+{
+ Assert((i<2), ExcInvalidIndex(i));
+ switch (i)
+ {
+ case 0: return Point<1>(-1.);
+ case 1: return Point<1>(1.);
+ }
+ return Point<1>();
+};
+
+
+
+template <>
+void FEQuarticSub<1>::get_ansatz_points (const typename DoFHandler<1>::cell_iterator &cell,
+ const Boundary<1> &boundary,
+ vector<Point<1> > &ansatz_points) const {
+ FiniteElement<1>::get_ansatz_points (cell, boundary, ansatz_points);
+};
+
+
+
+template <>
+void FEQuarticSub<1>::get_face_ansatz_points (const typename DoFHandler<1>::face_iterator &,
+ const Boundary<1> &,
+ vector<Point<1> > &) const {
+ Assert (false, ExcInternalError());
+};
+
+
+
+template <>
+void FEQuarticSub<1>::get_face_jacobians (const DoFHandler<1>::face_iterator &,
+ const Boundary<1> &,
+ const vector<Point<0> > &,
+ vector<double> &) const {
+ Assert (false, ExcInternalError());
+};
+
+
+
+template <>
+void FEQuarticSub<1>::get_subface_jacobians (const DoFHandler<1>::face_iterator &,
+ const unsigned int ,
+ const vector<Point<0> > &,
+ vector<double> &) const {
+ Assert (false, ExcInternalError());
+};
+
+
+
+template <>
+void FEQuarticSub<1>::get_normal_vectors (const DoFHandler<1>::cell_iterator &,
+ const unsigned int,
+ const Boundary<1> &,
+ const vector<Point<0> > &,
+ vector<Point<1> > &) const {
+ Assert (false, ExcInternalError());
+};
+
+
+
+template <>
+void FEQuarticSub<1>::get_normal_vectors (const DoFHandler<1>::cell_iterator &,
+ const unsigned int,
+ const unsigned int,
+ const vector<Point<0> > &,
+ vector<Point<1> > &) const {
+ Assert (false, ExcInternalError());
+};
+
+
+
+template <>
+void FEQuarticSub<1>::get_local_mass_matrix (const DoFHandler<1>::cell_iterator &cell,
+ const Boundary<1> &,
+ dFMatrix &local_mass_matrix) const {
+ Assert (local_mass_matrix.n() == total_dofs,
+ ExcWrongFieldDimension(local_mass_matrix.n(),total_dofs));
+ Assert (local_mass_matrix.m() == total_dofs,
+ ExcWrongFieldDimension(local_mass_matrix.m(),total_dofs));
+
+ const double h = cell->vertex(1)(0) - cell->vertex(0)(0);
+ Assert (h>0, ExcJacobiDeterminantHasWrongSign());
+
+ const double t1 8.0/105.0*h;
+ const double t2 19.0/1680.0*h;
+ const double t3 33.0/560.0*h;
+ const double t4 3.0/140.0*h;
+ const double t5 27.0/70.0*h;
+ const double t6 27.0/560.0*h;
+ local_mass_matrix(0,0) = t1;
+ local_mass_matrix(0,1) = t2;
+ local_mass_matrix(0,2) = t3;
+ local_mass_matrix(0,3) = -t4;
+ local_mass_matrix(1,0) = t2;
+ local_mass_matrix(1,1) = t1;
+ local_mass_matrix(1,2) = -t4;
+ local_mass_matrix(1,3) = t3;
+ local_mass_matrix(2,0) = t3;
+ local_mass_matrix(2,1) = -t4;
+ local_mass_matrix(2,2) = t5;
+ local_mass_matrix(2,3) = -t6;
+ local_mass_matrix(3,0) = -t4;
+ local_mass_matrix(3,1) = t3;
+ local_mass_matrix(3,2) = -t6;
+ local_mass_matrix(3,3) = t5;
+};
+
+#endif
+
+
+
+
+#if deal_II_dimension == 2
+
+template <>
+FEQuarticSub<2>::FEQuarticSub () :
+ FiniteElement<2> (1, 1, 1)
+{
+ interface_constraints(0,3) = 1.0;
+ interface_constraints(1,0) = 35.0/128.0;
+ interface_constraints(1,1) = -5.0/128.0;
+ interface_constraints(1,2) = 35.0/32.0;
+ interface_constraints(1,3) = -35.0/64.0;
+ interface_constraints(1,4) = 7.0/32.0;
+ interface_constraints(2,2) = 1.0;
+ interface_constraints(3,0) = -5.0/128.0;
+ interface_constraints(3,1) = 3.0/128.0;
+ interface_constraints(3,2) = 15.0/32.0;
+ interface_constraints(3,3) = 45.0/64.0;
+ interface_constraints(3,4) = -5.0/32.0;
+ interface_constraints(4,0) = 3.0/128.0;
+ interface_constraints(4,1) = -5.0/128.0;
+ interface_constraints(4,2) = -5.0/32.0;
+ interface_constraints(4,3) = 45.0/64.0;
+ interface_constraints(4,4) = 15.0/32.0;
+ interface_constraints(5,4) = 1.0;
+ interface_constraints(6,0) = -5.0/128.0;
+ interface_constraints(6,1) = 35.0/128.0;
+ interface_constraints(6,2) = 7.0/32.0;
+ interface_constraints(6,3) = -35.0/64.0;
+ interface_constraints(6,4) = 35.0/32.0;
+
+ prolongation[0](0,0) = 1.0;
+ prolongation[0](1,5) = 1.0;
+ prolongation[0](2,24) = 1.0;
+ prolongation[0](3,14) = 1.0;
+ prolongation[0](4,0) = 35.0/128.0;
+ prolongation[0](4,1) = -5.0/128.0;
+ prolongation[0](4,4) = 35.0/32.0;
+ prolongation[0](4,5) = -35.0/64.0;
+ prolongation[0](4,6) = 7.0/32.0;
+ prolongation[0](5,4) = 1.0;
+ prolongation[0](6,0) = -5.0/128.0;
+ prolongation[0](6,1) = 3.0/128.0;
+ prolongation[0](6,4) = 15.0/32.0;
+ prolongation[0](6,5) = 45.0/64.0;
+ prolongation[0](6,6) = -5.0/32.0;
+ prolongation[0](7,5) = 35.0/128.0;
+ prolongation[0](7,11) = -5.0/128.0;
+ prolongation[0](7,20) = 35.0/32.0;
+ prolongation[0](7,22) = 7.0/32.0;
+ prolongation[0](7,24) = -35.0/64.0;
+ prolongation[0](8,20) = 1.0;
+ prolongation[0](9,5) = -5.0/128.0;
+ prolongation[0](9,11) = 3.0/128.0;
+ prolongation[0](9,20) = 15.0/32.0;
+ prolongation[0](9,22) = -5.0/32.0;
+ prolongation[0](9,24) = 45.0/64.0;
+ prolongation[0](10,8) = -5.0/128.0;
+ prolongation[0](10,14) = 35.0/128.0;
+ prolongation[0](10,21) = 7.0/32.0;
+ prolongation[0](10,23) = 35.0/32.0;
+ prolongation[0](10,24) = -35.0/64.0;
+ prolongation[0](11,23) = 1.0;
+ prolongation[0](12,8) = 3.0/128.0;
+ prolongation[0](12,14) = -5.0/128.0;
+ prolongation[0](12,21) = -5.0/32.0;
+ prolongation[0](12,23) = 15.0/32.0;
+ prolongation[0](12,24) = 45.0/64.0;
+ prolongation[0](13,0) = 35.0/128.0;
+ prolongation[0](13,3) = -5.0/128.0;
+ prolongation[0](13,13) = 35.0/32.0;
+ prolongation[0](13,14) = -35.0/64.0;
+ prolongation[0](13,15) = 7.0/32.0;
+ prolongation[0](14,13) = 1.0;
+ prolongation[0](15,0) = -5.0/128.0;
+ prolongation[0](15,3) = 3.0/128.0;
+ prolongation[0](15,13) = 15.0/32.0;
+ prolongation[0](15,14) = 45.0/64.0;
+ prolongation[0](15,15) = -5.0/32.0;
+ prolongation[0](16,0) = 1225.0/16384.0;
+ prolongation[0](16,1) = -175.0/16384.0;
+ prolongation[0](16,2) = 25.0/16384.0;
+ prolongation[0](16,3) = -175.0/16384.0;
+ prolongation[0](16,4) = 1225.0/4096.0;
+ prolongation[0](16,5) = -1225.0/8192.0;
+ prolongation[0](16,6) = 245.0/4096.0;
+ prolongation[0](16,7) = -175.0/4096.0;
+ prolongation[0](16,8) = 175.0/8192.0;
+ prolongation[0](16,9) = -35.0/4096.0;
+ prolongation[0](16,10) = -175.0/4096.0;
+ prolongation[0](16,11) = 175.0/8192.0;
+ prolongation[0](16,12) = -35.0/4096.0;
+ prolongation[0](16,13) = 1225.0/4096.0;
+ prolongation[0](16,14) = -1225.0/8192.0;
+ prolongation[0](16,15) = 245.0/4096.0;
+ prolongation[0](16,16) = 1225.0/1024.0;
+ prolongation[0](16,17) = 245.0/1024.0;
+ prolongation[0](16,18) = 49.0/1024.0;
+ prolongation[0](16,19) = 245.0/1024.0;
+ prolongation[0](16,20) = -1225.0/2048.0;
+ prolongation[0](16,21) = -245.0/2048.0;
+ prolongation[0](16,22) = -245.0/2048.0;
+ prolongation[0](16,23) = -1225.0/2048.0;
+ prolongation[0](16,24) = 1225.0/4096.0;
+ prolongation[0](17,0) = -175.0/16384.0;
+ prolongation[0](17,1) = 105.0/16384.0;
+ prolongation[0](17,2) = -15.0/16384.0;
+ prolongation[0](17,3) = 25.0/16384.0;
+ prolongation[0](17,4) = 525.0/4096.0;
+ prolongation[0](17,5) = 1575.0/8192.0;
+ prolongation[0](17,6) = -175.0/4096.0;
+ prolongation[0](17,7) = 105.0/4096.0;
+ prolongation[0](17,8) = -105.0/8192.0;
+ prolongation[0](17,9) = 21.0/4096.0;
+ prolongation[0](17,10) = -75.0/4096.0;
+ prolongation[0](17,11) = -225.0/8192.0;
+ prolongation[0](17,12) = 25.0/4096.0;
+ prolongation[0](17,13) = -175.0/4096.0;
+ prolongation[0](17,14) = 175.0/8192.0;
+ prolongation[0](17,15) = -35.0/4096.0;
+ prolongation[0](17,16) = 525.0/1024.0;
+ prolongation[0](17,17) = -175.0/1024.0;
+ prolongation[0](17,18) = -35.0/1024.0;
+ prolongation[0](17,19) = 105.0/1024.0;
+ prolongation[0](17,20) = 1575.0/2048.0;
+ prolongation[0](17,21) = 175.0/2048.0;
+ prolongation[0](17,22) = 315.0/2048.0;
+ prolongation[0](17,23) = -525.0/2048.0;
+ prolongation[0](17,24) = -1575.0/4096.0;
+ prolongation[0](18,0) = 25.0/16384.0;
+ prolongation[0](18,1) = -15.0/16384.0;
+ prolongation[0](18,2) = 9.0/16384.0;
+ prolongation[0](18,3) = -15.0/16384.0;
+ prolongation[0](18,4) = -75.0/4096.0;
+ prolongation[0](18,5) = -225.0/8192.0;
+ prolongation[0](18,6) = 25.0/4096.0;
+ prolongation[0](18,7) = 45.0/4096.0;
+ prolongation[0](18,8) = 135.0/8192.0;
+ prolongation[0](18,9) = -15.0/4096.0;
+ prolongation[0](18,10) = 45.0/4096.0;
+ prolongation[0](18,11) = 135.0/8192.0;
+ prolongation[0](18,12) = -15.0/4096.0;
+ prolongation[0](18,13) = -75.0/4096.0;
+ prolongation[0](18,14) = -225.0/8192.0;
+ prolongation[0](18,15) = 25.0/4096.0;
+ prolongation[0](18,16) = 225.0/1024.0;
+ prolongation[0](18,17) = -75.0/1024.0;
+ prolongation[0](18,18) = 25.0/1024.0;
+ prolongation[0](18,19) = -75.0/1024.0;
+ prolongation[0](18,20) = 675.0/2048.0;
+ prolongation[0](18,21) = -225.0/2048.0;
+ prolongation[0](18,22) = -225.0/2048.0;
+ prolongation[0](18,23) = 675.0/2048.0;
+ prolongation[0](18,24) = 2025.0/4096.0;
+ prolongation[0](19,0) = -175.0/16384.0;
+ prolongation[0](19,1) = 25.0/16384.0;
+ prolongation[0](19,2) = -15.0/16384.0;
+ prolongation[0](19,3) = 105.0/16384.0;
+ prolongation[0](19,4) = -175.0/4096.0;
+ prolongation[0](19,5) = 175.0/8192.0;
+ prolongation[0](19,6) = -35.0/4096.0;
+ prolongation[0](19,7) = -75.0/4096.0;
+ prolongation[0](19,8) = -225.0/8192.0;
+ prolongation[0](19,9) = 25.0/4096.0;
+ prolongation[0](19,10) = 105.0/4096.0;
+ prolongation[0](19,11) = -105.0/8192.0;
+ prolongation[0](19,12) = 21.0/4096.0;
+ prolongation[0](19,13) = 525.0/4096.0;
+ prolongation[0](19,14) = 1575.0/8192.0;
+ prolongation[0](19,15) = -175.0/4096.0;
+ prolongation[0](19,16) = 525.0/1024.0;
+ prolongation[0](19,17) = 105.0/1024.0;
+ prolongation[0](19,18) = -35.0/1024.0;
+ prolongation[0](19,19) = -175.0/1024.0;
+ prolongation[0](19,20) = -525.0/2048.0;
+ prolongation[0](19,21) = 315.0/2048.0;
+ prolongation[0](19,22) = 175.0/2048.0;
+ prolongation[0](19,23) = 1575.0/2048.0;
+ prolongation[0](19,24) = -1575.0/4096.0;
+ prolongation[0](20,4) = 35.0/128.0;
+ prolongation[0](20,10) = -5.0/128.0;
+ prolongation[0](20,16) = 35.0/32.0;
+ prolongation[0](20,19) = 7.0/32.0;
+ prolongation[0](20,23) = -35.0/64.0;
+ prolongation[0](21,7) = 3.0/128.0;
+ prolongation[0](21,13) = -5.0/128.0;
+ prolongation[0](21,16) = 15.0/32.0;
+ prolongation[0](21,17) = -5.0/32.0;
+ prolongation[0](21,20) = 45.0/64.0;
+ prolongation[0](22,4) = -5.0/128.0;
+ prolongation[0](22,10) = 3.0/128.0;
+ prolongation[0](22,16) = 15.0/32.0;
+ prolongation[0](22,19) = -5.0/32.0;
+ prolongation[0](22,23) = 45.0/64.0;
+ prolongation[0](23,7) = -5.0/128.0;
+ prolongation[0](23,13) = 35.0/128.0;
+ prolongation[0](23,16) = 35.0/32.0;
+ prolongation[0](23,17) = 7.0/32.0;
+ prolongation[0](23,20) = -35.0/64.0;
+ prolongation[0](24,16) = 1.0;
+ prolongation[1](0,5) = 1.0;
+ prolongation[1](1,1) = 1.0;
+ prolongation[1](2,8) = 1.0;
+ prolongation[1](3,24) = 1.0;
+ prolongation[1](4,0) = 3.0/128.0;
+ prolongation[1](4,1) = -5.0/128.0;
+ prolongation[1](4,4) = -5.0/32.0;
+ prolongation[1](4,5) = 45.0/64.0;
+ prolongation[1](4,6) = 15.0/32.0;
+ prolongation[1](5,6) = 1.0;
+ prolongation[1](6,0) = -5.0/128.0;
+ prolongation[1](6,1) = 35.0/128.0;
+ prolongation[1](6,4) = 7.0/32.0;
+ prolongation[1](6,5) = -35.0/64.0;
+ prolongation[1](6,6) = 35.0/32.0;
+ prolongation[1](7,1) = 35.0/128.0;
+ prolongation[1](7,2) = -5.0/128.0;
+ prolongation[1](7,7) = 35.0/32.0;
+ prolongation[1](7,8) = -35.0/64.0;
+ prolongation[1](7,9) = 7.0/32.0;
+ prolongation[1](8,7) = 1.0;
+ prolongation[1](9,1) = -5.0/128.0;
+ prolongation[1](9,2) = 3.0/128.0;
+ prolongation[1](9,7) = 15.0/32.0;
+ prolongation[1](9,8) = 45.0/64.0;
+ prolongation[1](9,9) = -5.0/32.0;
+ prolongation[1](10,8) = -5.0/128.0;
+ prolongation[1](10,14) = 3.0/128.0;
+ prolongation[1](10,21) = 15.0/32.0;
+ prolongation[1](10,23) = -5.0/32.0;
+ prolongation[1](10,24) = 45.0/64.0;
+ prolongation[1](11,21) = 1.0;
+ prolongation[1](12,8) = 35.0/128.0;
+ prolongation[1](12,14) = -5.0/128.0;
+ prolongation[1](12,21) = 35.0/32.0;
+ prolongation[1](12,23) = 7.0/32.0;
+ prolongation[1](12,24) = -35.0/64.0;
+ prolongation[1](13,5) = 35.0/128.0;
+ prolongation[1](13,11) = -5.0/128.0;
+ prolongation[1](13,20) = 35.0/32.0;
+ prolongation[1](13,22) = 7.0/32.0;
+ prolongation[1](13,24) = -35.0/64.0;
+ prolongation[1](14,20) = 1.0;
+ prolongation[1](15,5) = -5.0/128.0;
+ prolongation[1](15,11) = 3.0/128.0;
+ prolongation[1](15,20) = 15.0/32.0;
+ prolongation[1](15,22) = -5.0/32.0;
+ prolongation[1](15,24) = 45.0/64.0;
+ prolongation[1](16,0) = 105.0/16384.0;
+ prolongation[1](16,1) = -175.0/16384.0;
+ prolongation[1](16,2) = 25.0/16384.0;
+ prolongation[1](16,3) = -15.0/16384.0;
+ prolongation[1](16,4) = -175.0/4096.0;
+ prolongation[1](16,5) = 1575.0/8192.0;
+ prolongation[1](16,6) = 525.0/4096.0;
+ prolongation[1](16,7) = -175.0/4096.0;
+ prolongation[1](16,8) = 175.0/8192.0;
+ prolongation[1](16,9) = -35.0/4096.0;
+ prolongation[1](16,10) = 25.0/4096.0;
+ prolongation[1](16,11) = -225.0/8192.0;
+ prolongation[1](16,12) = -75.0/4096.0;
+ prolongation[1](16,13) = 105.0/4096.0;
+ prolongation[1](16,14) = -105.0/8192.0;
+ prolongation[1](16,15) = 21.0/4096.0;
+ prolongation[1](16,16) = -175.0/1024.0;
+ prolongation[1](16,17) = 525.0/1024.0;
+ prolongation[1](16,18) = 105.0/1024.0;
+ prolongation[1](16,19) = -35.0/1024.0;
+ prolongation[1](16,20) = 1575.0/2048.0;
+ prolongation[1](16,21) = -525.0/2048.0;
+ prolongation[1](16,22) = 315.0/2048.0;
+ prolongation[1](16,23) = 175.0/2048.0;
+ prolongation[1](16,24) = -1575.0/4096.0;
+ prolongation[1](17,0) = -175.0/16384.0;
+ prolongation[1](17,1) = 1225.0/16384.0;
+ prolongation[1](17,2) = -175.0/16384.0;
+ prolongation[1](17,3) = 25.0/16384.0;
+ prolongation[1](17,4) = 245.0/4096.0;
+ prolongation[1](17,5) = -1225.0/8192.0;
+ prolongation[1](17,6) = 1225.0/4096.0;
+ prolongation[1](17,7) = 1225.0/4096.0;
+ prolongation[1](17,8) = -1225.0/8192.0;
+ prolongation[1](17,9) = 245.0/4096.0;
+ prolongation[1](17,10) = -35.0/4096.0;
+ prolongation[1](17,11) = 175.0/8192.0;
+ prolongation[1](17,12) = -175.0/4096.0;
+ prolongation[1](17,13) = -175.0/4096.0;
+ prolongation[1](17,14) = 175.0/8192.0;
+ prolongation[1](17,15) = -35.0/4096.0;
+ prolongation[1](17,16) = 245.0/1024.0;
+ prolongation[1](17,17) = 1225.0/1024.0;
+ prolongation[1](17,18) = 245.0/1024.0;
+ prolongation[1](17,19) = 49.0/1024.0;
+ prolongation[1](17,20) = -1225.0/2048.0;
+ prolongation[1](17,21) = -1225.0/2048.0;
+ prolongation[1](17,22) = -245.0/2048.0;
+ prolongation[1](17,23) = -245.0/2048.0;
+ prolongation[1](17,24) = 1225.0/4096.0;
+ prolongation[1](18,0) = 25.0/16384.0;
+ prolongation[1](18,1) = -175.0/16384.0;
+ prolongation[1](18,2) = 105.0/16384.0;
+ prolongation[1](18,3) = -15.0/16384.0;
+ prolongation[1](18,4) = -35.0/4096.0;
+ prolongation[1](18,5) = 175.0/8192.0;
+ prolongation[1](18,6) = -175.0/4096.0;
+ prolongation[1](18,7) = 525.0/4096.0;
+ prolongation[1](18,8) = 1575.0/8192.0;
+ prolongation[1](18,9) = -175.0/4096.0;
+ prolongation[1](18,10) = 21.0/4096.0;
+ prolongation[1](18,11) = -105.0/8192.0;
+ prolongation[1](18,12) = 105.0/4096.0;
+ prolongation[1](18,13) = -75.0/4096.0;
+ prolongation[1](18,14) = -225.0/8192.0;
+ prolongation[1](18,15) = 25.0/4096.0;
+ prolongation[1](18,16) = 105.0/1024.0;
+ prolongation[1](18,17) = 525.0/1024.0;
+ prolongation[1](18,18) = -175.0/1024.0;
+ prolongation[1](18,19) = -35.0/1024.0;
+ prolongation[1](18,20) = -525.0/2048.0;
+ prolongation[1](18,21) = 1575.0/2048.0;
+ prolongation[1](18,22) = 175.0/2048.0;
+ prolongation[1](18,23) = 315.0/2048.0;
+ prolongation[1](18,24) = -1575.0/4096.0;
+ prolongation[1](19,0) = -15.0/16384.0;
+ prolongation[1](19,1) = 25.0/16384.0;
+ prolongation[1](19,2) = -15.0/16384.0;
+ prolongation[1](19,3) = 9.0/16384.0;
+ prolongation[1](19,4) = 25.0/4096.0;
+ prolongation[1](19,5) = -225.0/8192.0;
+ prolongation[1](19,6) = -75.0/4096.0;
+ prolongation[1](19,7) = -75.0/4096.0;
+ prolongation[1](19,8) = -225.0/8192.0;
+ prolongation[1](19,9) = 25.0/4096.0;
+ prolongation[1](19,10) = -15.0/4096.0;
+ prolongation[1](19,11) = 135.0/8192.0;
+ prolongation[1](19,12) = 45.0/4096.0;
+ prolongation[1](19,13) = 45.0/4096.0;
+ prolongation[1](19,14) = 135.0/8192.0;
+ prolongation[1](19,15) = -15.0/4096.0;
+ prolongation[1](19,16) = -75.0/1024.0;
+ prolongation[1](19,17) = 225.0/1024.0;
+ prolongation[1](19,18) = -75.0/1024.0;
+ prolongation[1](19,19) = 25.0/1024.0;
+ prolongation[1](19,20) = 675.0/2048.0;
+ prolongation[1](19,21) = 675.0/2048.0;
+ prolongation[1](19,22) = -225.0/2048.0;
+ prolongation[1](19,23) = -225.0/2048.0;
+ prolongation[1](19,24) = 2025.0/4096.0;
+ prolongation[1](20,6) = 35.0/128.0;
+ prolongation[1](20,12) = -5.0/128.0;
+ prolongation[1](20,17) = 35.0/32.0;
+ prolongation[1](20,18) = 7.0/32.0;
+ prolongation[1](20,21) = -35.0/64.0;
+ prolongation[1](21,7) = 35.0/128.0;
+ prolongation[1](21,13) = -5.0/128.0;
+ prolongation[1](21,16) = 7.0/32.0;
+ prolongation[1](21,17) = 35.0/32.0;
+ prolongation[1](21,20) = -35.0/64.0;
+ prolongation[1](22,6) = -5.0/128.0;
+ prolongation[1](22,12) = 3.0/128.0;
+ prolongation[1](22,17) = 15.0/32.0;
+ prolongation[1](22,18) = -5.0/32.0;
+ prolongation[1](22,21) = 45.0/64.0;
+ prolongation[1](23,7) = -5.0/128.0;
+ prolongation[1](23,13) = 3.0/128.0;
+ prolongation[1](23,16) = -5.0/32.0;
+ prolongation[1](23,17) = 15.0/32.0;
+ prolongation[1](23,20) = 45.0/64.0;
+ prolongation[1](24,17) = 1.0;
+ prolongation[2](0,24) = 1.0;
+ prolongation[2](1,8) = 1.0;
+ prolongation[2](2,2) = 1.0;
+ prolongation[2](3,11) = 1.0;
+ prolongation[2](4,8) = -5.0/128.0;
+ prolongation[2](4,14) = 3.0/128.0;
+ prolongation[2](4,21) = 15.0/32.0;
+ prolongation[2](4,23) = -5.0/32.0;
+ prolongation[2](4,24) = 45.0/64.0;
+ prolongation[2](5,21) = 1.0;
+ prolongation[2](6,8) = 35.0/128.0;
+ prolongation[2](6,14) = -5.0/128.0;
+ prolongation[2](6,21) = 35.0/32.0;
+ prolongation[2](6,23) = 7.0/32.0;
+ prolongation[2](6,24) = -35.0/64.0;
+ prolongation[2](7,1) = 3.0/128.0;
+ prolongation[2](7,2) = -5.0/128.0;
+ prolongation[2](7,7) = -5.0/32.0;
+ prolongation[2](7,8) = 45.0/64.0;
+ prolongation[2](7,9) = 15.0/32.0;
+ prolongation[2](8,9) = 1.0;
+ prolongation[2](9,1) = -5.0/128.0;
+ prolongation[2](9,2) = 35.0/128.0;
+ prolongation[2](9,7) = 7.0/32.0;
+ prolongation[2](9,8) = -35.0/64.0;
+ prolongation[2](9,9) = 35.0/32.0;
+ prolongation[2](10,2) = -5.0/128.0;
+ prolongation[2](10,3) = 3.0/128.0;
+ prolongation[2](10,10) = -5.0/32.0;
+ prolongation[2](10,11) = 45.0/64.0;
+ prolongation[2](10,12) = 15.0/32.0;
+ prolongation[2](11,12) = 1.0;
+ prolongation[2](12,2) = 35.0/128.0;
+ prolongation[2](12,3) = -5.0/128.0;
+ prolongation[2](12,10) = 7.0/32.0;
+ prolongation[2](12,11) = -35.0/64.0;
+ prolongation[2](12,12) = 35.0/32.0;
+ prolongation[2](13,5) = 3.0/128.0;
+ prolongation[2](13,11) = -5.0/128.0;
+ prolongation[2](13,20) = -5.0/32.0;
+ prolongation[2](13,22) = 15.0/32.0;
+ prolongation[2](13,24) = 45.0/64.0;
+ prolongation[2](14,22) = 1.0;
+ prolongation[2](15,5) = -5.0/128.0;
+ prolongation[2](15,11) = 35.0/128.0;
+ prolongation[2](15,20) = 7.0/32.0;
+ prolongation[2](15,22) = 35.0/32.0;
+ prolongation[2](15,24) = -35.0/64.0;
+ prolongation[2](16,0) = 9.0/16384.0;
+ prolongation[2](16,1) = -15.0/16384.0;
+ prolongation[2](16,2) = 25.0/16384.0;
+ prolongation[2](16,3) = -15.0/16384.0;
+ prolongation[2](16,4) = -15.0/4096.0;
+ prolongation[2](16,5) = 135.0/8192.0;
+ prolongation[2](16,6) = 45.0/4096.0;
+ prolongation[2](16,7) = 25.0/4096.0;
+ prolongation[2](16,8) = -225.0/8192.0;
+ prolongation[2](16,9) = -75.0/4096.0;
+ prolongation[2](16,10) = 25.0/4096.0;
+ prolongation[2](16,11) = -225.0/8192.0;
+ prolongation[2](16,12) = -75.0/4096.0;
+ prolongation[2](16,13) = -15.0/4096.0;
+ prolongation[2](16,14) = 135.0/8192.0;
+ prolongation[2](16,15) = 45.0/4096.0;
+ prolongation[2](16,16) = 25.0/1024.0;
+ prolongation[2](16,17) = -75.0/1024.0;
+ prolongation[2](16,18) = 225.0/1024.0;
+ prolongation[2](16,19) = -75.0/1024.0;
+ prolongation[2](16,20) = -225.0/2048.0;
+ prolongation[2](16,21) = 675.0/2048.0;
+ prolongation[2](16,22) = 675.0/2048.0;
+ prolongation[2](16,23) = -225.0/2048.0;
+ prolongation[2](16,24) = 2025.0/4096.0;
+ prolongation[2](17,0) = -15.0/16384.0;
+ prolongation[2](17,1) = 105.0/16384.0;
+ prolongation[2](17,2) = -175.0/16384.0;
+ prolongation[2](17,3) = 25.0/16384.0;
+ prolongation[2](17,4) = 21.0/4096.0;
+ prolongation[2](17,5) = -105.0/8192.0;
+ prolongation[2](17,6) = 105.0/4096.0;
+ prolongation[2](17,7) = -175.0/4096.0;
+ prolongation[2](17,8) = 1575.0/8192.0;
+ prolongation[2](17,9) = 525.0/4096.0;
+ prolongation[2](17,10) = -35.0/4096.0;
+ prolongation[2](17,11) = 175.0/8192.0;
+ prolongation[2](17,12) = -175.0/4096.0;
+ prolongation[2](17,13) = 25.0/4096.0;
+ prolongation[2](17,14) = -225.0/8192.0;
+ prolongation[2](17,15) = -75.0/4096.0;
+ prolongation[2](17,16) = -35.0/1024.0;
+ prolongation[2](17,17) = -175.0/1024.0;
+ prolongation[2](17,18) = 525.0/1024.0;
+ prolongation[2](17,19) = 105.0/1024.0;
+ prolongation[2](17,20) = 175.0/2048.0;
+ prolongation[2](17,21) = 1575.0/2048.0;
+ prolongation[2](17,22) = -525.0/2048.0;
+ prolongation[2](17,23) = 315.0/2048.0;
+ prolongation[2](17,24) = -1575.0/4096.0;
+ prolongation[2](18,0) = 25.0/16384.0;
+ prolongation[2](18,1) = -175.0/16384.0;
+ prolongation[2](18,2) = 1225.0/16384.0;
+ prolongation[2](18,3) = -175.0/16384.0;
+ prolongation[2](18,4) = -35.0/4096.0;
+ prolongation[2](18,5) = 175.0/8192.0;
+ prolongation[2](18,6) = -175.0/4096.0;
+ prolongation[2](18,7) = 245.0/4096.0;
+ prolongation[2](18,8) = -1225.0/8192.0;
+ prolongation[2](18,9) = 1225.0/4096.0;
+ prolongation[2](18,10) = 245.0/4096.0;
+ prolongation[2](18,11) = -1225.0/8192.0;
+ prolongation[2](18,12) = 1225.0/4096.0;
+ prolongation[2](18,13) = -35.0/4096.0;
+ prolongation[2](18,14) = 175.0/8192.0;
+ prolongation[2](18,15) = -175.0/4096.0;
+ prolongation[2](18,16) = 49.0/1024.0;
+ prolongation[2](18,17) = 245.0/1024.0;
+ prolongation[2](18,18) = 1225.0/1024.0;
+ prolongation[2](18,19) = 245.0/1024.0;
+ prolongation[2](18,20) = -245.0/2048.0;
+ prolongation[2](18,21) = -1225.0/2048.0;
+ prolongation[2](18,22) = -1225.0/2048.0;
+ prolongation[2](18,23) = -245.0/2048.0;
+ prolongation[2](18,24) = 1225.0/4096.0;
+ prolongation[2](19,0) = -15.0/16384.0;
+ prolongation[2](19,1) = 25.0/16384.0;
+ prolongation[2](19,2) = -175.0/16384.0;
+ prolongation[2](19,3) = 105.0/16384.0;
+ prolongation[2](19,4) = 25.0/4096.0;
+ prolongation[2](19,5) = -225.0/8192.0;
+ prolongation[2](19,6) = -75.0/4096.0;
+ prolongation[2](19,7) = -35.0/4096.0;
+ prolongation[2](19,8) = 175.0/8192.0;
+ prolongation[2](19,9) = -175.0/4096.0;
+ prolongation[2](19,10) = -175.0/4096.0;
+ prolongation[2](19,11) = 1575.0/8192.0;
+ prolongation[2](19,12) = 525.0/4096.0;
+ prolongation[2](19,13) = 21.0/4096.0;
+ prolongation[2](19,14) = -105.0/8192.0;
+ prolongation[2](19,15) = 105.0/4096.0;
+ prolongation[2](19,16) = -35.0/1024.0;
+ prolongation[2](19,17) = 105.0/1024.0;
+ prolongation[2](19,18) = 525.0/1024.0;
+ prolongation[2](19,19) = -175.0/1024.0;
+ prolongation[2](19,20) = 315.0/2048.0;
+ prolongation[2](19,21) = -525.0/2048.0;
+ prolongation[2](19,22) = 1575.0/2048.0;
+ prolongation[2](19,23) = 175.0/2048.0;
+ prolongation[2](19,24) = -1575.0/4096.0;
+ prolongation[2](20,6) = 3.0/128.0;
+ prolongation[2](20,12) = -5.0/128.0;
+ prolongation[2](20,17) = -5.0/32.0;
+ prolongation[2](20,18) = 15.0/32.0;
+ prolongation[2](20,21) = 45.0/64.0;
+ prolongation[2](21,9) = 35.0/128.0;
+ prolongation[2](21,15) = -5.0/128.0;
+ prolongation[2](21,18) = 35.0/32.0;
+ prolongation[2](21,19) = 7.0/32.0;
+ prolongation[2](21,22) = -35.0/64.0;
+ prolongation[2](22,6) = -5.0/128.0;
+ prolongation[2](22,12) = 35.0/128.0;
+ prolongation[2](22,17) = 7.0/32.0;
+ prolongation[2](22,18) = 35.0/32.0;
+ prolongation[2](22,21) = -35.0/64.0;
+ prolongation[2](23,9) = -5.0/128.0;
+ prolongation[2](23,15) = 3.0/128.0;
+ prolongation[2](23,18) = 15.0/32.0;
+ prolongation[2](23,19) = -5.0/32.0;
+ prolongation[2](23,22) = 45.0/64.0;
+ prolongation[2](24,18) = 1.0;
+ prolongation[3](0,14) = 1.0;
+ prolongation[3](1,24) = 1.0;
+ prolongation[3](2,11) = 1.0;
+ prolongation[3](3,3) = 1.0;
+ prolongation[3](4,8) = -5.0/128.0;
+ prolongation[3](4,14) = 35.0/128.0;
+ prolongation[3](4,21) = 7.0/32.0;
+ prolongation[3](4,23) = 35.0/32.0;
+ prolongation[3](4,24) = -35.0/64.0;
+ prolongation[3](5,23) = 1.0;
+ prolongation[3](6,8) = 3.0/128.0;
+ prolongation[3](6,14) = -5.0/128.0;
+ prolongation[3](6,21) = -5.0/32.0;
+ prolongation[3](6,23) = 15.0/32.0;
+ prolongation[3](6,24) = 45.0/64.0;
+ prolongation[3](7,5) = 3.0/128.0;
+ prolongation[3](7,11) = -5.0/128.0;
+ prolongation[3](7,20) = -5.0/32.0;
+ prolongation[3](7,22) = 15.0/32.0;
+ prolongation[3](7,24) = 45.0/64.0;
+ prolongation[3](8,22) = 1.0;
+ prolongation[3](9,5) = -5.0/128.0;
+ prolongation[3](9,11) = 35.0/128.0;
+ prolongation[3](9,20) = 7.0/32.0;
+ prolongation[3](9,22) = 35.0/32.0;
+ prolongation[3](9,24) = -35.0/64.0;
+ prolongation[3](10,2) = -5.0/128.0;
+ prolongation[3](10,3) = 35.0/128.0;
+ prolongation[3](10,10) = 35.0/32.0;
+ prolongation[3](10,11) = -35.0/64.0;
+ prolongation[3](10,12) = 7.0/32.0;
+ prolongation[3](11,10) = 1.0;
+ prolongation[3](12,2) = 3.0/128.0;
+ prolongation[3](12,3) = -5.0/128.0;
+ prolongation[3](12,10) = 15.0/32.0;
+ prolongation[3](12,11) = 45.0/64.0;
+ prolongation[3](12,12) = -5.0/32.0;
+ prolongation[3](13,0) = 3.0/128.0;
+ prolongation[3](13,3) = -5.0/128.0;
+ prolongation[3](13,13) = -5.0/32.0;
+ prolongation[3](13,14) = 45.0/64.0;
+ prolongation[3](13,15) = 15.0/32.0;
+ prolongation[3](14,15) = 1.0;
+ prolongation[3](15,0) = -5.0/128.0;
+ prolongation[3](15,3) = 35.0/128.0;
+ prolongation[3](15,13) = 7.0/32.0;
+ prolongation[3](15,14) = -35.0/64.0;
+ prolongation[3](15,15) = 35.0/32.0;
+ prolongation[3](16,0) = 105.0/16384.0;
+ prolongation[3](16,1) = -15.0/16384.0;
+ prolongation[3](16,2) = 25.0/16384.0;
+ prolongation[3](16,3) = -175.0/16384.0;
+ prolongation[3](16,4) = 105.0/4096.0;
+ prolongation[3](16,5) = -105.0/8192.0;
+ prolongation[3](16,6) = 21.0/4096.0;
+ prolongation[3](16,7) = 25.0/4096.0;
+ prolongation[3](16,8) = -225.0/8192.0;
+ prolongation[3](16,9) = -75.0/4096.0;
+ prolongation[3](16,10) = -175.0/4096.0;
+ prolongation[3](16,11) = 175.0/8192.0;
+ prolongation[3](16,12) = -35.0/4096.0;
+ prolongation[3](16,13) = -175.0/4096.0;
+ prolongation[3](16,14) = 1575.0/8192.0;
+ prolongation[3](16,15) = 525.0/4096.0;
+ prolongation[3](16,16) = -175.0/1024.0;
+ prolongation[3](16,17) = -35.0/1024.0;
+ prolongation[3](16,18) = 105.0/1024.0;
+ prolongation[3](16,19) = 525.0/1024.0;
+ prolongation[3](16,20) = 175.0/2048.0;
+ prolongation[3](16,21) = 315.0/2048.0;
+ prolongation[3](16,22) = -525.0/2048.0;
+ prolongation[3](16,23) = 1575.0/2048.0;
+ prolongation[3](16,24) = -1575.0/4096.0;
+ prolongation[3](17,0) = -15.0/16384.0;
+ prolongation[3](17,1) = 9.0/16384.0;
+ prolongation[3](17,2) = -15.0/16384.0;
+ prolongation[3](17,3) = 25.0/16384.0;
+ prolongation[3](17,4) = 45.0/4096.0;
+ prolongation[3](17,5) = 135.0/8192.0;
+ prolongation[3](17,6) = -15.0/4096.0;
+ prolongation[3](17,7) = -15.0/4096.0;
+ prolongation[3](17,8) = 135.0/8192.0;
+ prolongation[3](17,9) = 45.0/4096.0;
+ prolongation[3](17,10) = -75.0/4096.0;
+ prolongation[3](17,11) = -225.0/8192.0;
+ prolongation[3](17,12) = 25.0/4096.0;
+ prolongation[3](17,13) = 25.0/4096.0;
+ prolongation[3](17,14) = -225.0/8192.0;
+ prolongation[3](17,15) = -75.0/4096.0;
+ prolongation[3](17,16) = -75.0/1024.0;
+ prolongation[3](17,17) = 25.0/1024.0;
+ prolongation[3](17,18) = -75.0/1024.0;
+ prolongation[3](17,19) = 225.0/1024.0;
+ prolongation[3](17,20) = -225.0/2048.0;
+ prolongation[3](17,21) = -225.0/2048.0;
+ prolongation[3](17,22) = 675.0/2048.0;
+ prolongation[3](17,23) = 675.0/2048.0;
+ prolongation[3](17,24) = 2025.0/4096.0;
+ prolongation[3](18,0) = 25.0/16384.0;
+ prolongation[3](18,1) = -15.0/16384.0;
+ prolongation[3](18,2) = 105.0/16384.0;
+ prolongation[3](18,3) = -175.0/16384.0;
+ prolongation[3](18,4) = -75.0/4096.0;
+ prolongation[3](18,5) = -225.0/8192.0;
+ prolongation[3](18,6) = 25.0/4096.0;
+ prolongation[3](18,7) = 21.0/4096.0;
+ prolongation[3](18,8) = -105.0/8192.0;
+ prolongation[3](18,9) = 105.0/4096.0;
+ prolongation[3](18,10) = 525.0/4096.0;
+ prolongation[3](18,11) = 1575.0/8192.0;
+ prolongation[3](18,12) = -175.0/4096.0;
+ prolongation[3](18,13) = -35.0/4096.0;
+ prolongation[3](18,14) = 175.0/8192.0;
+ prolongation[3](18,15) = -175.0/4096.0;
+ prolongation[3](18,16) = 105.0/1024.0;
+ prolongation[3](18,17) = -35.0/1024.0;
+ prolongation[3](18,18) = -175.0/1024.0;
+ prolongation[3](18,19) = 525.0/1024.0;
+ prolongation[3](18,20) = 315.0/2048.0;
+ prolongation[3](18,21) = 175.0/2048.0;
+ prolongation[3](18,22) = 1575.0/2048.0;
+ prolongation[3](18,23) = -525.0/2048.0;
+ prolongation[3](18,24) = -1575.0/4096.0;
+ prolongation[3](19,0) = -175.0/16384.0;
+ prolongation[3](19,1) = 25.0/16384.0;
+ prolongation[3](19,2) = -175.0/16384.0;
+ prolongation[3](19,3) = 1225.0/16384.0;
+ prolongation[3](19,4) = -175.0/4096.0;
+ prolongation[3](19,5) = 175.0/8192.0;
+ prolongation[3](19,6) = -35.0/4096.0;
+ prolongation[3](19,7) = -35.0/4096.0;
+ prolongation[3](19,8) = 175.0/8192.0;
+ prolongation[3](19,9) = -175.0/4096.0;
+ prolongation[3](19,10) = 1225.0/4096.0;
+ prolongation[3](19,11) = -1225.0/8192.0;
+ prolongation[3](19,12) = 245.0/4096.0;
+ prolongation[3](19,13) = 245.0/4096.0;
+ prolongation[3](19,14) = -1225.0/8192.0;
+ prolongation[3](19,15) = 1225.0/4096.0;
+ prolongation[3](19,16) = 245.0/1024.0;
+ prolongation[3](19,17) = 49.0/1024.0;
+ prolongation[3](19,18) = 245.0/1024.0;
+ prolongation[3](19,19) = 1225.0/1024.0;
+ prolongation[3](19,20) = -245.0/2048.0;
+ prolongation[3](19,21) = -245.0/2048.0;
+ prolongation[3](19,22) = -1225.0/2048.0;
+ prolongation[3](19,23) = -1225.0/2048.0;
+ prolongation[3](19,24) = 1225.0/4096.0;
+ prolongation[3](20,4) = 3.0/128.0;
+ prolongation[3](20,10) = -5.0/128.0;
+ prolongation[3](20,16) = -5.0/32.0;
+ prolongation[3](20,19) = 15.0/32.0;
+ prolongation[3](20,23) = 45.0/64.0;
+ prolongation[3](21,9) = 3.0/128.0;
+ prolongation[3](21,15) = -5.0/128.0;
+ prolongation[3](21,18) = -5.0/32.0;
+ prolongation[3](21,19) = 15.0/32.0;
+ prolongation[3](21,22) = 45.0/64.0;
+ prolongation[3](22,4) = -5.0/128.0;
+ prolongation[3](22,10) = 35.0/128.0;
+ prolongation[3](22,16) = 7.0/32.0;
+ prolongation[3](22,19) = 35.0/32.0;
+ prolongation[3](22,23) = -35.0/64.0;
+ prolongation[3](23,9) = -5.0/128.0;
+ prolongation[3](23,15) = 35.0/128.0;
+ prolongation[3](23,18) = 7.0/32.0;
+ prolongation[3](23,19) = 35.0/32.0;
+ prolongation[3](23,22) = -35.0/64.0;
+ prolongation[3](24,19) = 1.0;
+};
+
+
+template <>
+double
+FEQuarticSub<2>::shape_value (const unsigned int i,
+ const Point<2> &p) const
+{
+ Assert (i<total_dofs, ExcInvalidIndex(i));
+
+ const double xi = p(0),
+ eta= p(1);
+ switch (i)
+ {
+ case 0: return 1.0-25.0/3.0*xi+70.0/3.0*xi*xi-80.0/3.0*xi*xi*xi+32.0/
+3.0*xi*xi*xi*xi+(-25.0/3.0+625.0/9.0*xi-1750.0/9.0*xi*xi+2000.0/9.0*xi*xi*xi
+-800.0/9.0*xi*xi*xi*xi)*eta+(70.0/3.0-1750.0/9.0*xi+4900.0/9.0*xi*xi-5600.0/9.0
+*xi*xi*xi+2240.0/9.0*xi*xi*xi*xi)*eta*eta+(-80.0/3.0+2000.0/9.0*xi-5600.0/9.0*
+xi*xi+6400.0/9.0*xi*xi*xi-2560.0/9.0*xi*xi*xi*xi)*eta*eta*eta+(32.0/3.0-800.0/
+9.0*xi+2240.0/9.0*xi*xi-2560.0/9.0*xi*xi*xi+1024.0/9.0*xi*xi*xi*xi)*eta*eta*eta
+*eta;
+ case 1: return -xi+22.0/3.0*xi*xi-16.0*xi*xi*xi+32.0/3.0*xi*xi*xi*xi+(
+25.0/3.0*xi-550.0/9.0*xi*xi+400.0/3.0*xi*xi*xi-800.0/9.0*xi*xi*xi*xi)*eta+(
+-70.0/3.0*xi+1540.0/9.0*xi*xi-1120.0/3.0*xi*xi*xi+2240.0/9.0*xi*xi*xi*xi)*eta*
+eta+(80.0/3.0*xi-1760.0/9.0*xi*xi+1280.0/3.0*xi*xi*xi-2560.0/9.0*xi*xi*xi*xi)*
+eta*eta*eta+(-32.0/3.0*xi+704.0/9.0*xi*xi-512.0/3.0*xi*xi*xi+1024.0/9.0*xi*xi*
+xi*xi)*eta*eta*eta*eta;
+ case 2: return (xi-22.0/3.0*xi*xi+16.0*xi*xi*xi-32.0/3.0*xi*xi*xi*xi)*
+eta+(-22.0/3.0*xi+484.0/9.0*xi*xi-352.0/3.0*xi*xi*xi+704.0/9.0*xi*xi*xi*xi)*eta
+*eta+(16.0*xi-352.0/3.0*xi*xi+256.0*xi*xi*xi-512.0/3.0*xi*xi*xi*xi)*eta*eta*eta
++(-32.0/3.0*xi+704.0/9.0*xi*xi-512.0/3.0*xi*xi*xi+1024.0/9.0*xi*xi*xi*xi)*eta*
+eta*eta*eta;
+ case 3: return (-1.0+25.0/3.0*xi-70.0/3.0*xi*xi+80.0/3.0*xi*xi*xi-32.0/
+3.0*xi*xi*xi*xi)*eta+(22.0/3.0-550.0/9.0*xi+1540.0/9.0*xi*xi-1760.0/9.0*xi*xi*
+xi+704.0/9.0*xi*xi*xi*xi)*eta*eta+(-16.0+400.0/3.0*xi-1120.0/3.0*xi*xi+1280.0/
+3.0*xi*xi*xi-512.0/3.0*xi*xi*xi*xi)*eta*eta*eta+(32.0/3.0-800.0/9.0*xi+2240.0/
+9.0*xi*xi-2560.0/9.0*xi*xi*xi+1024.0/9.0*xi*xi*xi*xi)*eta*eta*eta*eta;
+ case 4: return 16.0*xi-208.0/3.0*xi*xi+96.0*xi*xi*xi-128.0/3.0*xi*xi*xi
+*xi+(-400.0/3.0*xi+5200.0/9.0*xi*xi-800.0*xi*xi*xi+3200.0/9.0*xi*xi*xi*xi)*eta+
+(1120.0/3.0*xi-14560.0/9.0*xi*xi+2240.0*xi*xi*xi-8960.0/9.0*xi*xi*xi*xi)*eta*
+eta+(-1280.0/3.0*xi+16640.0/9.0*xi*xi-2560.0*xi*xi*xi+10240.0/9.0*xi*xi*xi*xi)*
+eta*eta*eta+(512.0/3.0*xi-6656.0/9.0*xi*xi+1024.0*xi*xi*xi-4096.0/9.0*xi*xi*xi*
+xi)*eta*eta*eta*eta;
+ case 5: return -12.0*xi+76.0*xi*xi-128.0*xi*xi*xi+64.0*xi*xi*xi*xi+(
+100.0*xi-1900.0/3.0*xi*xi+3200.0/3.0*xi*xi*xi-1600.0/3.0*xi*xi*xi*xi)*eta+(
+-280.0*xi+5320.0/3.0*xi*xi-8960.0/3.0*xi*xi*xi+4480.0/3.0*xi*xi*xi*xi)*eta*eta+
+(320.0*xi-6080.0/3.0*xi*xi+10240.0/3.0*xi*xi*xi-5120.0/3.0*xi*xi*xi*xi)*eta*eta
+*eta+(-128.0*xi+2432.0/3.0*xi*xi-4096.0/3.0*xi*xi*xi+2048.0/3.0*xi*xi*xi*xi)*
+eta*eta*eta*eta;
+ case 6: return 16.0/3.0*xi-112.0/3.0*xi*xi+224.0/3.0*xi*xi*xi-128.0/3.0
+*xi*xi*xi*xi+(-400.0/9.0*xi+2800.0/9.0*xi*xi-5600.0/9.0*xi*xi*xi+3200.0/9.0*xi*
+xi*xi*xi)*eta+(1120.0/9.0*xi-7840.0/9.0*xi*xi+15680.0/9.0*xi*xi*xi-8960.0/9.0*
+xi*xi*xi*xi)*eta*eta+(-1280.0/9.0*xi+8960.0/9.0*xi*xi-17920.0/9.0*xi*xi*xi+
+10240.0/9.0*xi*xi*xi*xi)*eta*eta*eta+(512.0/9.0*xi-3584.0/9.0*xi*xi+7168.0/9.0*
+xi*xi*xi-4096.0/9.0*xi*xi*xi*xi)*eta*eta*eta*eta;
+ case 7: return (-16.0*xi+352.0/3.0*xi*xi-256.0*xi*xi*xi+512.0/3.0*xi*xi
+*xi*xi)*eta+(208.0/3.0*xi-4576.0/9.0*xi*xi+3328.0/3.0*xi*xi*xi-6656.0/9.0*xi*xi
+*xi*xi)*eta*eta+(-96.0*xi+704.0*xi*xi-1536.0*xi*xi*xi+1024.0*xi*xi*xi*xi)*eta*
+eta*eta+(128.0/3.0*xi-2816.0/9.0*xi*xi+2048.0/3.0*xi*xi*xi-4096.0/9.0*xi*xi*xi*
+xi)*eta*eta*eta*eta;
+ case 8: return (12.0*xi-88.0*xi*xi+192.0*xi*xi*xi-128.0*xi*xi*xi*xi)*
+eta+(-76.0*xi+1672.0/3.0*xi*xi-1216.0*xi*xi*xi+2432.0/3.0*xi*xi*xi*xi)*eta*eta+
+(128.0*xi-2816.0/3.0*xi*xi+2048.0*xi*xi*xi-4096.0/3.0*xi*xi*xi*xi)*eta*eta*eta+
+(-64.0*xi+1408.0/3.0*xi*xi-1024.0*xi*xi*xi+2048.0/3.0*xi*xi*xi*xi)*eta*eta*eta*
+eta;
+ case 9: return (-16.0/3.0*xi+352.0/9.0*xi*xi-256.0/3.0*xi*xi*xi+512.0/
+9.0*xi*xi*xi*xi)*eta+(112.0/3.0*xi-2464.0/9.0*xi*xi+1792.0/3.0*xi*xi*xi-3584.0/
+9.0*xi*xi*xi*xi)*eta*eta+(-224.0/3.0*xi+4928.0/9.0*xi*xi-3584.0/3.0*xi*xi*xi+
+7168.0/9.0*xi*xi*xi*xi)*eta*eta*eta+(128.0/3.0*xi-2816.0/9.0*xi*xi+2048.0/3.0*
+xi*xi*xi-4096.0/9.0*xi*xi*xi*xi)*eta*eta*eta*eta;
+ case 10: return (-16.0*xi+208.0/3.0*xi*xi-96.0*xi*xi*xi+128.0/3.0*xi*xi
+*xi*xi)*eta+(352.0/3.0*xi-4576.0/9.0*xi*xi+704.0*xi*xi*xi-2816.0/9.0*xi*xi*xi*
+xi)*eta*eta+(-256.0*xi+3328.0/3.0*xi*xi-1536.0*xi*xi*xi+2048.0/3.0*xi*xi*xi*xi)
+*eta*eta*eta+(512.0/3.0*xi-6656.0/9.0*xi*xi+1024.0*xi*xi*xi-4096.0/9.0*xi*xi*xi
+*xi)*eta*eta*eta*eta;
+ case 11: return (12.0*xi-76.0*xi*xi+128.0*xi*xi*xi-64.0*xi*xi*xi*xi)*
+eta+(-88.0*xi+1672.0/3.0*xi*xi-2816.0/3.0*xi*xi*xi+1408.0/3.0*xi*xi*xi*xi)*eta*
+eta+(192.0*xi-1216.0*xi*xi+2048.0*xi*xi*xi-1024.0*xi*xi*xi*xi)*eta*eta*eta+(
+-128.0*xi+2432.0/3.0*xi*xi-4096.0/3.0*xi*xi*xi+2048.0/3.0*xi*xi*xi*xi)*eta*eta*
+eta*eta;
+ case 12: return (-16.0/3.0*xi+112.0/3.0*xi*xi-224.0/3.0*xi*xi*xi+128.0/
+3.0*xi*xi*xi*xi)*eta+(352.0/9.0*xi-2464.0/9.0*xi*xi+4928.0/9.0*xi*xi*xi-2816.0/
+9.0*xi*xi*xi*xi)*eta*eta+(-256.0/3.0*xi+1792.0/3.0*xi*xi-3584.0/3.0*xi*xi*xi+
+2048.0/3.0*xi*xi*xi*xi)*eta*eta*eta+(512.0/9.0*xi-3584.0/9.0*xi*xi+7168.0/9.0*
+xi*xi*xi-4096.0/9.0*xi*xi*xi*xi)*eta*eta*eta*eta;
+ case 13: return (16.0-400.0/3.0*xi+1120.0/3.0*xi*xi-1280.0/3.0*xi*xi*xi
++512.0/3.0*xi*xi*xi*xi)*eta+(-208.0/3.0+5200.0/9.0*xi-14560.0/9.0*xi*xi+16640.0
+/9.0*xi*xi*xi-6656.0/9.0*xi*xi*xi*xi)*eta*eta+(96.0-800.0*xi+2240.0*xi*xi
+-2560.0*xi*xi*xi+1024.0*xi*xi*xi*xi)*eta*eta*eta+(-128.0/3.0+3200.0/9.0*xi
+-8960.0/9.0*xi*xi+10240.0/9.0*xi*xi*xi-4096.0/9.0*xi*xi*xi*xi)*eta*eta*eta*eta;
+ case 14: return (-12.0+100.0*xi-280.0*xi*xi+320.0*xi*xi*xi-128.0*xi*xi*
+xi*xi)*eta+(76.0-1900.0/3.0*xi+5320.0/3.0*xi*xi-6080.0/3.0*xi*xi*xi+2432.0/3.0*
+xi*xi*xi*xi)*eta*eta+(-128.0+3200.0/3.0*xi-8960.0/3.0*xi*xi+10240.0/3.0*xi*xi*
+xi-4096.0/3.0*xi*xi*xi*xi)*eta*eta*eta+(64.0-1600.0/3.0*xi+4480.0/3.0*xi*xi
+-5120.0/3.0*xi*xi*xi+2048.0/3.0*xi*xi*xi*xi)*eta*eta*eta*eta;
+ case 15: return (16.0/3.0-400.0/9.0*xi+1120.0/9.0*xi*xi-1280.0/9.0*xi*
+xi*xi+512.0/9.0*xi*xi*xi*xi)*eta+(-112.0/3.0+2800.0/9.0*xi-7840.0/9.0*xi*xi+
+8960.0/9.0*xi*xi*xi-3584.0/9.0*xi*xi*xi*xi)*eta*eta+(224.0/3.0-5600.0/9.0*xi+
+15680.0/9.0*xi*xi-17920.0/9.0*xi*xi*xi+7168.0/9.0*xi*xi*xi*xi)*eta*eta*eta+(
+-128.0/3.0+3200.0/9.0*xi-8960.0/9.0*xi*xi+10240.0/9.0*xi*xi*xi-4096.0/9.0*xi*xi
+*xi*xi)*eta*eta*eta*eta;
+ case 16: return (256.0*xi-3328.0/3.0*xi*xi+1536.0*xi*xi*xi-2048.0/3.0*
+xi*xi*xi*xi)*eta+(-3328.0/3.0*xi+43264.0/9.0*xi*xi-6656.0*xi*xi*xi+26624.0/9.0*
+xi*xi*xi*xi)*eta*eta+(1536.0*xi-6656.0*xi*xi+9216.0*xi*xi*xi-4096.0*xi*xi*xi*xi
+)*eta*eta*eta+(-2048.0/3.0*xi+26624.0/9.0*xi*xi-4096.0*xi*xi*xi+16384.0/9.0*xi*
+xi*xi*xi)*eta*eta*eta*eta;
+ case 17: return (256.0/3.0*xi-1792.0/3.0*xi*xi+3584.0/3.0*xi*xi*xi
+-2048.0/3.0*xi*xi*xi*xi)*eta+(-3328.0/9.0*xi+23296.0/9.0*xi*xi-46592.0/9.0*xi*
+xi*xi+26624.0/9.0*xi*xi*xi*xi)*eta*eta+(512.0*xi-3584.0*xi*xi+7168.0*xi*xi*xi
+-4096.0*xi*xi*xi*xi)*eta*eta*eta+(-2048.0/9.0*xi+14336.0/9.0*xi*xi-28672.0/9.0*
+xi*xi*xi+16384.0/9.0*xi*xi*xi*xi)*eta*eta*eta*eta;
+ case 18: return (256.0/9.0*xi-1792.0/9.0*xi*xi+3584.0/9.0*xi*xi*xi
+-2048.0/9.0*xi*xi*xi*xi)*eta+(-1792.0/9.0*xi+12544.0/9.0*xi*xi-25088.0/9.0*xi*
+xi*xi+14336.0/9.0*xi*xi*xi*xi)*eta*eta+(3584.0/9.0*xi-25088.0/9.0*xi*xi+50176.0
+/9.0*xi*xi*xi-28672.0/9.0*xi*xi*xi*xi)*eta*eta*eta+(-2048.0/9.0*xi+14336.0/9.0*
+xi*xi-28672.0/9.0*xi*xi*xi+16384.0/9.0*xi*xi*xi*xi)*eta*eta*eta*eta;
+ case 19: return (256.0/3.0*xi-3328.0/9.0*xi*xi+512.0*xi*xi*xi-2048.0/
+9.0*xi*xi*xi*xi)*eta+(-1792.0/3.0*xi+23296.0/9.0*xi*xi-3584.0*xi*xi*xi+14336.0/
+9.0*xi*xi*xi*xi)*eta*eta+(3584.0/3.0*xi-46592.0/9.0*xi*xi+7168.0*xi*xi*xi
+-28672.0/9.0*xi*xi*xi*xi)*eta*eta*eta+(-2048.0/3.0*xi+26624.0/9.0*xi*xi-4096.0*
+xi*xi*xi+16384.0/9.0*xi*xi*xi*xi)*eta*eta*eta*eta;
+ case 20: return (-192.0*xi+1216.0*xi*xi-2048.0*xi*xi*xi+1024.0*xi*xi*xi
+*xi)*eta+(832.0*xi-15808.0/3.0*xi*xi+26624.0/3.0*xi*xi*xi-13312.0/3.0*xi*xi*xi*
+xi)*eta*eta+(-1152.0*xi+7296.0*xi*xi-12288.0*xi*xi*xi+6144.0*xi*xi*xi*xi)*eta*
+eta*eta+(512.0*xi-9728.0/3.0*xi*xi+16384.0/3.0*xi*xi*xi-8192.0/3.0*xi*xi*xi*xi)
+*eta*eta*eta*eta;
+ case 21: return (-64.0*xi+448.0*xi*xi-896.0*xi*xi*xi+512.0*xi*xi*xi*xi)
+*eta+(1216.0/3.0*xi-8512.0/3.0*xi*xi+17024.0/3.0*xi*xi*xi-9728.0/3.0*xi*xi*xi*
+xi)*eta*eta+(-2048.0/3.0*xi+14336.0/3.0*xi*xi-28672.0/3.0*xi*xi*xi+16384.0/3.0*
+xi*xi*xi*xi)*eta*eta*eta+(1024.0/3.0*xi-7168.0/3.0*xi*xi+14336.0/3.0*xi*xi*xi
+-8192.0/3.0*xi*xi*xi*xi)*eta*eta*eta*eta;
+ case 22: return (-64.0*xi+1216.0/3.0*xi*xi-2048.0/3.0*xi*xi*xi+1024.0/
+3.0*xi*xi*xi*xi)*eta+(448.0*xi-8512.0/3.0*xi*xi+14336.0/3.0*xi*xi*xi-7168.0/3.0
+*xi*xi*xi*xi)*eta*eta+(-896.0*xi+17024.0/3.0*xi*xi-28672.0/3.0*xi*xi*xi+14336.0
+/3.0*xi*xi*xi*xi)*eta*eta*eta+(512.0*xi-9728.0/3.0*xi*xi+16384.0/3.0*xi*xi*xi
+-8192.0/3.0*xi*xi*xi*xi)*eta*eta*eta*eta;
+ case 23: return (-192.0*xi+832.0*xi*xi-1152.0*xi*xi*xi+512.0*xi*xi*xi*
+xi)*eta+(1216.0*xi-15808.0/3.0*xi*xi+7296.0*xi*xi*xi-9728.0/3.0*xi*xi*xi*xi)*
+eta*eta+(-2048.0*xi+26624.0/3.0*xi*xi-12288.0*xi*xi*xi+16384.0/3.0*xi*xi*xi*xi)
+*eta*eta*eta+(1024.0*xi-13312.0/3.0*xi*xi+6144.0*xi*xi*xi-8192.0/3.0*xi*xi*xi*
+xi)*eta*eta*eta*eta;
+ case 24: return (144.0*xi-912.0*xi*xi+1536.0*xi*xi*xi-768.0*xi*xi*xi*xi
+)*eta+(-912.0*xi+5776.0*xi*xi-9728.0*xi*xi*xi+4864.0*xi*xi*xi*xi)*eta*eta+(
+1536.0*xi-9728.0*xi*xi+16384.0*xi*xi*xi-8192.0*xi*xi*xi*xi)*eta*eta*eta+(-768.0
+*xi+4864.0*xi*xi-8192.0*xi*xi*xi+4096.0*xi*xi*xi*xi)*eta*eta*eta*eta;
+ };
+ return 0;
+};
+
+
+
+template <>
+inline
+double
+FEQuarticSub<2>::linear_shape_value (const unsigned int i,
+ const Point<2>& p) const
+{
+ Assert((i<4), ExcInvalidIndex(i));
+ switch (i)
+ {
+ case 0: return (1.-p(0)) * (1.-p(1));
+ case 1: return p(0) * (1.-p(1));
+ case 2: return p(0) * p(1);
+ case 3: return (1.-p(0)) * p(1);
+ }
+ return 0.;
+};
+
+
+
+template <>
+Point<2>
+FEQuarticSub<2>::shape_grad (const unsigned int i,
+ const Point<2> &p) const
+{
+ Assert (i<total_dofs, ExcInvalidIndex(i));
+
+ const double xi = p(0),
+ eta= p(1);
+ switch (i)
+ {
+ case 0: return Point<2>(-25.0/3.0+140.0/3.0*xi-80.0*xi*xi+128.0/3.0*xi*xi*xi+(625.0/9.0-3500.0/9.0*xi+2000.0/3.0*xi*xi-3200.0/9.0*xi*xi*xi)*eta+(-1750.0/9.0+9800.0/9.0*xi-5600.0/3.0*xi*xi+8960.0/9.0*xi*xi*xi)*eta*eta+(2000.0/9.0-11200.0/9.0*xi+6400.0/3.0*xi*xi-10240.0/9.0*xi*xi*xi)*eta*eta*eta+(-800.0/9.0+4480.0/9.0*xi-2560.0/3.0*xi*xi+4096.0/9.0*xi*xi*xi)*eta*eta*eta*eta,
+ -25.0/3.0+625.0/9.0*xi-1750.0/9.0*xi*xi+2000.0/9.0*xi*xi*xi-800.0/9.0*xi*xi*xi*xi+2.0*(70.0/3.0-1750.0/9.0*xi+4900.0/9.0*xi*xi-5600.0/9.0*xi*xi*xi+2240.0/9.0*xi*xi*xi*xi)*eta+3.0*(-80.0/3.0+2000.0/9.0*xi-5600.0/9.0*xi*xi+6400.0/9.0*xi*xi*xi-2560.0/9.0*xi*xi*xi*xi)*eta*eta+4.0*(32.0/3.0-800.0/9.0*xi+2240.0/9.0*xi*xi-2560.0/9.0*xi*xi*xi+1024.0/9.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 1: return Point<2>(-1.0+44.0/3.0*xi-48.0*xi*xi+128.0/3.0*xi*xi*xi+(25.0/3.0-1100.0/9.0*xi+400.0*xi*xi-3200.0/9.0*xi*xi*xi)*eta+(-70.0/3.0+3080.0/9.0*xi-1120.0*xi*xi+8960.0/9.0*xi*xi*xi)*eta*eta+(80.0/3.0-3520.0/9.0*xi+1280.0*xi*xi-10240.0/9.0*xi*xi*xi)*eta*eta*eta+(-32.0/3.0+1408.0/9.0*xi-512.0*xi*xi+4096.0/9.0*xi*xi*xi)*eta*eta*eta*eta,
+ 25.0/3.0*xi-550.0/9.0*xi*xi+400.0/3.0*xi*xi*xi-800.0/9.0*xi*xi*xi*xi+2.0*(-70.0/3.0*xi+1540.0/9.0*xi*xi-1120.0/3.0*xi*xi*xi+2240.0/9.0*xi*xi*xi*xi)*eta+3.0*(80.0/3.0*xi-1760.0/9.0*xi*xi+1280.0/3.0*xi*xi*xi-2560.0/9.0*xi*xi*xi*xi)*eta*eta+4.0*(-32.0/3.0*xi+704.0/9.0*xi*xi-512.0/3.0*xi*xi*xi+1024.0/9.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 2: return Point<2>((1.0-44.0/3.0*xi+48.0*xi*xi-128.0/3.0*xi*xi*xi)*eta+(-22.0/3.0+968.0/9.0*xi-352.0*xi*xi+2816.0/9.0*xi*xi*xi)*eta*eta+(16.0-704.0/3.0*xi+768.0*xi*xi-2048.0/3.0*xi*xi*xi)*eta*eta*eta+(-32.0/3.0+1408.0/9.0*xi-512.0*xi*xi+4096.0/9.0*xi*xi*xi)*eta*eta*eta*eta,
+ xi-22.0/3.0*xi*xi+16.0*xi*xi*xi-32.0/3.0*xi*xi*xi*xi+2.0*(-22.0/3.0*xi+484.0/9.0*xi*xi-352.0/3.0*xi*xi*xi+704.0/9.0*xi*xi*xi*xi)*eta+3.0*(16.0*xi-352.0/3.0*xi*xi+256.0*xi*xi*xi-512.0/3.0*xi*xi*xi*xi)*eta*eta+4.0*(-32.0/3.0*xi+704.0/9.0*xi*xi-512.0/3.0*xi*xi*xi+1024.0/9.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 3: return Point<2>((25.0/3.0-140.0/3.0*xi+80.0*xi*xi-128.0/3.0*xi*xi*xi)*eta+(-550.0/9.0+3080.0/9.0*xi-1760.0/3.0*xi*xi+2816.0/9.0*xi*xi*xi)*eta*eta+(400.0/3.0-2240.0/3.0*xi+1280.0*xi*xi-2048.0/3.0*xi*xi*xi)*eta*eta*eta+(-800.0/9.0+4480.0/9.0*xi-2560.0/3.0*xi*xi+4096.0/9.0*xi*xi*xi)*eta*eta*eta*eta,
+ -1.0+25.0/3.0*xi-70.0/3.0*xi*xi+80.0/3.0*xi*xi*xi-32.0/3.0*xi*xi*xi*xi+2.0*(22.0/3.0-550.0/9.0*xi+1540.0/9.0*xi*xi-1760.0/9.0*xi*xi*xi+704.0/9.0*xi*xi*xi*xi)*eta+3.0*(-16.0+400.0/3.0*xi-1120.0/3.0*xi*xi+1280.0/3.0*xi*xi*xi-512.0/3.0*xi*xi*xi*xi)*eta*eta+4.0*(32.0/3.0-800.0/9.0*xi+2240.0/9.0*xi*xi-2560.0/9.0*xi*xi*xi+1024.0/9.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 4: return Point<2>(16.0-416.0/3.0*xi+288.0*xi*xi-512.0/3.0*xi*xi*xi+(-400.0/3.0+10400.0/9.0*xi-2400.0*xi*xi+12800.0/9.0*xi*xi*xi)*eta+(1120.0/3.0-29120.0/9.0*xi+6720.0*xi*xi-35840.0/9.0*xi*xi*xi)*eta*eta+(-1280.0/3.0+33280.0/9.0*xi-7680.0*xi*xi+40960.0/9.0*xi*xi*xi)*eta*eta*eta+(512.0/3.0-13312.0/9.0*xi+3072.0*xi*xi-16384.0/9.0*xi*xi*xi)*eta*eta*eta*eta,
+ -400.0/3.0*xi+5200.0/9.0*xi*xi-800.0*xi*xi*xi+3200.0/9.0*xi*xi*xi*xi+2.0*(1120.0/3.0*xi-14560.0/9.0*xi*xi+2240.0*xi*xi*xi-8960.0/9.0*xi*xi*xi*xi)*eta+3.0*(-1280.0/3.0*xi+16640.0/9.0*xi*xi-2560.0*xi*xi*xi+10240.0/9.0*xi*xi*xi*xi)*eta*eta+4.0*(512.0/3.0*xi-6656.0/9.0*xi*xi+1024.0*xi*xi*xi-4096.0/9.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 5: return Point<2>(-12.0+152.0*xi-384.0*xi*xi+256.0*xi*xi*xi+(100.0-3800.0/3.0*xi+3200.0*xi*xi-6400.0/3.0*xi*xi*xi)*eta+(-280.0+10640.0/3.0*xi-8960.0*xi*xi+17920.0/3.0*xi*xi*xi)*eta*eta+(320.0-12160.0/3.0*xi+10240.0*xi*xi-20480.0/3.0*xi*xi*xi)*eta*eta*eta+(-128.0+4864.0/3.0*xi-4096.0*xi*xi+8192.0/3.0*xi*xi*xi)*eta*eta*eta*eta,
+ 100.0*xi-1900.0/3.0*xi*xi+3200.0/3.0*xi*xi*xi-1600.0/3.0*xi*xi*xi*xi+2.0*(-280.0*xi+5320.0/3.0*xi*xi-8960.0/3.0*xi*xi*xi+4480.0/3.0*xi*xi*xi*xi)*eta+3.0*(320.0*xi-6080.0/3.0*xi*xi+10240.0/3.0*xi*xi*xi-5120.0/3.0*xi*xi*xi*xi)*eta*eta+4.0*(-128.0*xi+2432.0/3.0*xi*xi-4096.0/3.0*xi*xi*xi+2048.0/3.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 6: return Point<2>(16.0/3.0-224.0/3.0*xi+224.0*xi*xi-512.0/3.0*xi*xi*xi+(-400.0/9.0+5600.0/9.0*xi-5600.0/3.0*xi*xi+12800.0/9.0*xi*xi*xi)*eta+(1120.0/9.0-15680.0/9.0*xi+15680.0/3.0*xi*xi-35840.0/9.0*xi*xi*xi)*eta*eta+(-1280.0/9.0+17920.0/9.0*xi-17920.0/3.0*xi*xi+40960.0/9.0*xi*xi*xi)*eta*eta*eta+(512.0/9.0-7168.0/9.0*xi+7168.0/3.0*xi*xi-16384.0/9.0*xi*xi*xi)*eta*eta*eta*eta,
+ -400.0/9.0*xi+2800.0/9.0*xi*xi-5600.0/9.0*xi*xi*xi+3200.0/9.0*xi*xi*xi*xi+2.0*(1120.0/9.0*xi-7840.0/9.0*xi*xi+15680.0/9.0*xi*xi*xi-8960.0/9.0*xi*xi*xi*xi)*eta+3.0*(-1280.0/9.0*xi+8960.0/9.0*xi*xi-17920.0/9.0*xi*xi*xi+10240.0/9.0*xi*xi*xi*xi)*eta*eta+4.0*(512.0/9.0*xi-3584.0/9.0*xi*xi+7168.0/9.0*xi*xi*xi-4096.0/9.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 7: return Point<2>((-16.0+704.0/3.0*xi-768.0*xi*xi+2048.0/3.0*xi*xi*xi)*eta+(208.0/3.0-9152.0/9.0*xi+3328.0*xi*xi-26624.0/9.0*xi*xi*xi)*eta*eta+(-96.0+1408.0*xi-4608.0*xi*xi+4096.0*xi*xi*xi)*eta*eta*eta+(128.0/3.0-5632.0/9.0*xi+2048.0*xi*xi-16384.0/9.0*xi*xi*xi)*eta*eta*eta*eta,
+ -16.0*xi+352.0/3.0*xi*xi-256.0*xi*xi*xi+512.0/3.0*xi*xi*xi*xi+2.0*(208.0/3.0*xi-4576.0/9.0*xi*xi+3328.0/3.0*xi*xi*xi-6656.0/9.0*xi*xi*xi*xi)*eta+3.0*(-96.0*xi+704.0*xi*xi-1536.0*xi*xi*xi+1024.0*xi*xi*xi*xi)*eta*eta+4.0*(128.0/3.0*xi-2816.0/9.0*xi*xi+2048.0/3.0*xi*xi*xi-4096.0/9.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 8: return Point<2>((12.0-176.0*xi+576.0*xi*xi-512.0*xi*xi*xi)*eta+(-76.0+3344.0/3.0*xi-3648.0*xi*xi+9728.0/3.0*xi*xi*xi)*eta*eta+(128.0-5632.0/3.0*xi+6144.0*xi*xi-16384.0/3.0*xi*xi*xi)*eta*eta*eta+(-64.0+2816.0/3.0*xi-3072.0*xi*xi+8192.0/3.0*xi*xi*xi)*eta*eta*eta*eta,
+ 12.0*xi-88.0*xi*xi+192.0*xi*xi*xi-128.0*xi*xi*xi*xi+2.0*(-76.0*xi+1672.0/3.0*xi*xi-1216.0*xi*xi*xi+2432.0/3.0*xi*xi*xi*xi)*eta+3.0*(128.0*xi-2816.0/3.0*xi*xi+2048.0*xi*xi*xi-4096.0/3.0*xi*xi*xi*xi)*eta*eta+4.0*(-64.0*xi+1408.0/3.0*xi*xi-1024.0*xi*xi*xi+2048.0/3.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 9: return Point<2>((-16.0/3.0+704.0/9.0*xi-256.0*xi*xi+2048.0/9.0*xi*xi*xi)*eta+(112.0/3.0-4928.0/9.0*xi+1792.0*xi*xi-14336.0/9.0*xi*xi*xi)*eta*eta+(-224.0/3.0+9856.0/9.0*xi-3584.0*xi*xi+28672.0/9.0*xi*xi*xi)*eta*eta*eta+(128.0/3.0-5632.0/9.0*xi+2048.0*xi*xi-16384.0/9.0*xi*xi*xi)*eta*eta*eta*eta,
+ -16.0/3.0*xi+352.0/9.0*xi*xi-256.0/3.0*xi*xi*xi+512.0/9.0*xi*xi*xi*xi+2.0*(112.0/3.0*xi-2464.0/9.0*xi*xi+1792.0/3.0*xi*xi*xi-3584.0/9.0*xi*xi*xi*xi)*eta+3.0*(-224.0/3.0*xi+4928.0/9.0*xi*xi-3584.0/3.0*xi*xi*xi+7168.0/9.0*xi*xi*xi*xi)*eta*eta+4.0*(128.0/3.0*xi-2816.0/9.0*xi*xi+2048.0/3.0*xi*xi*xi-4096.0/9.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 10: return Point<2>((-16.0+416.0/3.0*xi-288.0*xi*xi+512.0/3.0*xi*xi*xi)*eta+(352.0/3.0-9152.0/9.0*xi+2112.0*xi*xi-11264.0/9.0*xi*xi*xi)*eta*eta+(-256.0+6656.0/3.0*xi-4608.0*xi*xi+8192.0/3.0*xi*xi*xi)*eta*eta*eta+(512.0/3.0-13312.0/9.0*xi+3072.0*xi*xi-16384.0/9.0*xi*xi*xi)*eta*eta*eta*eta,
+ -16.0*xi+208.0/3.0*xi*xi-96.0*xi*xi*xi+128.0/3.0*xi*xi*xi*xi+2.0*(352.0/3.0*xi-4576.0/9.0*xi*xi+704.0*xi*xi*xi-2816.0/9.0*xi*xi*xi*xi)*eta+3.0*(-256.0*xi+3328.0/3.0*xi*xi-1536.0*xi*xi*xi+2048.0/3.0*xi*xi*xi*xi)*eta*eta+4.0*(512.0/3.0*xi-6656.0/9.0*xi*xi+1024.0*xi*xi*xi-4096.0/9.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 11: return Point<2>((12.0-152.0*xi+384.0*xi*xi-256.0*xi*xi*xi)*eta+(-88.0+3344.0/3.0*xi-2816.0*xi*xi+5632.0/3.0*xi*xi*xi)*eta*eta+(192.0-2432.0*xi+6144.0*xi*xi-4096.0*xi*xi*xi)*eta*eta*eta+(-128.0+4864.0/3.0*xi-4096.0*xi*xi+8192.0/3.0*xi*xi*xi)*eta*eta*eta*eta,
+ 12.0*xi-76.0*xi*xi+128.0*xi*xi*xi-64.0*xi*xi*xi*xi+2.0*(-88.0*xi+1672.0/3.0*xi*xi-2816.0/3.0*xi*xi*xi+1408.0/3.0*xi*xi*xi*xi)*eta+3.0*(192.0*xi-1216.0*xi*xi+2048.0*xi*xi*xi-1024.0*xi*xi*xi*xi)*eta*eta+4.0*(-128.0*xi+2432.0/3.0*xi*xi-4096.0/3.0*xi*xi*xi+2048.0/3.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 12: return Point<2>((-16.0/3.0+224.0/3.0*xi-224.0*xi*xi+512.0/3.0*xi*xi*xi)*eta+(352.0/9.0-4928.0/9.0*xi+4928.0/3.0*xi*xi-11264.0/9.0*xi*xi*xi)*eta*eta+(-256.0/3.0+3584.0/3.0*xi-3584.0*xi*xi+8192.0/3.0*xi*xi*xi)*eta*eta*eta+(512.0/9.0-7168.0/9.0*xi+7168.0/3.0*xi*xi-16384.0/9.0*xi*xi*xi)*eta*eta*eta*eta,
+ -16.0/3.0*xi+112.0/3.0*xi*xi-224.0/3.0*xi*xi*xi+128.0/3.0*xi*xi*xi*xi+2.0*(352.0/9.0*xi-2464.0/9.0*xi*xi+4928.0/9.0*xi*xi*xi-2816.0/9.0*xi*xi*xi*xi)*eta+3.0*(-256.0/3.0*xi+1792.0/3.0*xi*xi-3584.0/3.0*xi*xi*xi+2048.0/3.0*xi*xi*xi*xi)*eta*eta+4.0*(512.0/9.0*xi-3584.0/9.0*xi*xi+7168.0/9.0*xi*xi*xi-4096.0/9.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 13: return Point<2>((-400.0/3.0+2240.0/3.0*xi-1280.0*xi*xi+2048.0/3.0*xi*xi*xi)*eta+(5200.0/9.0-29120.0/9.0*xi+16640.0/3.0*xi*xi-26624.0/9.0*xi*xi*xi)*eta*eta+(-800.0+4480.0*xi-7680.0*xi*xi+4096.0*xi*xi*xi)*eta*eta*eta+(3200.0/9.0-17920.0/9.0*xi+10240.0/3.0*xi*xi-16384.0/9.0*xi*xi*xi)*eta*eta*eta*eta,
+ 16.0-400.0/3.0*xi+1120.0/3.0*xi*xi-1280.0/3.0*xi*xi*xi+512.0/3.0*xi*xi*xi*xi+2.0*(-208.0/3.0+5200.0/9.0*xi-14560.0/9.0*xi*xi+16640.0/9.0*xi*xi*xi-6656.0/9.0*xi*xi*xi*xi)*eta+3.0*(96.0-800.0*xi+2240.0*xi*xi-2560.0*xi*xi*xi+1024.0*xi*xi*xi*xi)*eta*eta+4.0*(-128.0/3.0+3200.0/9.0*xi-8960.0/9.0*xi*xi+10240.0/9.0*xi*xi*xi-4096.0/9.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 14: return Point<2>((100.0-560.0*xi+960.0*xi*xi-512.0*xi*xi*xi)*eta+(-1900.0/3.0+10640.0/3.0*xi-6080.0*xi*xi+9728.0/3.0*xi*xi*xi)*eta*eta+(3200.0/3.0-17920.0/3.0*xi+10240.0*xi*xi-16384.0/3.0*xi*xi*xi)*eta*eta*eta+(-1600.0/3.0+8960.0/3.0*xi-5120.0*xi*xi+8192.0/3.0*xi*xi*xi)*eta*eta*eta*eta,
+ -12.0+100.0*xi-280.0*xi*xi+320.0*xi*xi*xi-128.0*xi*xi*xi*xi+2.0*(76.0-1900.0/3.0*xi+5320.0/3.0*xi*xi-6080.0/3.0*xi*xi*xi+2432.0/3.0*xi*xi*xi*xi)*eta+3.0*(-128.0+3200.0/3.0*xi-8960.0/3.0*xi*xi+10240.0/3.0*xi*xi*xi-4096.0/3.0*xi*xi*xi*xi)*eta*eta+4.0*(64.0-1600.0/3.0*xi+4480.0/3.0*xi*xi-5120.0/3.0*xi*xi*xi+2048.0/3.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 15: return Point<2>((-400.0/9.0+2240.0/9.0*xi-1280.0/3.0*xi*xi+2048.0/9.0*xi*xi*xi)*eta+(2800.0/9.0-15680.0/9.0*xi+8960.0/3.0*xi*xi-14336.0/9.0*xi*xi*xi)*eta*eta+(-5600.0/9.0+31360.0/9.0*xi-17920.0/3.0*xi*xi+28672.0/9.0*xi*xi*xi)*eta*eta*eta+(3200.0/9.0-17920.0/9.0*xi+10240.0/3.0*xi*xi-16384.0/9.0*xi*xi*xi)*eta*eta*eta*eta,
+ 16.0/3.0-400.0/9.0*xi+1120.0/9.0*xi*xi-1280.0/9.0*xi*xi*xi+512.0/9.0*xi*xi*xi*xi+2.0*(-112.0/3.0+2800.0/9.0*xi-7840.0/9.0*xi*xi+8960.0/9.0*xi*xi*xi-3584.0/9.0*xi*xi*xi*xi)*eta+3.0*(224.0/3.0-5600.0/9.0*xi+15680.0/9.0*xi*xi-17920.0/9.0*xi*xi*xi+7168.0/9.0*xi*xi*xi*xi)*eta*eta+4.0*(-128.0/3.0+3200.0/9.0*xi-8960.0/9.0*xi*xi+10240.0/9.0*xi*xi*xi-4096.0/9.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 16: return Point<2>((256.0-6656.0/3.0*xi+4608.0*xi*xi-8192.0/3.0*xi*xi*xi)*eta+(-3328.0/3.0+86528.0/9.0*xi-19968.0*xi*xi+106496.0/9.0*xi*xi*xi)*eta*eta+(1536.0-13312.0*xi+27648.0*xi*xi-16384.0*xi*xi*xi)*eta*eta*eta+(-2048.0/3.0+53248.0/9.0*xi-12288.0*xi*xi+65536.0/9.0*xi*xi*xi)*eta*eta*eta*eta,
+ 256.0*xi-3328.0/3.0*xi*xi+1536.0*xi*xi*xi-2048.0/3.0*xi*xi*xi*xi+2.0*(-3328.0/3.0*xi+43264.0/9.0*xi*xi-6656.0*xi*xi*xi+26624.0/9.0*xi*xi*xi*xi)*eta+3.0*(1536.0*xi-6656.0*xi*xi+9216.0*xi*xi*xi-4096.0*xi*xi*xi*xi)*eta*eta+4.0*(-2048.0/3.0*xi+26624.0/9.0*xi*xi-4096.0*xi*xi*xi+16384.0/9.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 17: return Point<2>((256.0/3.0-3584.0/3.0*xi+3584.0*xi*xi-8192.0/3.0*xi*xi*xi)*eta+(-3328.0/9.0+46592.0/9.0*xi-46592.0/3.0*xi*xi+106496.0/9.0*xi*xi*xi)*eta*eta+(512.0-7168.0*xi+21504.0*xi*xi-16384.0*xi*xi*xi)*eta*eta*eta+(-2048.0/9.0+28672.0/9.0*xi-28672.0/3.0*xi*xi+65536.0/9.0*xi*xi*xi)*eta*eta*eta*eta,
+ 256.0/3.0*xi-1792.0/3.0*xi*xi+3584.0/3.0*xi*xi*xi-2048.0/3.0*xi*xi*xi*xi+2.0*(-3328.0/9.0*xi+23296.0/9.0*xi*xi-46592.0/9.0*xi*xi*xi+26624.0/9.0*xi*xi*xi*xi)*eta+3.0*(512.0*xi-3584.0*xi*xi+7168.0*xi*xi*xi-4096.0*xi*xi*xi*xi)*eta*eta+4.0*(-2048.0/9.0*xi+14336.0/9.0*xi*xi-28672.0/9.0*xi*xi*xi+16384.0/9.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 18: return Point<2>((256.0/9.0-3584.0/9.0*xi+3584.0/3.0*xi*xi-8192.0/9.0*xi*xi*xi)*eta+(-1792.0/9.0+25088.0/9.0*xi-25088.0/3.0*xi*xi+57344.0/9.0*xi*xi*xi)*eta*eta+(3584.0/9.0-50176.0/9.0*xi+50176.0/3.0*xi*xi-114688.0/9.0*xi*xi*xi)*eta*eta*eta+(-2048.0/9.0+28672.0/9.0*xi-28672.0/3.0*xi*xi+65536.0/9.0*xi*xi*xi)*eta*eta*eta*eta,
+ 256.0/9.0*xi-1792.0/9.0*xi*xi+3584.0/9.0*xi*xi*xi-2048.0/9.0*xi*xi*xi*xi+2.0*(-1792.0/9.0*xi+12544.0/9.0*xi*xi-25088.0/9.0*xi*xi*xi+14336.0/9.0*xi*xi*xi*xi)*eta+3.0*(3584.0/9.0*xi-25088.0/9.0*xi*xi+50176.0/9.0*xi*xi*xi-28672.0/9.0*xi*xi*xi*xi)*eta*eta+4.0*(-2048.0/9.0*xi+14336.0/9.0*xi*xi-28672.0/9.0*xi*xi*xi+16384.0/9.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 19: return Point<2>((256.0/3.0-6656.0/9.0*xi+1536.0*xi*xi-8192.0/9.0*xi*xi*xi)*eta+(-1792.0/3.0+46592.0/9.0*xi-10752.0*xi*xi+57344.0/9.0*xi*xi*xi)*eta*eta+(3584.0/3.0-93184.0/9.0*xi+21504.0*xi*xi-114688.0/9.0*xi*xi*xi)*eta*eta*eta+(-2048.0/3.0+53248.0/9.0*xi-12288.0*xi*xi+65536.0/9.0*xi*xi*xi)*eta*eta*eta*eta,
+ 256.0/3.0*xi-3328.0/9.0*xi*xi+512.0*xi*xi*xi-2048.0/9.0*xi*xi*xi*xi+2.0*(-1792.0/3.0*xi+23296.0/9.0*xi*xi-3584.0*xi*xi*xi+14336.0/9.0*xi*xi*xi*xi)*eta+3.0*(3584.0/3.0*xi-46592.0/9.0*xi*xi+7168.0*xi*xi*xi-28672.0/9.0*xi*xi*xi*xi)*eta*eta+4.0*(-2048.0/3.0*xi+26624.0/9.0*xi*xi-4096.0*xi*xi*xi+16384.0/9.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 20: return Point<2>((-192.0+2432.0*xi-6144.0*xi*xi+4096.0*xi*xi*xi)*eta+(832.0-31616.0/3.0*xi+26624.0*xi*xi-53248.0/3.0*xi*xi*xi)*eta*eta+(-1152.0+14592.0*xi-36864.0*xi*xi+24576.0*xi*xi*xi)*eta*eta*eta+(512.0-19456.0/3.0*xi+16384.0*xi*xi-32768.0/3.0*xi*xi*xi)*eta*eta*eta*eta,
+ -192.0*xi+1216.0*xi*xi-2048.0*xi*xi*xi+1024.0*xi*xi*xi*xi+2.0*(832.0*xi-15808.0/3.0*xi*xi+26624.0/3.0*xi*xi*xi-13312.0/3.0*xi*xi*xi*xi)*eta+3.0*(-1152.0*xi+7296.0*xi*xi-12288.0*xi*xi*xi+6144.0*xi*xi*xi*xi)*eta*eta+4.0*(512.0*xi-9728.0/3.0*xi*xi+16384.0/3.0*xi*xi*xi-8192.0/3.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 21: return Point<2>((-64.0+896.0*xi-2688.0*xi*xi+2048.0*xi*xi*xi)*eta+(1216.0/3.0-17024.0/3.0*xi+17024.0*xi*xi-38912.0/3.0*xi*xi*xi)*eta*eta+(-2048.0/3.0+28672.0/3.0*xi-28672.0*xi*xi+65536.0/3.0*xi*xi*xi)*eta*eta*eta+(1024.0/3.0-14336.0/3.0*xi+14336.0*xi*xi-32768.0/3.0*xi*xi*xi)*eta*eta*eta*eta,
+ -64.0*xi+448.0*xi*xi-896.0*xi*xi*xi+512.0*xi*xi*xi*xi+2.0*(1216.0/3.0*xi-8512.0/3.0*xi*xi+17024.0/3.0*xi*xi*xi-9728.0/3.0*xi*xi*xi*xi)*eta+3.0*(-2048.0/3.0*xi+14336.0/3.0*xi*xi-28672.0/3.0*xi*xi*xi+16384.0/3.0*xi*xi*xi*xi)*eta*eta+4.0*(1024.0/3.0*xi-7168.0/3.0*xi*xi+14336.0/3.0*xi*xi*xi-8192.0/3.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 22: return Point<2>((-64.0+2432.0/3.0*xi-2048.0*xi*xi+4096.0/3.0*xi*xi*xi)*eta+(448.0-17024.0/3.0*xi+14336.0*xi*xi-28672.0/3.0*xi*xi*xi)*eta*eta+(-896.0+34048.0/3.0*xi-28672.0*xi*xi+57344.0/3.0*xi*xi*xi)*eta*eta*eta+(512.0-19456.0/3.0*xi+16384.0*xi*xi-32768.0/3.0*xi*xi*xi)*eta*eta*eta*eta,
+ -64.0*xi+1216.0/3.0*xi*xi-2048.0/3.0*xi*xi*xi+1024.0/3.0*xi*xi*xi*xi+2.0*(448.0*xi-8512.0/3.0*xi*xi+14336.0/3.0*xi*xi*xi-7168.0/3.0*xi*xi*xi*xi)*eta+3.0*(-896.0*xi+17024.0/3.0*xi*xi-28672.0/3.0*xi*xi*xi+14336.0/3.0*xi*xi*xi*xi)*eta*eta+4.0*(512.0*xi-9728.0/3.0*xi*xi+16384.0/3.0*xi*xi*xi-8192.0/3.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 23: return Point<2>((-192.0+1664.0*xi-3456.0*xi*xi+2048.0*xi*xi*xi)*eta+(1216.0-31616.0/3.0*xi+21888.0*xi*xi-38912.0/3.0*xi*xi*xi)*eta*eta+(-2048.0+53248.0/3.0*xi-36864.0*xi*xi+65536.0/3.0*xi*xi*xi)*eta*eta*eta+(1024.0-26624.0/3.0*xi+18432.0*xi*xi-32768.0/3.0*xi*xi*xi)*eta*eta*eta*eta,
+ -192.0*xi+832.0*xi*xi-1152.0*xi*xi*xi+512.0*xi*xi*xi*xi+2.0*(1216.0*xi-15808.0/3.0*xi*xi+7296.0*xi*xi*xi-9728.0/3.0*xi*xi*xi*xi)*eta+3.0*(-2048.0*xi+26624.0/3.0*xi*xi-12288.0*xi*xi*xi+16384.0/3.0*xi*xi*xi*xi)*eta*eta+4.0*(1024.0*xi-13312.0/3.0*xi*xi+6144.0*xi*xi*xi-8192.0/3.0*xi*xi*xi*xi)*eta*eta*eta);
+ case 24: return Point<2>((144.0-1824.0*xi+4608.0*xi*xi-3072.0*xi*xi*xi)*eta+(-912.0+11552.0*xi-29184.0*xi*xi+19456.0*xi*xi*xi)*eta*eta+(1536.0-19456.0*xi+49152.0*xi*xi-32768.0*xi*xi*xi)*eta*eta*eta+(-768.0+9728.0*xi-24576.0*xi*xi+16384.0*xi*xi*xi)*eta*eta*eta*eta,
+ 144.0*xi-912.0*xi*xi+1536.0*xi*xi*xi-768.0*xi*xi*xi*xi+2.0*(-912.0*xi+5776.0*xi*xi-9728.0*xi*xi*xi+4864.0*xi*xi*xi*xi)*eta+3.0*(1536.0*xi-9728.0*xi*xi+16384.0*xi*xi*xi-8192.0*xi*xi*xi*xi)*eta*eta+4.0*(-768.0*xi+4864.0*xi*xi-8192.0*xi*xi*xi+4096.0*xi*xi*xi*xi)*eta*eta*eta);
+ };
+ return Point<2> ();
+};
+
+
+
+template <>
+inline
+Point<2>
+FEQuarticSub<2>::linear_shape_grad (const unsigned int i,
+ const Point<2>& p) const
+{
+ Assert((i<4), ExcInvalidIndex(i));
+ switch (i)
+ {
+ case 0: return Point<2> (p(1)-1., p(0)-1.);
+ case 1: return Point<2> (1.-p(1), -p(0));
+ case 2: return Point<2> (p(1), p(0));
+ case 3: return Point<2> (-p(1), 1.-p(0));
+ }
+ return Point<2> ();
+};
+
+
+
+template <>
+void FEQuarticSub<2>::get_local_mass_matrix (const DoFHandler<2>::cell_iterator &cell,
+ const Boundary<2> &,
+ dFMatrix &local_mass_matrix) const {
+ Assert (local_mass_matrix.n() == total_dofs,
+ ExcWrongFieldDimension(local_mass_matrix.n(),total_dofs));
+ Assert (local_mass_matrix.m() == total_dofs,
+ ExcWrongFieldDimension(local_mass_matrix.m(),total_dofs));
+
+ const double x[4] = { cell->vertex(0)(0),
+ cell->vertex(1)(0),
+ cell->vertex(2)(0),
+ cell->vertex(3)(0) };
+ const double y[4] = { cell->vertex(0)(1),
+ cell->vertex(1)(1),
+ cell->vertex(2)(1),
+ cell->vertex(3)(1) };
+
+/* check that the Jacobi determinant
+
+ t0 = (-x[0]*(1.0-eta)+x[1]*(1.0-eta)+x[2]*eta-x[3]*eta) *
+ (-y[0]*(1.0-xi)-y[1]*xi+y[2]*xi+y[3]*(1.0-xi)) -
+ (-x[0]*(1.0-xi)-x[1]*xi+x[2]*xi+x[3]*(1.0-xi)) *
+ (-y[0]*(1.0-eta)+y[1]*(1.0-eta)+y[2]*eta-y[3]*eta)
+
+ has the right sign.
+
+ We do not attempt to check its (hopefully) positive sign at all points
+ on the unit cell, but we check that it is positive in the four corners,
+ which is sufficient since $det J$ is a bilinear function.
+*/
+ Assert ((-x[0]+x[1])*(-y[0]+y[3])-(-x[0]+x[3])*(-y[0]+y[1]), // xi=eta=0
+ ExcJacobiDeterminantHasWrongSign());
+ Assert ((x[2]-x[3])*(-y[0]+y[3])-(-x[0]+x[3])*(y[2]-y[3]), // xi=0, eta=1
+ ExcJacobiDeterminantHasWrongSign());
+ Assert ((x[2]-x[3])*(-y[1]+y[2])-(-x[1]+x[2])*(y[2]-y[3]), // xi=eta=1
+ ExcJacobiDeterminantHasWrongSign());
+ Assert ((-x[0]+x[1])*(-y[1]+y[2])-(-x[1]+x[2])*(-y[0]+y[1]), // xi=1, eta=0
+ ExcJacobiDeterminantHasWrongSign());
+
+ const double t1 = -x[0]+x[1];
+ const double t2 = y[0]-y[1]+y[2]-y[3];
+ const double t3 = t1*t2;
+ const double t4 = 2117.0/16074450.0*t3;
+ const double t5 = x[0]-x[1]+x[2]-x[3];
+ const double t6 = -y[0]+y[1];
+ const double t7 = t5*t6;
+ const double t8 = 2117.0/16074450.0*t7;
+ const double t9 = -y[0]+y[3];
+ const double t10 = t1*t9;
+ const double t11 = 21316.0/8037225.0*t10;
+ const double t12 = t5*t9;
+ const double t13 = 2117.0/16074450.0*t12;
+ const double t14 = -x[0]+x[3];
+ const double t15 = t14*t6;
+ const double t16 = 21316.0/8037225.0*t15;
+ const double t17 = t14*t2;
+ const double t18 = 2117.0/16074450.0*t17;
+ const double t20 = 2117.0/8037225.0*t10;
+ const double t21 = 841.0/64297800.0*t12;
+ const double t22 = 2117.0/8037225.0*t15;
+ const double t23 = 841.0/64297800.0*t17;
+ const double t24 = -t4+t8-t20-t21+t22+t23;
+ const double t25 = 841.0/64297800.0*t3;
+ const double t26 = 841.0/64297800.0*t7;
+ const double t29 = t25-t26+841.0/32148900.0*t10+t21-841.0/32148900.0*t15-t23;
+ const double t30 = -t25+t26-t20-t13+t22+t18;
+ const double t31 = 1168.0/8037225.0*t3;
+ const double t32 = 1168.0/8037225.0*t7;
+ const double t33 = 21608.0/8037225.0*t10;
+ const double t34 = 1073.0/8037225.0*t12;
+ const double t35 = 21608.0/8037225.0*t15;
+ const double t36 = 1073.0/8037225.0*t17;
+ const double t37 = t31-t32+t33+t34-t35-t36;
+ const double t38 = 4234.0/2679075.0*t10;
+ const double t39 = 841.0/10716300.0*t12;
+ const double t40 = 4234.0/2679075.0*t15;
+ const double t41 = 841.0/10716300.0*t17;
+ const double t42 = -t38-t39+t40+t41;
+ const double t43 = 584.0/1148175.0*t10;
+ const double t44 = 29.0/1148175.0*t12;
+ const double t45 = 584.0/1148175.0*t15;
+ const double t46 = 29.0/1148175.0*t17;
+ const double t47 = -t31+t32+t43+t44-t45-t46;
+ const double t48 = 1073.0/8037225.0*t3;
+ const double t49 = 1073.0/8037225.0*t7;
+ const double t50 = 2146.0/8037225.0*t10;
+ const double t51 = 116.0/8037225.0*t12;
+ const double t52 = 2146.0/8037225.0*t15;
+ const double t53 = 116.0/8037225.0*t17;
+ const double t54 = -t48+t49-t50-t51+t52+t53;
+ const double t55 = 841.0/10716300.0*t3;
+ const double t56 = 841.0/10716300.0*t7;
+ const double t57 = 841.0/5358150.0*t10;
+ const double t58 = 841.0/5358150.0*t15;
+ const double t59 = t55-t56+t57-t58;
+ const double t60 = 29.0/1148175.0*t3;
+ const double t61 = 29.0/1148175.0*t7;
+ const double t62 = 58.0/1148175.0*t10;
+ const double t63 = 58.0/1148175.0*t15;
+ const double t64 = -t60+t61-t62+t51+t63-t53;
+ const double t65 = 116.0/8037225.0*t3;
+ const double t66 = 116.0/8037225.0*t7;
+ const double t67 = -t65+t66-t50-t34+t52+t36;
+ const double t68 = t57+t39-t58-t41;
+ const double t69 = t65-t66-t62-t44+t63+t46;
+ const double t70 = 1168.0/8037225.0*t12;
+ const double t71 = 1168.0/8037225.0*t17;
+ const double t72 = t48-t49+t33+t70-t35-t71;
+ const double t73 = -t55+t56-t38+t40;
+ const double t74 = t60-t61+t43-t70-t45+t71;
+ const double t75 = 1184.0/8037225.0*t3;
+ const double t76 = 1184.0/8037225.0*t7;
+ const double t77 = 21904.0/8037225.0*t10;
+ const double t78 = 1184.0/8037225.0*t12;
+ const double t79 = 21904.0/8037225.0*t15;
+ const double t80 = 1184.0/8037225.0*t17;
+ const double t81 = t75-t76+t77+t78-t79-t80;
+ const double t82 = 592.0/1148175.0*t10;
+ const double t83 = 32.0/1148175.0*t12;
+ const double t84 = 592.0/1148175.0*t15;
+ const double t85 = 32.0/1148175.0*t17;
+ const double t86 = -t75+t76+t82+t83-t84-t85;
+ const double t87 = 32.0/1148175.0*t3;
+ const double t88 = 32.0/1148175.0*t7;
+ const double t89 = 16.0/164025.0*t10;
+ const double t90 = 16.0/164025.0*t15;
+ const double t91 = -t87+t88+t89-t83-t90+t85;
+ const double t92 = t87-t88+t82-t78-t84+t80;
+ const double t93 = 4292.0/2679075.0*t10;
+ const double t94 = 232.0/2679075.0*t12;
+ const double t95 = 4292.0/2679075.0*t15;
+ const double t96 = 232.0/2679075.0*t17;
+ const double t97 = -t93-t94+t95+t96;
+ const double t98 = 232.0/2679075.0*t3;
+ const double t99 = 232.0/2679075.0*t7;
+ const double t100 = 116.0/382725.0*t10;
+ const double t101 = 116.0/382725.0*t15;
+ const double t102 = t98-t99-t100+t101;
+ const double t103 = -t100+t94+t101-t96;
+ const double t104 = -t98+t99-t93+t95;
+ const double t105 = t10-t15;
+ const double t106 = 2701.0/1071630.0*t3;
+ const double t107 = 2701.0/1071630.0*t7;
+ const double t111 = -1073.0/4286520.0*t3+1073.0/4286520.0*t7-t20-t13+t22+t18;
+ const double t112 = 584.0/893025.0*t3;
+ const double t113 = 584.0/893025.0*t7;
+ const double t114 = t112-t113+t43+t44-t45-t46;
+ const double t115 = 4234.0/2679075.0*t3;
+ const double t116 = 4234.0/2679075.0*t7;
+ const double t117 = -t115+t116-t38-t39+t40+t41;
+ const double t118 = 584.0/229635.0*t3;
+ const double t119 = 584.0/229635.0*t7;
+ const double t120 = t118-t119+t33+t34-t35-t36;
+ const double t121 = 1369.0/535815.0*t3;
+ const double t122 = 1369.0/535815.0*t7;
+ const double t123 = t121-t122+t33+t70-t35-t71;
+ const double t124 = 1073.0/714420.0*t3;
+ const double t125 = 1073.0/714420.0*t7;
+ const double t126 = -t124+t125-t38+t40;
+ const double t127 = 37.0/76545.0*t3;
+ const double t128 = 37.0/76545.0*t7;
+ const double t129 = t127-t128+t43-t70-t45+t71;
+ const double t132 = -58.0/893025.0*t3+58.0/893025.0*t7-t62-t44+t63+t46;
+ const double t135 = 841.0/5358150.0*t3-841.0/5358150.0*t7+t57+t39-t58-t41;
+ const double t138 = -58.0/229635.0*t3+58.0/229635.0*t7-t50-t34+t52+t36;
+ const double t139 = 592.0/893025.0*t3;
+ const double t140 = 592.0/893025.0*t7;
+ const double t141 = t139-t140+t82+t83-t84-t85;
+ const double t142 = 592.0/229635.0*t3;
+ const double t143 = 592.0/229635.0*t7;
+ const double t144 = t142-t143+t77+t78-t79-t80;
+ const double t145 = 16.0/32805.0*t3;
+ const double t146 = 16.0/32805.0*t7;
+ const double t147 = t145-t146+t82-t78-t84+t80;
+ const double t148 = 16.0/127575.0*t3;
+ const double t149 = 16.0/127575.0*t7;
+ const double t150 = t148-t149+t89-t83-t90+t85;
+ const double t151 = 4292.0/2679075.0*t3;
+ const double t152 = 4292.0/2679075.0*t7;
+ const double t153 = -t151+t152-t93-t94+t95+t96;
+ const double t154 = 116.0/76545.0*t3;
+ const double t155 = 116.0/76545.0*t7;
+ const double t156 = -t154+t155-t93+t95;
+ const double t157 = 116.0/382725.0*t3;
+ const double t158 = 116.0/382725.0*t7;
+ const double t159 = -t157+t158-t100+t94+t101-t96;
+ const double t160 = 116.0/297675.0*t3;
+ const double t161 = 116.0/297675.0*t7;
+ const double t162 = -t160+t161-t100+t101;
+ const double t163 = t3-t7+t10-t15;
+ const double t164 = 2701.0/1071630.0*t12;
+ const double t165 = 2701.0/1071630.0*t17;
+ const double t169 = -t4+t8-t20-1073.0/4286520.0*t12+t22+1073.0/4286520.0*t17;
+ const double t170 = 584.0/893025.0*t12;
+ const double t171 = 584.0/893025.0*t17;
+ const double t172 = t127-t128+t43+t170-t45-t171;
+ const double t173 = 4234.0/2679075.0*t12;
+ const double t174 = 4234.0/2679075.0*t17;
+ const double t175 = -t124+t125-t38-t173+t40+t174;
+ const double t176 = 584.0/229635.0*t12;
+ const double t177 = 584.0/229635.0*t17;
+ const double t178 = t121-t122+t33+t176-t35-t177;
+ const double t179 = 37.0/76545.0*t12;
+ const double t180 = 37.0/76545.0*t17;
+ const double t181 = t112-t113+t43+t179-t45-t180;
+ const double t182 = 1073.0/714420.0*t12;
+ const double t183 = 1073.0/714420.0*t17;
+ const double t184 = -t115+t116-t38-t182+t40+t183;
+ const double t185 = 1369.0/535815.0*t12;
+ const double t186 = 1369.0/535815.0*t17;
+ const double t187 = t118-t119+t33+t185-t35-t186;
+ const double t190 = -t60+t61-t62-58.0/893025.0*t12+t63+58.0/893025.0*t17;
+ const double t193 = t55-t56+t57+841.0/5358150.0*t12-t58-841.0/5358150.0*t17;
+ const double t196 = -t48+t49-t50-58.0/229635.0*t12+t52+58.0/229635.0*t17;
+ const double t197 = 16.0/127575.0*t12;
+ const double t198 = 16.0/127575.0*t17;
+ const double t199 = t148-t149+t89+t197-t90-t198;
+ const double t200 = 592.0/893025.0*t12;
+ const double t201 = 592.0/893025.0*t17;
+ const double t202 = t145-t146+t82+t200-t84-t201;
+ const double t203 = 592.0/229635.0*t12;
+ const double t204 = 592.0/229635.0*t17;
+ const double t205 = t142-t143+t77+t203-t79-t204;
+ const double t206 = 16.0/32805.0*t12;
+ const double t207 = 16.0/32805.0*t17;
+ const double t208 = t139-t140+t82+t206-t84-t207;
+ const double t209 = 116.0/297675.0*t12;
+ const double t210 = 116.0/297675.0*t17;
+ const double t211 = -t157+t158-t100-t209+t101+t210;
+ const double t212 = 4292.0/2679075.0*t12;
+ const double t213 = 4292.0/2679075.0*t17;
+ const double t214 = -t154+t155-t93-t212+t95+t213;
+ const double t215 = 116.0/76545.0*t12;
+ const double t216 = 116.0/76545.0*t17;
+ const double t217 = -t151+t152-t93-t215+t95+t216;
+ const double t218 = 116.0/382725.0*t12;
+ const double t219 = 116.0/382725.0*t17;
+ const double t220 = -t160+t161-t100-t218+t101+t219;
+ const double t221 = t3-t7+t10+t12-t15-t17;
+ const double t223 = t31-t32+t33+t185-t35-t186;
+ const double t224 = -t38-t182+t40+t183;
+ const double t225 = -t31+t32+t43+t179-t45-t180;
+ const double t226 = t60-t61+t43+t170-t45-t171;
+ const double t227 = -t55+t56-t38-t173+t40+t174;
+ const double t228 = t48-t49+t33+t176-t35-t177;
+ const double t229 = t87-t88+t82+t200-t84-t201;
+ const double t230 = -t87+t88+t89+t197-t90-t198;
+ const double t231 = -t75+t76+t82+t206-t84-t207;
+ const double t232 = t75-t76+t77+t203-t79-t204;
+ const double t233 = -t100-t209+t101+t210;
+ const double t234 = t98-t99-t100-t218+t101+t219;
+ const double t235 = -t93-t215+t95+t216;
+ const double t236 = -t98+t99-t93-t212+t95+t213;
+ const double t237 = t10+t12-t15-t17;
+ const double t238 = 9344.0/2679075.0*t3;
+ const double t239 = 9344.0/2679075.0*t7;
+ const double t240 = 18688.0/1148175.0*t10;
+ const double t241 = 928.0/1148175.0*t12;
+ const double t242 = 18688.0/1148175.0*t15;
+ const double t243 = 928.0/1148175.0*t17;
+ const double t245 = 2336.0/2679075.0*t3;
+ const double t246 = 2336.0/2679075.0*t7;
+ const double t247 = 9344.0/2679075.0*t10;
+ const double t248 = 464.0/2679075.0*t12;
+ const double t249 = 9344.0/2679075.0*t15;
+ const double t250 = 464.0/2679075.0*t17;
+ const double t251 = -t245+t246-t247-t248+t249+t250;
+ const double t252 = 9344.0/8037225.0*t3;
+ const double t253 = 9344.0/8037225.0*t7;
+ const double t254 = 18688.0/8037225.0*t10;
+ const double t255 = 928.0/8037225.0*t12;
+ const double t256 = 18688.0/8037225.0*t15;
+ const double t257 = 928.0/8037225.0*t17;
+ const double t258 = t252-t253+t254+t255-t256-t257;
+ const double t261 = 1856.0/1148175.0*t10;
+ const double t262 = 1856.0/1148175.0*t15;
+ const double t263 = -928.0/2679075.0*t3+928.0/2679075.0*t7-t261-t241+t262+t243;
+ const double t264 = 928.0/2679075.0*t10;
+ const double t265 = 928.0/2679075.0*t15;
+ const double t266 = t98-t99+t264+t248-t265-t250;
+ const double t267 = 928.0/8037225.0*t3;
+ const double t268 = 928.0/8037225.0*t7;
+ const double t271 = -t267+t268-1856.0/8037225.0*t10-t255+1856.0/8037225.0*t15+t257;
+ const double t272 = 9472.0/2679075.0*t3;
+ const double t273 = 9472.0/2679075.0*t7;
+ const double t274 = 18944.0/1148175.0*t10;
+ const double t275 = 1024.0/1148175.0*t12;
+ const double t276 = 18944.0/1148175.0*t15;
+ const double t277 = 1024.0/1148175.0*t17;
+ const double t278 = t272-t273+t274+t275-t276-t277;
+ const double t279 = 9472.0/8037225.0*t3;
+ const double t280 = 9472.0/8037225.0*t7;
+ const double t281 = 18944.0/8037225.0*t10;
+ const double t282 = 1024.0/8037225.0*t12;
+ const double t283 = 18944.0/8037225.0*t15;
+ const double t284 = 1024.0/8037225.0*t17;
+ const double t285 = t279-t280+t281+t282-t283-t284;
+ const double t286 = 256.0/1148175.0*t3;
+ const double t287 = 256.0/1148175.0*t7;
+ const double t288 = 512.0/1148175.0*t10;
+ const double t289 = 512.0/1148175.0*t15;
+ const double t290 = t286-t287+t288-t282-t289+t284;
+ const double t291 = 256.0/382725.0*t3;
+ const double t292 = 256.0/382725.0*t7;
+ const double t293 = 512.0/164025.0*t10;
+ const double t294 = 512.0/164025.0*t15;
+ const double t295 = t291-t292+t293-t275-t294+t277;
+ const double t296 = 2368.0/2679075.0*t3;
+ const double t297 = 2368.0/2679075.0*t7;
+ const double t298 = 9472.0/2679075.0*t10;
+ const double t299 = 512.0/2679075.0*t12;
+ const double t300 = 9472.0/2679075.0*t15;
+ const double t301 = 512.0/2679075.0*t17;
+ const double t302 = -t296+t297-t298-t299+t300+t301;
+ const double t303 = 1856.0/2679075.0*t3;
+ const double t304 = 1856.0/2679075.0*t7;
+ const double t305 = 3712.0/2679075.0*t10;
+ const double t306 = 3712.0/2679075.0*t15;
+ const double t307 = -t303+t304-t305+t306;
+ const double t308 = 64.0/382725.0*t3;
+ const double t309 = 64.0/382725.0*t7;
+ const double t310 = 256.0/382725.0*t10;
+ const double t311 = 256.0/382725.0*t15;
+ const double t312 = -t308+t309-t310+t299+t311-t301;
+ const double t313 = 1856.0/893025.0*t3;
+ const double t314 = 1856.0/893025.0*t7;
+ const double t315 = 3712.0/382725.0*t10;
+ const double t316 = 3712.0/382725.0*t15;
+ const double t317 = -t313+t314-t315+t316;
+ const double t318 = 464.0/893025.0*t3;
+ const double t319 = 464.0/893025.0*t7;
+ const double t320 = 1856.0/893025.0*t10;
+ const double t321 = 1856.0/893025.0*t15;
+ const double t322 = t318-t319+t320-t321;
+ const double t323 = 7592.0/893025.0*t3;
+ const double t324 = 7592.0/893025.0*t7;
+ const double t325 = 15184.0/893025.0*t10;
+ const double t326 = 754.0/893025.0*t12;
+ const double t327 = 15184.0/893025.0*t15;
+ const double t328 = 754.0/893025.0*t17;
+ const double t330 = 2336.0/893025.0*t3;
+ const double t331 = 2336.0/893025.0*t7;
+ const double t332 = -t330+t331-t247-t248+t249+t250;
+ const double t333 = 754.0/893025.0*t3;
+ const double t334 = 754.0/893025.0*t7;
+ const double t337 = -t333+t334-1508.0/893025.0*t10-t326+1508.0/893025.0*t15+t328;
+ const double t340 = 232.0/893025.0*t3-232.0/893025.0*t7+t264+t248-t265-t250;
+ const double t341 = 2368.0/893025.0*t3;
+ const double t342 = 2368.0/893025.0*t7;
+ const double t343 = -t341+t342-t298-t299+t300+t301;
+ const double t344 = 64.0/127575.0*t3;
+ const double t345 = 64.0/127575.0*t7;
+ const double t346 = -t344+t345-t310+t299+t311-t301;
+ const double t347 = 7696.0/893025.0*t3;
+ const double t348 = 7696.0/893025.0*t7;
+ const double t349 = 15392.0/893025.0*t10;
+ const double t350 = 832.0/893025.0*t12;
+ const double t351 = 15392.0/893025.0*t15;
+ const double t352 = 832.0/893025.0*t17;
+ const double t353 = t347-t348+t349+t350-t351-t352;
+ const double t354 = 464.0/297675.0*t3;
+ const double t355 = 464.0/297675.0*t7;
+ const double t356 = t354-t355+t320-t321;
+ const double t357 = 208.0/127575.0*t3;
+ const double t358 = 208.0/127575.0*t7;
+ const double t359 = 416.0/127575.0*t10;
+ const double t360 = 416.0/127575.0*t15;
+ const double t361 = t357-t358+t359-t350-t360+t352;
+ const double t362 = 1508.0/297675.0*t3;
+ const double t363 = 1508.0/297675.0*t7;
+ const double t364 = 3016.0/297675.0*t10;
+ const double t365 = 3016.0/297675.0*t15;
+ const double t366 = -t362+t363-t364+t365;
+ const double t367 = 102784.0/8037225.0*t3;
+ const double t368 = 102784.0/8037225.0*t7;
+ const double t372 = -10208.0/8037225.0*t3+10208.0/8037225.0*t7-t261-t241+t262+t243;
+ const double t373 = 104192.0/8037225.0*t3;
+ const double t374 = 104192.0/8037225.0*t7;
+ const double t375 = t373-t374+t274+t275-t276-t277;
+ const double t376 = 2816.0/1148175.0*t3;
+ const double t377 = 2816.0/1148175.0*t7;
+ const double t378 = t376-t377+t293-t275-t294+t277;
+ const double t379 = 20416.0/2679075.0*t3;
+ const double t380 = 20416.0/2679075.0*t7;
+ const double t381 = -t379+t380-t315+t316;
+ const double t382 = 1184.0/76545.0*t3;
+ const double t383 = 1184.0/76545.0*t7;
+ const double t384 = 9344.0/2679075.0*t12;
+ const double t385 = 9344.0/2679075.0*t17;
+ const double t387 = 592.0/178605.0*t3;
+ const double t388 = 592.0/178605.0*t7;
+ const double t389 = 2336.0/2679075.0*t12;
+ const double t390 = 2336.0/2679075.0*t17;
+ const double t391 = -t387+t388-t247-t389+t249+t390;
+ const double t394 = 9344.0/8037225.0*t12;
+ const double t395 = 9344.0/8037225.0*t17;
+ const double t396 = 1184.0/535815.0*t3-1184.0/535815.0*t7+t254+t394-t256-t395;
+ const double t397 = 928.0/1148175.0*t3;
+ const double t398 = 928.0/1148175.0*t7;
+ const double t401 = -t397+t398-t261-928.0/2679075.0*t12+t262+928.0/2679075.0*t17;
+ const double t402 = 464.0/2679075.0*t3;
+ const double t403 = 464.0/2679075.0*t7;
+ const double t404 = t402-t403+t264+t94-t265-t96;
+ const double t405 = 512.0/127575.0*t3;
+ const double t406 = 512.0/127575.0*t7;
+ const double t407 = 256.0/382725.0*t12;
+ const double t408 = 256.0/382725.0*t17;
+ const double t409 = t405-t406+t293+t407-t294-t408;
+ const double t410 = 512.0/32805.0*t3;
+ const double t411 = 512.0/32805.0*t7;
+ const double t412 = 9472.0/2679075.0*t12;
+ const double t413 = 9472.0/2679075.0*t17;
+ const double t414 = t410-t411+t274+t412-t276-t413;
+ const double t417 = 9472.0/8037225.0*t12;
+ const double t418 = 9472.0/8037225.0*t17;
+ const double t419 = 512.0/229635.0*t3-512.0/229635.0*t7+t281+t417-t283-t418;
+ const double t422 = 256.0/1148175.0*t12;
+ const double t423 = 256.0/1148175.0*t17;
+ const double t424 = 512.0/893025.0*t3-512.0/893025.0*t7+t288+t422-t289-t423;
+ const double t425 = 3712.0/382725.0*t3;
+ const double t426 = 3712.0/382725.0*t7;
+ const double t427 = 1856.0/893025.0*t12;
+ const double t428 = 1856.0/893025.0*t17;
+ const double t429 = -t425+t426-t315-t427+t316+t428;
+ const double t430 = 256.0/76545.0*t3;
+ const double t431 = 256.0/76545.0*t7;
+ const double t432 = 2368.0/2679075.0*t12;
+ const double t433 = 2368.0/2679075.0*t17;
+ const double t434 = -t430+t431-t298-t432+t300+t433;
+ const double t437 = 1856.0/2679075.0*t12;
+ const double t438 = 1856.0/2679075.0*t17;
+ const double t439 = -3712.0/2679075.0*t3+3712.0/2679075.0*t7-t305-t437+t306+t438;
+ const double t440 = 256.0/297675.0*t3;
+ const double t441 = 256.0/297675.0*t7;
+ const double t442 = 64.0/382725.0*t12;
+ const double t443 = 64.0/382725.0*t17;
+ const double t444 = -t440+t441-t310-t442+t311+t443;
+ const double t445 = 464.0/893025.0*t12;
+ const double t446 = 464.0/893025.0*t17;
+ const double t447 = t313-t314+t320+t445-t321-t446;
+ const double t450 = 7592.0/893025.0*t12;
+ const double t451 = 7592.0/893025.0*t17;
+ const double t453 = 2336.0/893025.0*t12;
+ const double t454 = 2336.0/893025.0*t17;
+ const double t455 = -t387+t388-t247-t453+t249+t454;
+ const double t458 = t402-t403+t264+232.0/893025.0*t12-t265-232.0/893025.0*t17;
+ const double t459 = 2368.0/893025.0*t12;
+ const double t460 = 2368.0/893025.0*t17;
+ const double t461 = -t430+t431-t298-t459+t300+t460;
+ const double t462 = 64.0/127575.0*t12;
+ const double t463 = 64.0/127575.0*t17;
+ const double t464 = -t440+t441-t310-t462+t311+t463;
+ const double t467 = 7696.0/893025.0*t12;
+ const double t468 = 7696.0/893025.0*t17;
+ const double t469 = 416.0/25515.0*t3-416.0/25515.0*t7+t349+t467-t351-t468;
+ const double t470 = 464.0/297675.0*t12;
+ const double t471 = 464.0/297675.0*t17;
+ const double t472 = t313-t314+t320+t470-t321-t471;
+ const double t475 = 208.0/127575.0*t12;
+ const double t476 = 208.0/127575.0*t17;
+ const double t477 = 416.0/99225.0*t3-416.0/99225.0*t7+t359+t475-t360-t476;
+ const double t480 = 1508.0/297675.0*t12;
+ const double t481 = 1508.0/297675.0*t17;
+ const double t482 = -3016.0/297675.0*t3+3016.0/297675.0*t7-t364-t480+t365+t481;
+ const double t483 = 102784.0/8037225.0*t12;
+ const double t484 = 102784.0/8037225.0*t17;
+ const double t488 = -t397+t398-t261-10208.0/8037225.0*t12+t262+10208.0/8037225.0*t17;
+ const double t489 = 104192.0/8037225.0*t12;
+ const double t490 = 104192.0/8037225.0*t17;
+ const double t491 = t410-t411+t274+t489-t276-t490;
+ const double t492 = 2816.0/1148175.0*t12;
+ const double t493 = 2816.0/1148175.0*t17;
+ const double t494 = t405-t406+t293+t492-t294-t493;
+ const double t495 = 20416.0/2679075.0*t12;
+ const double t496 = 20416.0/2679075.0*t17;
+ const double t497 = -t425+t426-t315-t495+t316+t496;
+ const double t498 = 1184.0/76545.0*t12;
+ const double t499 = 1184.0/76545.0*t17;
+ const double t501 = 592.0/178605.0*t12;
+ const double t502 = 592.0/178605.0*t17;
+ const double t503 = -t245+t246-t247-t501+t249+t502;
+ const double t506 = t252-t253+t254+1184.0/535815.0*t12-t256-1184.0/535815.0*t17;
+ const double t507 = 512.0/127575.0*t12;
+ const double t508 = 512.0/127575.0*t17;
+ const double t509 = t291-t292+t293+t507-t294-t508;
+ const double t512 = t286-t287+t288+512.0/893025.0*t12-t289-512.0/893025.0*t17;
+ const double t515 = t279-t280+t281+512.0/229635.0*t12-t283-512.0/229635.0*t17;
+ const double t516 = 512.0/32805.0*t12;
+ const double t517 = 512.0/32805.0*t17;
+ const double t518 = t272-t273+t274+t516-t276-t517;
+ const double t519 = 256.0/297675.0*t12;
+ const double t520 = 256.0/297675.0*t17;
+ const double t521 = -t308+t309-t310-t519+t311+t520;
+ const double t524 = -t303+t304-t305-3712.0/2679075.0*t12+t306+3712.0/2679075.0*t17;
+ const double t525 = 256.0/76545.0*t12;
+ const double t526 = 256.0/76545.0*t17;
+ const double t527 = -t296+t297-t298-t525+t300+t526;
+ const double t528 = 3712.0/382725.0*t12;
+ const double t529 = 3712.0/382725.0*t17;
+ const double t530 = -t313+t314-t315-t528+t316+t529;
+ const double t531 = t318-t319+t320+t427-t321-t428;
+ const double t535 = -t330+t331-t247-t501+t249+t502;
+ const double t536 = -t344+t345-t310-t519+t311+t520;
+ const double t537 = -t341+t342-t298-t525+t300+t526;
+ const double t540 = t357-t358+t359+416.0/99225.0*t12-t360-416.0/99225.0*t17;
+ const double t541 = t354-t355+t320+t427-t321-t428;
+ const double t544 = t347-t348+t349+416.0/25515.0*t12-t351-416.0/25515.0*t17;
+ const double t547 = -t362+t363-t364-3016.0/297675.0*t12+t365+3016.0/297675.0*t17;
+ const double t549 = t376-t377+t293+t507-t294-t508;
+ const double t550 = t373-t374+t274+t516-t276-t517;
+ const double t551 = -t379+t380-t315-t528+t316+t529;
+ const double t553 = -t402+t403-t247-t389+t249+t390;
+ const double t554 = t267-t268+t254+t394-t256-t395;
+ const double t555 = 1024.0/1148175.0*t3;
+ const double t556 = 1024.0/1148175.0*t7;
+ const double t557 = t555-t556+t274+t412-t276-t413;
+ const double t558 = -t555+t556+t293+t407-t294-t408;
+ const double t559 = 1024.0/8037225.0*t3;
+ const double t560 = 1024.0/8037225.0*t7;
+ const double t561 = -t559+t560+t288+t422-t289-t423;
+ const double t562 = t559-t560+t281+t417-t283-t418;
+ const double t563 = -t315-t427+t316+t428;
+ const double t564 = 512.0/2679075.0*t3;
+ const double t565 = 512.0/2679075.0*t7;
+ const double t566 = t564-t565-t310-t442+t311+t443;
+ const double t567 = -t305-t437+t306+t438;
+ const double t568 = -t564+t565-t298-t432+t300+t433;
+ const double t569 = t320+t445-t321-t446;
+ const double t571 = -t402+t403-t247-t453+t249+t454;
+ const double t572 = t564-t565-t310-t462+t311+t463;
+ const double t573 = -t564+t565-t298-t459+t300+t460;
+ const double t574 = 832.0/893025.0*t3;
+ const double t575 = 832.0/893025.0*t7;
+ const double t576 = -t574+t575+t359+t475-t360-t476;
+ const double t577 = t320+t470-t321-t471;
+ const double t578 = t574-t575+t349+t467-t351-t468;
+ const double t579 = -t364-t480+t365+t481;
+ const double t581 = -t555+t556+t293+t492-t294-t493;
+ const double t582 = t555-t556+t274+t489-t276-t490;
+ const double t583 = -t315-t495+t316+t496;
+ const double t584 = 8192.0/382725.0*t3;
+ const double t585 = 8192.0/382725.0*t7;
+ const double t586 = 16384.0/164025.0*t10;
+ const double t587 = 8192.0/382725.0*t12;
+ const double t588 = 16384.0/164025.0*t15;
+ const double t589 = 8192.0/382725.0*t17;
+ const double t591 = 8192.0/1148175.0*t3;
+ const double t592 = 8192.0/1148175.0*t7;
+ const double t593 = 16384.0/1148175.0*t10;
+ const double t595 = 16384.0/1148175.0*t15;
+ const double t597 = t591-t592+t593+8192.0/2679075.0*t12-t595-8192.0/2679075.0*t17;
+ const double t604 = 8192.0/8037225.0*t3-8192.0/8037225.0*t7+16384.0/8037225.0*t10+
+8192.0/8037225.0*t12-16384.0/8037225.0*t15-8192.0/8037225.0*t17;
+ const double t607 = 8192.0/1148175.0*t12;
+ const double t608 = 8192.0/1148175.0*t17;
+ const double t609 = 8192.0/2679075.0*t3-8192.0/2679075.0*t7+t593+t607-t595-t608;
+ const double t610 = 2048.0/382725.0*t3;
+ const double t611 = 2048.0/382725.0*t7;
+ const double t612 = 8192.0/382725.0*t10;
+ const double t613 = 4096.0/893025.0*t12;
+ const double t614 = 8192.0/382725.0*t15;
+ const double t615 = 4096.0/893025.0*t17;
+ const double t616 = -t610+t611-t612-t613+t614+t615;
+ const double t617 = 4096.0/2679075.0*t3;
+ const double t618 = 4096.0/2679075.0*t7;
+ const double t619 = 8192.0/2679075.0*t10;
+ const double t621 = 8192.0/2679075.0*t15;
+ const double t623 = -t617+t618-t619-2048.0/2679075.0*t12+t621+2048.0/2679075.0*t17;
+ const double t626 = 4096.0/2679075.0*t12;
+ const double t627 = 4096.0/2679075.0*t17;
+ const double t628 = -2048.0/2679075.0*t3+2048.0/2679075.0*t7-t619-t626+t621+t627;
+ const double t629 = 4096.0/893025.0*t3;
+ const double t630 = 4096.0/893025.0*t7;
+ const double t631 = 2048.0/382725.0*t12;
+ const double t632 = 2048.0/382725.0*t17;
+ const double t633 = -t629+t630-t612-t631+t614+t632;
+ const double t634 = 1024.0/893025.0*t3;
+ const double t635 = 1024.0/893025.0*t7;
+ const double t636 = 4096.0/893025.0*t10;
+ const double t637 = 1024.0/893025.0*t12;
+ const double t638 = 4096.0/893025.0*t15;
+ const double t639 = 1024.0/893025.0*t17;
+ const double t640 = t634-t635+t636+t637-t638-t639;
+ const double t641 = 90112.0/1148175.0*t3;
+ const double t642 = 90112.0/1148175.0*t7;
+ const double t646 = 90112.0/8037225.0*t3-90112.0/8037225.0*t7+t593+t607-t595-t608;
+ const double t647 = 2048.0/127575.0*t3;
+ const double t648 = 2048.0/127575.0*t7;
+ const double t649 = -t647+t648-t612-t613+t614+t615;
+ const double t650 = 45056.0/2679075.0*t3;
+ const double t651 = 45056.0/2679075.0*t7;
+ const double t652 = -t650+t651-t612-t631+t614+t632;
+ const double t655 = -2048.0/893025.0*t3+2048.0/893025.0*t7-t619-t626+t621+t627;
+ const double t656 = 1024.0/297675.0*t3;
+ const double t657 = 1024.0/297675.0*t7;
+ const double t658 = t656-t657+t636+t637-t638-t639;
+ const double t659 = 90112.0/1148175.0*t12;
+ const double t660 = 90112.0/1148175.0*t17;
+ const double t664 = t591-t592+t593+90112.0/8037225.0*t12-t595-90112.0/8037225.0*t17;
+ const double t665 = 2048.0/127575.0*t12;
+ const double t666 = 2048.0/127575.0*t17;
+ const double t667 = -t650+t651-t612-t665+t614+t666;
+ const double t668 = 45056.0/2679075.0*t12;
+ const double t669 = 45056.0/2679075.0*t17;
+ const double t670 = -t647+t648-t612-t668+t614+t669;
+ const double t673 = -t617+t618-t619-2048.0/893025.0*t12+t621+2048.0/893025.0*t17;
+ const double t674 = 1024.0/297675.0*t12;
+ const double t675 = 1024.0/297675.0*t17;
+ const double t676 = t656-t657+t636+t674-t638-t675;
+ const double t678 = -t610+t611-t612-t668+t614+t669;
+ const double t679 = -t629+t630-t612-t665+t614+t666;
+ const double t680 = t634-t635+t636+t674-t638-t675;
+ const double t681 = 6656.0/127575.0*t3;
+ const double t682 = 6656.0/127575.0*t7;
+ const double t683 = 13312.0/127575.0*t10;
+ const double t685 = 13312.0/127575.0*t15;
+ const double t694 = 6656.0/893025.0*t3-6656.0/893025.0*t7+13312.0/893025.0*t10+6656.0/
+893025.0*t12-13312.0/893025.0*t15-6656.0/893025.0*t17;
+ const double t695 = 3328.0/297675.0*t3;
+ const double t696 = 3328.0/297675.0*t7;
+ const double t697 = 6656.0/297675.0*t10;
+ const double t699 = 6656.0/297675.0*t15;
+ const double t701 = -t695+t696-t697-1664.0/297675.0*t12+t699+1664.0/297675.0*t17;
+ const double t704 = 6656.0/127575.0*t12;
+ const double t705 = 6656.0/127575.0*t17;
+ const double t709 = 3328.0/297675.0*t12;
+ const double t710 = 3328.0/297675.0*t17;
+ const double t711 = -1664.0/99225.0*t3+1664.0/99225.0*t7-t697-t709+t699+t710;
+ const double t717 = -t695+t696-t697-1664.0/99225.0*t12+t699+1664.0/99225.0*t17;
+ const double t723 = -1664.0/297675.0*t3+1664.0/297675.0*t7-t697-t709+t699+t710;
+ local_mass_matrix(0,0) = t4-t8+t11+t13-t16-t18;
+ local_mass_matrix(0,1) = t24;
+ local_mass_matrix(0,2) = t29;
+ local_mass_matrix(0,3) = t30;
+ local_mass_matrix(0,4) = t37;
+ local_mass_matrix(0,5) = t42;
+ local_mass_matrix(0,6) = t47;
+ local_mass_matrix(0,7) = t54;
+ local_mass_matrix(0,8) = t59;
+ local_mass_matrix(0,9) = t64;
+ local_mass_matrix(0,10) = t67;
+ local_mass_matrix(0,11) = t68;
+ local_mass_matrix(0,12) = t69;
+ local_mass_matrix(0,13) = t72;
+ local_mass_matrix(0,14) = t73;
+ local_mass_matrix(0,15) = t74;
+ local_mass_matrix(0,16) = t81;
+ local_mass_matrix(0,17) = t86;
+ local_mass_matrix(0,18) = t91;
+ local_mass_matrix(0,19) = t92;
+ local_mass_matrix(0,20) = t97;
+ local_mass_matrix(0,21) = t102;
+ local_mass_matrix(0,22) = t103;
+ local_mass_matrix(0,23) = t104;
+ local_mass_matrix(0,24) = 841.0/893025.0*t105;
+ local_mass_matrix(1,0) = t24;
+ local_mass_matrix(1,1) = t106-t107+t11+t13-t16-t18;
+ local_mass_matrix(1,2) = t111;
+ local_mass_matrix(1,3) = t29;
+ local_mass_matrix(1,4) = t114;
+ local_mass_matrix(1,5) = t117;
+ local_mass_matrix(1,6) = t120;
+ local_mass_matrix(1,7) = t123;
+ local_mass_matrix(1,8) = t126;
+ local_mass_matrix(1,9) = t129;
+ local_mass_matrix(1,10) = t132;
+ local_mass_matrix(1,11) = t135;
+ local_mass_matrix(1,12) = t138;
+ local_mass_matrix(1,13) = t54;
+ local_mass_matrix(1,14) = t59;
+ local_mass_matrix(1,15) = t64;
+ local_mass_matrix(1,16) = t141;
+ local_mass_matrix(1,17) = t144;
+ local_mass_matrix(1,18) = t147;
+ local_mass_matrix(1,19) = t150;
+ local_mass_matrix(1,20) = t153;
+ local_mass_matrix(1,21) = t156;
+ local_mass_matrix(1,22) = t159;
+ local_mass_matrix(1,23) = t162;
+ local_mass_matrix(1,24) = 841.0/893025.0*t163;
+ local_mass_matrix(2,0) = t29;
+ local_mass_matrix(2,1) = t111;
+ local_mass_matrix(2,2) = t106-t107+t11+t164-t16-t165;
+ local_mass_matrix(2,3) = t169;
+ local_mass_matrix(2,4) = t132;
+ local_mass_matrix(2,5) = t135;
+ local_mass_matrix(2,6) = t138;
+ local_mass_matrix(2,7) = t172;
+ local_mass_matrix(2,8) = t175;
+ local_mass_matrix(2,9) = t178;
+ local_mass_matrix(2,10) = t181;
+ local_mass_matrix(2,11) = t184;
+ local_mass_matrix(2,12) = t187;
+ local_mass_matrix(2,13) = t190;
+ local_mass_matrix(2,14) = t193;
+ local_mass_matrix(2,15) = t196;
+ local_mass_matrix(2,16) = t199;
+ local_mass_matrix(2,17) = t202;
+ local_mass_matrix(2,18) = t205;
+ local_mass_matrix(2,19) = t208;
+ local_mass_matrix(2,20) = t211;
+ local_mass_matrix(2,21) = t214;
+ local_mass_matrix(2,22) = t217;
+ local_mass_matrix(2,23) = t220;
+ local_mass_matrix(2,24) = 841.0/893025.0*t221;
+ local_mass_matrix(3,0) = t30;
+ local_mass_matrix(3,1) = t29;
+ local_mass_matrix(3,2) = t169;
+ local_mass_matrix(3,3) = t4-t8+t11+t164-t16-t165;
+ local_mass_matrix(3,4) = t67;
+ local_mass_matrix(3,5) = t68;
+ local_mass_matrix(3,6) = t69;
+ local_mass_matrix(3,7) = t190;
+ local_mass_matrix(3,8) = t193;
+ local_mass_matrix(3,9) = t196;
+ local_mass_matrix(3,10) = t223;
+ local_mass_matrix(3,11) = t224;
+ local_mass_matrix(3,12) = t225;
+ local_mass_matrix(3,13) = t226;
+ local_mass_matrix(3,14) = t227;
+ local_mass_matrix(3,15) = t228;
+ local_mass_matrix(3,16) = t229;
+ local_mass_matrix(3,17) = t230;
+ local_mass_matrix(3,18) = t231;
+ local_mass_matrix(3,19) = t232;
+ local_mass_matrix(3,20) = t233;
+ local_mass_matrix(3,21) = t234;
+ local_mass_matrix(3,22) = t235;
+ local_mass_matrix(3,23) = t236;
+ local_mass_matrix(3,24) = 841.0/893025.0*t237;
+ local_mass_matrix(4,0) = t37;
+ local_mass_matrix(4,1) = t114;
+ local_mass_matrix(4,2) = t132;
+ local_mass_matrix(4,3) = t67;
+ local_mass_matrix(4,4) = t238-t239+t240+t241-t242-t243;
+ local_mass_matrix(4,5) = t251;
+ local_mass_matrix(4,6) = t258;
+ local_mass_matrix(4,7) = t141;
+ local_mass_matrix(4,8) = t162;
+ local_mass_matrix(4,9) = t150;
+ local_mass_matrix(4,10) = t263;
+ local_mass_matrix(4,11) = t266;
+ local_mass_matrix(4,12) = t271;
+ local_mass_matrix(4,13) = t81;
+ local_mass_matrix(4,14) = t104;
+ local_mass_matrix(4,15) = t92;
+ local_mass_matrix(4,16) = t278;
+ local_mass_matrix(4,17) = t285;
+ local_mass_matrix(4,18) = t290;
+ local_mass_matrix(4,19) = t295;
+ local_mass_matrix(4,20) = t302;
+ local_mass_matrix(4,21) = t307;
+ local_mass_matrix(4,22) = t312;
+ local_mass_matrix(4,23) = t317;
+ local_mass_matrix(4,24) = t322;
+ local_mass_matrix(5,0) = t42;
+ local_mass_matrix(5,1) = t117;
+ local_mass_matrix(5,2) = t135;
+ local_mass_matrix(5,3) = t68;
+ local_mass_matrix(5,4) = t251;
+ local_mass_matrix(5,5) = t323-t324+t325+t326-t327-t328;
+ local_mass_matrix(5,6) = t332;
+ local_mass_matrix(5,7) = t153;
+ local_mass_matrix(5,8) = 841.0/893025.0*t163;
+ local_mass_matrix(5,9) = t159;
+ local_mass_matrix(5,10) = t266;
+ local_mass_matrix(5,11) = t337;
+ local_mass_matrix(5,12) = t340;
+ local_mass_matrix(5,13) = t97;
+ local_mass_matrix(5,14) = 841.0/893025.0*t105;
+ local_mass_matrix(5,15) = t103;
+ local_mass_matrix(5,16) = t302;
+ local_mass_matrix(5,17) = t343;
+ local_mass_matrix(5,18) = t346;
+ local_mass_matrix(5,19) = t312;
+ local_mass_matrix(5,20) = t353;
+ local_mass_matrix(5,21) = t356;
+ local_mass_matrix(5,22) = t361;
+ local_mass_matrix(5,23) = t322;
+ local_mass_matrix(5,24) = t366;
+ local_mass_matrix(6,0) = t47;
+ local_mass_matrix(6,1) = t120;
+ local_mass_matrix(6,2) = t138;
+ local_mass_matrix(6,3) = t69;
+ local_mass_matrix(6,4) = t258;
+ local_mass_matrix(6,5) = t332;
+ local_mass_matrix(6,6) = t367-t368+t240+t241-t242-t243;
+ local_mass_matrix(6,7) = t144;
+ local_mass_matrix(6,8) = t156;
+ local_mass_matrix(6,9) = t147;
+ local_mass_matrix(6,10) = t271;
+ local_mass_matrix(6,11) = t340;
+ local_mass_matrix(6,12) = t372;
+ local_mass_matrix(6,13) = t86;
+ local_mass_matrix(6,14) = t102;
+ local_mass_matrix(6,15) = t91;
+ local_mass_matrix(6,16) = t285;
+ local_mass_matrix(6,17) = t375;
+ local_mass_matrix(6,18) = t378;
+ local_mass_matrix(6,19) = t290;
+ local_mass_matrix(6,20) = t343;
+ local_mass_matrix(6,21) = t381;
+ local_mass_matrix(6,22) = t346;
+ local_mass_matrix(6,23) = t307;
+ local_mass_matrix(6,24) = t356;
+ local_mass_matrix(7,0) = t54;
+ local_mass_matrix(7,1) = t123;
+ local_mass_matrix(7,2) = t172;
+ local_mass_matrix(7,3) = t190;
+ local_mass_matrix(7,4) = t141;
+ local_mass_matrix(7,5) = t153;
+ local_mass_matrix(7,6) = t144;
+ local_mass_matrix(7,7) = t382-t383+t240+t384-t242-t385;
+ local_mass_matrix(7,8) = t391;
+ local_mass_matrix(7,9) = t396;
+ local_mass_matrix(7,10) = t199;
+ local_mass_matrix(7,11) = t211;
+ local_mass_matrix(7,12) = t202;
+ local_mass_matrix(7,13) = t401;
+ local_mass_matrix(7,14) = t404;
+ local_mass_matrix(7,15) = t271;
+ local_mass_matrix(7,16) = t409;
+ local_mass_matrix(7,17) = t414;
+ local_mass_matrix(7,18) = t419;
+ local_mass_matrix(7,19) = t424;
+ local_mass_matrix(7,20) = t429;
+ local_mass_matrix(7,21) = t434;
+ local_mass_matrix(7,22) = t439;
+ local_mass_matrix(7,23) = t444;
+ local_mass_matrix(7,24) = t447;
+ local_mass_matrix(8,0) = t59;
+ local_mass_matrix(8,1) = t126;
+ local_mass_matrix(8,2) = t175;
+ local_mass_matrix(8,3) = t193;
+ local_mass_matrix(8,4) = t162;
+ local_mass_matrix(8,5) = 841.0/893025.0*t163;
+ local_mass_matrix(8,6) = t156;
+ local_mass_matrix(8,7) = t391;
+ local_mass_matrix(8,8) = 962.0/59535.0*t3-962.0/59535.0*t7+t325+t450-
+t327-t451;
+ local_mass_matrix(8,9) = t455;
+ local_mass_matrix(8,10) = t220;
+ local_mass_matrix(8,11) = 841.0/893025.0*t221;
+ local_mass_matrix(8,12) = t214;
+ local_mass_matrix(8,13) = t404;
+ local_mass_matrix(8,14) = t337;
+ local_mass_matrix(8,15) = t458;
+ local_mass_matrix(8,16) = t444;
+ local_mass_matrix(8,17) = t434;
+ local_mass_matrix(8,18) = t461;
+ local_mass_matrix(8,19) = t464;
+ local_mass_matrix(8,20) = t447;
+ local_mass_matrix(8,21) = t469;
+ local_mass_matrix(8,22) = t472;
+ local_mass_matrix(8,23) = t477;
+ local_mass_matrix(8,24) = t482;
+ local_mass_matrix(9,0) = t64;
+ local_mass_matrix(9,1) = t129;
+ local_mass_matrix(9,2) = t178;
+ local_mass_matrix(9,3) = t196;
+ local_mass_matrix(9,4) = t150;
+ local_mass_matrix(9,5) = t159;
+ local_mass_matrix(9,6) = t147;
+ local_mass_matrix(9,7) = t396;
+ local_mass_matrix(9,8) = t455;
+ local_mass_matrix(9,9) = t382-t383+t240+t483-t242-t484;
+ local_mass_matrix(9,10) = t208;
+ local_mass_matrix(9,11) = t217;
+ local_mass_matrix(9,12) = t205;
+ local_mass_matrix(9,13) = t271;
+ local_mass_matrix(9,14) = t458;
+ local_mass_matrix(9,15) = t488;
+ local_mass_matrix(9,16) = t424;
+ local_mass_matrix(9,17) = t419;
+ local_mass_matrix(9,18) = t491;
+ local_mass_matrix(9,19) = t494;
+ local_mass_matrix(9,20) = t439;
+ local_mass_matrix(9,21) = t461;
+ local_mass_matrix(9,22) = t497;
+ local_mass_matrix(9,23) = t464;
+ local_mass_matrix(9,24) = t472;
+ local_mass_matrix(10,0) = t67;
+ local_mass_matrix(10,1) = t132;
+ local_mass_matrix(10,2) = t181;
+ local_mass_matrix(10,3) = t223;
+ local_mass_matrix(10,4) = t263;
+ local_mass_matrix(10,5) = t266;
+ local_mass_matrix(10,6) = t271;
+ local_mass_matrix(10,7) = t199;
+ local_mass_matrix(10,8) = t220;
+ local_mass_matrix(10,9) = t208;
+ local_mass_matrix(10,10) = t238-t239+t240+t498-t242-t499;
+ local_mass_matrix(10,11) = t503;
+ local_mass_matrix(10,12) = t506;
+ local_mass_matrix(10,13) = t229;
+ local_mass_matrix(10,14) = t236;
+ local_mass_matrix(10,15) = t232;
+ local_mass_matrix(10,16) = t509;
+ local_mass_matrix(10,17) = t512;
+ local_mass_matrix(10,18) = t515;
+ local_mass_matrix(10,19) = t518;
+ local_mass_matrix(10,20) = t521;
+ local_mass_matrix(10,21) = t524;
+ local_mass_matrix(10,22) = t527;
+ local_mass_matrix(10,23) = t530;
+ local_mass_matrix(10,24) = t531;
+ local_mass_matrix(11,0) = t68;
+ local_mass_matrix(11,1) = t135;
+ local_mass_matrix(11,2) = t184;
+ local_mass_matrix(11,3) = t224;
+ local_mass_matrix(11,4) = t266;
+ local_mass_matrix(11,5) = t337;
+ local_mass_matrix(11,6) = t340;
+ local_mass_matrix(11,7) = t211;
+ local_mass_matrix(11,8) = 841.0/893025.0*t221;
+ local_mass_matrix(11,9) = t217;
+ local_mass_matrix(11,10) = t503;
+ local_mass_matrix(11,11) = t323-t324+t325+962.0/59535.0*t12-t327-962.0/
+59535.0*t17;
+ local_mass_matrix(11,12) = t535;
+ local_mass_matrix(11,13) = t233;
+ local_mass_matrix(11,14) = 841.0/893025.0*t237;
+ local_mass_matrix(11,15) = t235;
+ local_mass_matrix(11,16) = t521;
+ local_mass_matrix(11,17) = t536;
+ local_mass_matrix(11,18) = t537;
+ local_mass_matrix(11,19) = t527;
+ local_mass_matrix(11,20) = t540;
+ local_mass_matrix(11,21) = t541;
+ local_mass_matrix(11,22) = t544;
+ local_mass_matrix(11,23) = t531;
+ local_mass_matrix(11,24) = t547;
+ local_mass_matrix(12,0) = t69;
+ local_mass_matrix(12,1) = t138;
+ local_mass_matrix(12,2) = t187;
+ local_mass_matrix(12,3) = t225;
+ local_mass_matrix(12,4) = t271;
+ local_mass_matrix(12,5) = t340;
+ local_mass_matrix(12,6) = t372;
+ local_mass_matrix(12,7) = t202;
+ local_mass_matrix(12,8) = t214;
+ local_mass_matrix(12,9) = t205;
+ local_mass_matrix(12,10) = t506;
+ local_mass_matrix(12,11) = t535;
+ local_mass_matrix(12,12) = t367-t368+t240+t498-t242-t499;
+ local_mass_matrix(12,13) = t230;
+ local_mass_matrix(12,14) = t234;
+ local_mass_matrix(12,15) = t231;
+ local_mass_matrix(12,16) = t512;
+ local_mass_matrix(12,17) = t549;
+ local_mass_matrix(12,18) = t550;
+ local_mass_matrix(12,19) = t515;
+ local_mass_matrix(12,20) = t536;
+ local_mass_matrix(12,21) = t551;
+ local_mass_matrix(12,22) = t537;
+ local_mass_matrix(12,23) = t524;
+ local_mass_matrix(12,24) = t541;
+ local_mass_matrix(13,0) = t72;
+ local_mass_matrix(13,1) = t54;
+ local_mass_matrix(13,2) = t190;
+ local_mass_matrix(13,3) = t226;
+ local_mass_matrix(13,4) = t81;
+ local_mass_matrix(13,5) = t97;
+ local_mass_matrix(13,6) = t86;
+ local_mass_matrix(13,7) = t401;
+ local_mass_matrix(13,8) = t404;
+ local_mass_matrix(13,9) = t271;
+ local_mass_matrix(13,10) = t229;
+ local_mass_matrix(13,11) = t233;
+ local_mass_matrix(13,12) = t230;
+ local_mass_matrix(13,13) = t397-t398+t240+t384-t242-t385;
+ local_mass_matrix(13,14) = t553;
+ local_mass_matrix(13,15) = t554;
+ local_mass_matrix(13,16) = t557;
+ local_mass_matrix(13,17) = t558;
+ local_mass_matrix(13,18) = t561;
+ local_mass_matrix(13,19) = t562;
+ local_mass_matrix(13,20) = t563;
+ local_mass_matrix(13,21) = t566;
+ local_mass_matrix(13,22) = t567;
+ local_mass_matrix(13,23) = t568;
+ local_mass_matrix(13,24) = t569;
+ local_mass_matrix(14,0) = t73;
+ local_mass_matrix(14,1) = t59;
+ local_mass_matrix(14,2) = t193;
+ local_mass_matrix(14,3) = t227;
+ local_mass_matrix(14,4) = t104;
+ local_mass_matrix(14,5) = 841.0/893025.0*t105;
+ local_mass_matrix(14,6) = t102;
+ local_mass_matrix(14,7) = t404;
+ local_mass_matrix(14,8) = t337;
+ local_mass_matrix(14,9) = t458;
+ local_mass_matrix(14,10) = t236;
+ local_mass_matrix(14,11) = 841.0/893025.0*t237;
+ local_mass_matrix(14,12) = t234;
+ local_mass_matrix(14,13) = t553;
+ local_mass_matrix(14,14) = t333-t334+t325+t450-t327-t451;
+ local_mass_matrix(14,15) = t571;
+ local_mass_matrix(14,16) = t568;
+ local_mass_matrix(14,17) = t566;
+ local_mass_matrix(14,18) = t572;
+ local_mass_matrix(14,19) = t573;
+ local_mass_matrix(14,20) = t569;
+ local_mass_matrix(14,21) = t576;
+ local_mass_matrix(14,22) = t577;
+ local_mass_matrix(14,23) = t578;
+ local_mass_matrix(14,24) = t579;
+ local_mass_matrix(15,0) = t74;
+ local_mass_matrix(15,1) = t64;
+ local_mass_matrix(15,2) = t196;
+ local_mass_matrix(15,3) = t228;
+ local_mass_matrix(15,4) = t92;
+ local_mass_matrix(15,5) = t103;
+ local_mass_matrix(15,6) = t91;
+ local_mass_matrix(15,7) = t271;
+ local_mass_matrix(15,8) = t458;
+ local_mass_matrix(15,9) = t488;
+ local_mass_matrix(15,10) = t232;
+ local_mass_matrix(15,11) = t235;
+ local_mass_matrix(15,12) = t231;
+ local_mass_matrix(15,13) = t554;
+ local_mass_matrix(15,14) = t571;
+ local_mass_matrix(15,15) = t397-t398+t240+t483-t242-t484;
+ local_mass_matrix(15,16) = t562;
+ local_mass_matrix(15,17) = t561;
+ local_mass_matrix(15,18) = t581;
+ local_mass_matrix(15,19) = t582;
+ local_mass_matrix(15,20) = t567;
+ local_mass_matrix(15,21) = t572;
+ local_mass_matrix(15,22) = t583;
+ local_mass_matrix(15,23) = t573;
+ local_mass_matrix(15,24) = t577;
+ local_mass_matrix(16,0) = t81;
+ local_mass_matrix(16,1) = t141;
+ local_mass_matrix(16,2) = t199;
+ local_mass_matrix(16,3) = t229;
+ local_mass_matrix(16,4) = t278;
+ local_mass_matrix(16,5) = t302;
+ local_mass_matrix(16,6) = t285;
+ local_mass_matrix(16,7) = t409;
+ local_mass_matrix(16,8) = t444;
+ local_mass_matrix(16,9) = t424;
+ local_mass_matrix(16,10) = t509;
+ local_mass_matrix(16,11) = t521;
+ local_mass_matrix(16,12) = t512;
+ local_mass_matrix(16,13) = t557;
+ local_mass_matrix(16,14) = t568;
+ local_mass_matrix(16,15) = t562;
+ local_mass_matrix(16,16) = t584-t585+t586+t587-t588-t589;
+ local_mass_matrix(16,17) = t597;
+ local_mass_matrix(16,18) = t604;
+ local_mass_matrix(16,19) = t609;
+ local_mass_matrix(16,20) = t616;
+ local_mass_matrix(16,21) = t623;
+ local_mass_matrix(16,22) = t628;
+ local_mass_matrix(16,23) = t633;
+ local_mass_matrix(16,24) = t640;
+ local_mass_matrix(17,0) = t86;
+ local_mass_matrix(17,1) = t144;
+ local_mass_matrix(17,2) = t202;
+ local_mass_matrix(17,3) = t230;
+ local_mass_matrix(17,4) = t285;
+ local_mass_matrix(17,5) = t343;
+ local_mass_matrix(17,6) = t375;
+ local_mass_matrix(17,7) = t414;
+ local_mass_matrix(17,8) = t434;
+ local_mass_matrix(17,9) = t419;
+ local_mass_matrix(17,10) = t512;
+ local_mass_matrix(17,11) = t536;
+ local_mass_matrix(17,12) = t549;
+ local_mass_matrix(17,13) = t558;
+ local_mass_matrix(17,14) = t566;
+ local_mass_matrix(17,15) = t561;
+ local_mass_matrix(17,16) = t597;
+ local_mass_matrix(17,17) = t641-t642+t586+t587-t588-t589;
+ local_mass_matrix(17,18) = t646;
+ local_mass_matrix(17,19) = t604;
+ local_mass_matrix(17,20) = t649;
+ local_mass_matrix(17,21) = t652;
+ local_mass_matrix(17,22) = t655;
+ local_mass_matrix(17,23) = t623;
+ local_mass_matrix(17,24) = t658;
+ local_mass_matrix(18,0) = t91;
+ local_mass_matrix(18,1) = t147;
+ local_mass_matrix(18,2) = t205;
+ local_mass_matrix(18,3) = t231;
+ local_mass_matrix(18,4) = t290;
+ local_mass_matrix(18,5) = t346;
+ local_mass_matrix(18,6) = t378;
+ local_mass_matrix(18,7) = t419;
+ local_mass_matrix(18,8) = t461;
+ local_mass_matrix(18,9) = t491;
+ local_mass_matrix(18,10) = t515;
+ local_mass_matrix(18,11) = t537;
+ local_mass_matrix(18,12) = t550;
+ local_mass_matrix(18,13) = t561;
+ local_mass_matrix(18,14) = t572;
+ local_mass_matrix(18,15) = t581;
+ local_mass_matrix(18,16) = t604;
+ local_mass_matrix(18,17) = t646;
+ local_mass_matrix(18,18) = t641-t642+t586+t659-t588-t660;
+ local_mass_matrix(18,19) = t664;
+ local_mass_matrix(18,20) = t655;
+ local_mass_matrix(18,21) = t667;
+ local_mass_matrix(18,22) = t670;
+ local_mass_matrix(18,23) = t673;
+ local_mass_matrix(18,24) = t676;
+ local_mass_matrix(19,0) = t92;
+ local_mass_matrix(19,1) = t150;
+ local_mass_matrix(19,2) = t208;
+ local_mass_matrix(19,3) = t232;
+ local_mass_matrix(19,4) = t295;
+ local_mass_matrix(19,5) = t312;
+ local_mass_matrix(19,6) = t290;
+ local_mass_matrix(19,7) = t424;
+ local_mass_matrix(19,8) = t464;
+ local_mass_matrix(19,9) = t494;
+ local_mass_matrix(19,10) = t518;
+ local_mass_matrix(19,11) = t527;
+ local_mass_matrix(19,12) = t515;
+ local_mass_matrix(19,13) = t562;
+ local_mass_matrix(19,14) = t573;
+ local_mass_matrix(19,15) = t582;
+ local_mass_matrix(19,16) = t609;
+ local_mass_matrix(19,17) = t604;
+ local_mass_matrix(19,18) = t664;
+ local_mass_matrix(19,19) = t584-t585+t586+t659-t588-t660;
+ local_mass_matrix(19,20) = t628;
+ local_mass_matrix(19,21) = t673;
+ local_mass_matrix(19,22) = t678;
+ local_mass_matrix(19,23) = t679;
+ local_mass_matrix(19,24) = t680;
+ local_mass_matrix(20,0) = t97;
+ local_mass_matrix(20,1) = t153;
+ local_mass_matrix(20,2) = t211;
+ local_mass_matrix(20,3) = t233;
+ local_mass_matrix(20,4) = t302;
+ local_mass_matrix(20,5) = t353;
+ local_mass_matrix(20,6) = t343;
+ local_mass_matrix(20,7) = t429;
+ local_mass_matrix(20,8) = t447;
+ local_mass_matrix(20,9) = t439;
+ local_mass_matrix(20,10) = t521;
+ local_mass_matrix(20,11) = t540;
+ local_mass_matrix(20,12) = t536;
+ local_mass_matrix(20,13) = t563;
+ local_mass_matrix(20,14) = t569;
+ local_mass_matrix(20,15) = t567;
+ local_mass_matrix(20,16) = t616;
+ local_mass_matrix(20,17) = t649;
+ local_mass_matrix(20,18) = t655;
+ local_mass_matrix(20,19) = t628;
+ local_mass_matrix(20,20) = t681-t682+t683+6656.0/297675.0*t12-t685
+-6656.0/297675.0*t17;
+ local_mass_matrix(20,21) = t658;
+ local_mass_matrix(20,22) = t694;
+ local_mass_matrix(20,23) = t640;
+ local_mass_matrix(20,24) = t701;
+ local_mass_matrix(21,0) = t102;
+ local_mass_matrix(21,1) = t156;
+ local_mass_matrix(21,2) = t214;
+ local_mass_matrix(21,3) = t234;
+ local_mass_matrix(21,4) = t307;
+ local_mass_matrix(21,5) = t356;
+ local_mass_matrix(21,6) = t381;
+ local_mass_matrix(21,7) = t434;
+ local_mass_matrix(21,8) = t469;
+ local_mass_matrix(21,9) = t461;
+ local_mass_matrix(21,10) = t524;
+ local_mass_matrix(21,11) = t541;
+ local_mass_matrix(21,12) = t551;
+ local_mass_matrix(21,13) = t566;
+ local_mass_matrix(21,14) = t576;
+ local_mass_matrix(21,15) = t572;
+ local_mass_matrix(21,16) = t623;
+ local_mass_matrix(21,17) = t652;
+ local_mass_matrix(21,18) = t667;
+ local_mass_matrix(21,19) = t673;
+ local_mass_matrix(21,20) = t658;
+ local_mass_matrix(21,21) = 73216.0/893025.0*t3-73216.0/893025.0*t7+t683+
+t704-t685-t705;
+ local_mass_matrix(21,22) = t676;
+ local_mass_matrix(21,23) = t694;
+ local_mass_matrix(21,24) = t711;
+ local_mass_matrix(22,0) = t103;
+ local_mass_matrix(22,1) = t159;
+ local_mass_matrix(22,2) = t217;
+ local_mass_matrix(22,3) = t235;
+ local_mass_matrix(22,4) = t312;
+ local_mass_matrix(22,5) = t361;
+ local_mass_matrix(22,6) = t346;
+ local_mass_matrix(22,7) = t439;
+ local_mass_matrix(22,8) = t472;
+ local_mass_matrix(22,9) = t497;
+ local_mass_matrix(22,10) = t527;
+ local_mass_matrix(22,11) = t544;
+ local_mass_matrix(22,12) = t537;
+ local_mass_matrix(22,13) = t567;
+ local_mass_matrix(22,14) = t577;
+ local_mass_matrix(22,15) = t583;
+ local_mass_matrix(22,16) = t628;
+ local_mass_matrix(22,17) = t655;
+ local_mass_matrix(22,18) = t670;
+ local_mass_matrix(22,19) = t678;
+ local_mass_matrix(22,20) = t694;
+ local_mass_matrix(22,21) = t676;
+ local_mass_matrix(22,22) = t681-t682+t683+73216.0/893025.0*t12-t685
+-73216.0/893025.0*t17;
+ local_mass_matrix(22,23) = t680;
+ local_mass_matrix(22,24) = t717;
+ local_mass_matrix(23,0) = t104;
+ local_mass_matrix(23,1) = t162;
+ local_mass_matrix(23,2) = t220;
+ local_mass_matrix(23,3) = t236;
+ local_mass_matrix(23,4) = t317;
+ local_mass_matrix(23,5) = t322;
+ local_mass_matrix(23,6) = t307;
+ local_mass_matrix(23,7) = t444;
+ local_mass_matrix(23,8) = t477;
+ local_mass_matrix(23,9) = t464;
+ local_mass_matrix(23,10) = t530;
+ local_mass_matrix(23,11) = t531;
+ local_mass_matrix(23,12) = t524;
+ local_mass_matrix(23,13) = t568;
+ local_mass_matrix(23,14) = t578;
+ local_mass_matrix(23,15) = t573;
+ local_mass_matrix(23,16) = t633;
+ local_mass_matrix(23,17) = t623;
+ local_mass_matrix(23,18) = t673;
+ local_mass_matrix(23,19) = t679;
+ local_mass_matrix(23,20) = t640;
+ local_mass_matrix(23,21) = t694;
+ local_mass_matrix(23,22) = t680;
+ local_mass_matrix(23,23) = 6656.0/297675.0*t3-6656.0/297675.0*t7+t683+
+t704-t685-t705;
+ local_mass_matrix(23,24) = t723;
+ local_mass_matrix(24,0) = 841.0/893025.0*t105;
+ local_mass_matrix(24,1) = 841.0/893025.0*t163;
+ local_mass_matrix(24,2) = 841.0/893025.0*t221;
+ local_mass_matrix(24,3) = 841.0/893025.0*t237;
+ local_mass_matrix(24,4) = t322;
+ local_mass_matrix(24,5) = t366;
+ local_mass_matrix(24,6) = t356;
+ local_mass_matrix(24,7) = t447;
+ local_mass_matrix(24,8) = t482;
+ local_mass_matrix(24,9) = t472;
+ local_mass_matrix(24,10) = t531;
+ local_mass_matrix(24,11) = t547;
+ local_mass_matrix(24,12) = t541;
+ local_mass_matrix(24,13) = t569;
+ local_mass_matrix(24,14) = t579;
+ local_mass_matrix(24,15) = t577;
+ local_mass_matrix(24,16) = t640;
+ local_mass_matrix(24,17) = t658;
+ local_mass_matrix(24,18) = t676;
+ local_mass_matrix(24,19) = t680;
+ local_mass_matrix(24,20) = t701;
+ local_mass_matrix(24,21) = t711;
+ local_mass_matrix(24,22) = t717;
+ local_mass_matrix(24,23) = t723;
+ local_mass_matrix(24,24) = 5408.0/99225.0*t3-5408.0/99225.0*t7+10816.0/
+99225.0*t10+5408.0/99225.0*t12-10816.0/99225.0*t15-5408.0/99225.0*t17;
+};
+
+
+
+template <>
+void FEQuarticSub<2>::get_ansatz_points (const typename DoFHandler<2>::cell_iterator &cell,
+ const Boundary<2>&,
+ vector<Point<2> > &ansatz_points) const {
+ Assert (ansatz_points.size() == total_dofs,
+ ExcWrongFieldDimension (ansatz_points.size(), total_dofs));
+
+ const double x[4] = { cell->vertex(0)(0),
+ cell->vertex(1)(0),
+ cell->vertex(2)(0),
+ cell->vertex(3)(0) };
+ const double y[4] = { cell->vertex(0)(1),
+ cell->vertex(1)(1),
+ cell->vertex(2)(1),
+ cell->vertex(3)(1) };
+
+ const double t1 = 3.0/4.0*x[0];
+ const double t2 = x[1]/4.0;
+ const double t4 = 3.0/4.0*y[0];
+ const double t5 = y[1]/4.0;
+ const double t9 = x[0]/4.0;
+ const double t10 = 3.0/4.0*x[1];
+ const double t12 = y[0]/4.0;
+ const double t13 = 3.0/4.0*y[1];
+ const double t15 = x[2]/4.0;
+ const double t17 = y[2]/4.0;
+ const double t21 = 3.0/4.0*x[2];
+ const double t23 = 3.0/4.0*y[2];
+ const double t25 = 3.0/4.0*x[3];
+ const double t27 = 3.0/4.0*y[3];
+ const double t31 = x[3]/4.0;
+ const double t33 = y[3]/4.0;
+ const double t42 = 3.0/16.0*x[1];
+ const double t44 = 3.0/16.0*x[3];
+ const double t47 = 3.0/16.0*y[1];
+ const double t49 = 3.0/16.0*y[3];
+ const double t51 = 3.0/16.0*x[0];
+ const double t53 = 3.0/16.0*x[2];
+ const double t56 = 3.0/16.0*y[0];
+ const double t58 = 3.0/16.0*y[2];
+ const double t73 = 3.0/8.0*x[0];
+ const double t74 = 3.0/8.0*x[1];
+ const double t75 = x[2]/8.0;
+ const double t76 = x[3]/8.0;
+ const double t78 = 3.0/8.0*y[0];
+ const double t79 = 3.0/8.0*y[1];
+ const double t80 = y[2]/8.0;
+ const double t81 = y[3]/8.0;
+ const double t83 = x[0]/8.0;
+ const double t84 = 3.0/8.0*x[2];
+ const double t86 = y[0]/8.0;
+ const double t87 = 3.0/8.0*y[2];
+ const double t89 = x[1]/8.0;
+ const double t90 = 3.0/8.0*x[3];
+ const double t92 = y[1]/8.0;
+ const double t93 = 3.0/8.0*y[3];
+ ansatz_points[0](0) = x[0];
+ ansatz_points[0](1) = y[0];
+ ansatz_points[1](0) = x[1];
+ ansatz_points[1](1) = y[1];
+ ansatz_points[2](0) = x[2];
+ ansatz_points[2](1) = y[2];
+ ansatz_points[3](0) = x[3];
+ ansatz_points[3](1) = y[3];
+ ansatz_points[4](0) = t1+t2;
+ ansatz_points[4](1) = t4+t5;
+ ansatz_points[5](0) = x[0]/2.0+x[1]/2.0;
+ ansatz_points[5](1) = y[0]/2.0+y[1]/2.0;
+ ansatz_points[6](0) = t9+t10;
+ ansatz_points[6](1) = t12+t13;
+ ansatz_points[7](0) = t10+t15;
+ ansatz_points[7](1) = t13+t17;
+ ansatz_points[8](0) = x[1]/2.0+x[2]/2.0;
+ ansatz_points[8](1) = y[1]/2.0+y[2]/2.0;
+ ansatz_points[9](0) = t2+t21;
+ ansatz_points[9](1) = t5+t23;
+ ansatz_points[10](0) = t15+t25;
+ ansatz_points[10](1) = t17+t27;
+ ansatz_points[11](0) = x[2]/2.0+x[3]/2.0;
+ ansatz_points[11](1) = y[2]/2.0+y[3]/2.0;
+ ansatz_points[12](0) = t21+t31;
+ ansatz_points[12](1) = t23+t33;
+ ansatz_points[13](0) = t1+t31;
+ ansatz_points[13](1) = t4+t33;
+ ansatz_points[14](0) = x[0]/2.0+x[3]/2.0;
+ ansatz_points[14](1) = y[0]/2.0+y[3]/2.0;
+ ansatz_points[15](0) = t9+t25;
+ ansatz_points[15](1) = t12+t27;
+ ansatz_points[16](0) = 9.0/16.0*x[0]+t42+x[2]/16.0+t44;
+ ansatz_points[16](1) = 9.0/16.0*y[0]+t47+y[2]/16.0+t49;
+ ansatz_points[17](0) = t51+9.0/16.0*x[1]+t53+x[3]/16.0;
+ ansatz_points[17](1) = t56+9.0/16.0*y[1]+t58+y[3]/16.0;
+ ansatz_points[18](0) = x[0]/16.0+t42+9.0/16.0*x[2]+t44;
+ ansatz_points[18](1) = y[0]/16.0+t47+9.0/16.0*y[2]+t49;
+ ansatz_points[19](0) = t51+x[1]/16.0+t53+9.0/16.0*x[3];
+ ansatz_points[19](1) = t56+y[1]/16.0+t58+9.0/16.0*y[3];
+ ansatz_points[20](0) = t73+t74+t75+t76;
+ ansatz_points[20](1) = t78+t79+t80+t81;
+ ansatz_points[21](0) = t83+t74+t84+t76;
+ ansatz_points[21](1) = t86+t79+t87+t81;
+ ansatz_points[22](0) = t83+t89+t84+t90;
+ ansatz_points[22](1) = t86+t92+t87+t93;
+ ansatz_points[23](0) = t73+t89+t75+t90;
+ ansatz_points[23](1) = t78+t92+t80+t93;
+ ansatz_points[24](0) = x[0]/4.0+x[1]/4.0+x[2]/4.0+x[3]/4.0;
+ ansatz_points[24](1) = y[0]/4.0+y[1]/4.0+y[2]/4.0+y[3]/4.0;
+};
+
+
+
+template <>
+void FEQuarticSub<2>::get_face_ansatz_points (const typename DoFHandler<2>::face_iterator &face,
+ const Boundary<2> &,
+ vector<Point<2> > &ansatz_points) const {
+ Assert (ansatz_points.size() == dofs_per_face,
+ ExcWrongFieldDimension (ansatz_points.size(), dofs_per_face));
+
+ for (unsigned int vertex=0; vertex<2; ++vertex)
+ ansatz_points[vertex] = face->vertex(vertex);
+ ansatz_points[2] = (3*ansatz_points[0] + ansatz_points[1]) / 4;
+ ansatz_points[3] = (ansatz_points[0] + ansatz_points[1]) / 2;
+ ansatz_points[4] = (ansatz_points[0] + 3*ansatz_points[1]) / 4;
+};
+
+
+
+template <>
+void FEQuarticSub<2>::get_face_jacobians (const DoFHandler<2>::face_iterator &face,
+ const Boundary<2> &,
+ const vector<Point<1> > &unit_points,
+ vector<double> &face_jacobians) const {
+ // more or less copied from the linear
+ // finite element
+ Assert (unit_points.size() == face_jacobians.size(),
+ ExcWrongFieldDimension (unit_points.size(), face_jacobians.size()));
+
+ // a linear mapping for a single line
+ // produces particularly simple
+ // expressions for the jacobi
+ // determinant :-)
+ const double h = sqrt((face->vertex(1) - face->vertex(0)).square());
+ fill_n (face_jacobians.begin(),
+ unit_points.size(),
+ h);
+};
+
+
+
+template <>
+void FEQuarticSub<2>::get_subface_jacobians (const DoFHandler<2>::face_iterator &face,
+ const unsigned int ,
+ const vector<Point<1> > &unit_points,
+ vector<double> &face_jacobians) const {
+ // more or less copied from the linear
+ // finite element
+ Assert (unit_points.size() == face_jacobians.size(),
+ ExcWrongFieldDimension (unit_points.size(), face_jacobians.size()));
+ Assert (face->at_boundary() == false,
+ ExcBoundaryFaceUsed ());
+
+ // a linear mapping for a single line
+ // produces particularly simple
+ // expressions for the jacobi
+ // determinant :-)
+ const double h = sqrt((face->vertex(1) - face->vertex(0)).square());
+ fill_n (face_jacobians.begin(),
+ unit_points.size(),
+ h/2);
+};
+
+
+
+template <>
+void FEQuarticSub<2>::get_normal_vectors (const DoFHandler<2>::cell_iterator &cell,
+ const unsigned int face_no,
+ const Boundary<2> &,
+ const vector<Point<1> > &unit_points,
+ vector<Point<2> > &normal_vectors) const {
+ // more or less copied from the linear
+ // finite element
+ Assert (unit_points.size() == normal_vectors.size(),
+ ExcWrongFieldDimension (unit_points.size(), normal_vectors.size()));
+
+ const DoFHandler<2>::face_iterator face = cell->face(face_no);
+ // compute direction of line
+ const Point<2> line_direction = (face->vertex(1) - face->vertex(0));
+ // rotate to the right by 90 degrees
+ const Point<2> normal_direction(line_direction(1),
+ -line_direction(0));
+
+ if (face_no <= 1)
+ // for sides 0 and 1: return the correctly
+ // scaled vector
+ fill (normal_vectors.begin(), normal_vectors.end(),
+ normal_direction / sqrt(normal_direction.square()));
+ else
+ // for sides 2 and 3: scale and invert
+ // vector
+ fill (normal_vectors.begin(), normal_vectors.end(),
+ normal_direction / (-sqrt(normal_direction.square())));
+};
+
+
+
+template <>
+void FEQuarticSub<2>::get_normal_vectors (const DoFHandler<2>::cell_iterator &cell,
+ const unsigned int face_no,
+ const unsigned int,
+ const vector<Point<1> > &unit_points,
+ vector<Point<2> > &normal_vectors) const {
+ // more or less copied from the linear
+ // finite element
+ // note, that in 2D the normal vectors to the
+ // subface have the same direction as that
+ // for the face
+ Assert (unit_points.size() == normal_vectors.size(),
+ ExcWrongFieldDimension (unit_points.size(), normal_vectors.size()));
+ Assert (cell->face(face_no)->at_boundary() == false,
+ ExcBoundaryFaceUsed ());
+
+ const DoFHandler<2>::face_iterator face = cell->face(face_no);
+ // compute direction of line
+ const Point<2> line_direction = (face->vertex(1) - face->vertex(0));
+ // rotate to the right by 90 degrees
+ const Point<2> normal_direction(line_direction(1),
+ -line_direction(0));
+
+ if (face_no <= 1)
+ // for sides 0 and 1: return the correctly
+ // scaled vector
+ fill (normal_vectors.begin(), normal_vectors.end(),
+ normal_direction / sqrt(normal_direction.square()));
+ else
+ // for sides 2 and 3: scale and invert
+ // vector
+ fill (normal_vectors.begin(), normal_vectors.end(),
+ normal_direction / (-sqrt(normal_direction.square())));
+};
+
+#endif
+
+
+
+
+
+template <int dim>
+void FEQuarticSub<dim>::fill_fe_values (const DoFHandler<dim>::cell_iterator &cell,
+ const vector<Point<dim> > &unit_points,
+ vector<dFMatrix> &jacobians,
+ const bool compute_jacobians,
+ vector<Point<dim> > &ansatz_points,
+ const bool compute_ansatz_points,
+ vector<Point<dim> > &q_points,
+ const bool compute_q_points,
+ const Boundary<dim> &boundary) const {
+ Assert (jacobians.size() == unit_points.size(),
+ ExcWrongFieldDimension(jacobians.size(), unit_points.size()));
+ Assert (q_points.size() == unit_points.size(),
+ ExcWrongFieldDimension(q_points.size(), unit_points.size()));
+ Assert (ansatz_points.size() == total_dofs,
+ ExcWrongFieldDimension(ansatz_points.size(), total_dofs));
+
+
+ unsigned int n_points=unit_points.size();
+
+ Point<dim> vertices[GeometryInfo<dim>::vertices_per_cell];
+ for (unsigned int l=0; l<GeometryInfo<dim>::vertices_per_cell; ++l)
+ vertices[l] = cell->vertex(l);
+
+
+ if (compute_q_points)
+ {
+ // initialize points to zero
+ for (unsigned int i=0; i<n_points; ++i)
+ q_points[i] = Point<dim> ();
+
+ // note: let x_l be the vector of the
+ // lth quadrature point in real space and
+ // xi_l that on the unit cell, let further
+ // p_j be the vector of the jth vertex
+ // of the cell in real space and
+ // N_j(xi_l) be the value of the associated
+ // basis function at xi_l, then
+ // x_l(xi_l) = sum_j p_j N_j(xi_l)
+ //
+ // Here, N_j is the *linear* basis function,
+ // not that of the finite element, since we
+ // use a subparametric mapping
+ for (unsigned int j=0; j<GeometryInfo<dim>::vertices_per_cell; ++j)
+ for (unsigned int l=0; l<n_points; ++l)
+ q_points[l] += vertices[j] * linear_shape_value(j, unit_points[l]);
+ };
+
+
+/* jacobi matrices: compute d(x)/d(xi) and invert this
+ Let M(l) be the inverse of J at the quadrature point l, then
+ M_{ij}(l) = sum_s p_i(s) d(N_s(l))/d(xi_j)
+ where p_i(s) is the i-th coordinate of the s-th vertex vector,
+ N_s(l) is the value of the s-th vertex shape function at the
+ quadrature point l (linear shape functions implied, as these
+ are used for the mapping).
+
+ We could therefore write:
+ l=0..n_points-1
+ i=0..dim-1
+ j=0..dim-1
+ M_{ij}(l) = 0
+ s=0..n_vertices
+ M_{ij}(l) += p_i(s) d(N_s(l))/d(xi_j)
+
+ However, we rewrite the loops to only compute the gradient once for
+ each integration point and basis function.
+*/
+ if (compute_jacobians)
+ {
+ dFMatrix M(dim,dim);
+ for (unsigned int l=0; l<n_points; ++l)
+ {
+ M.clear ();
+ for (unsigned int s=0; s<GeometryInfo<dim>::vertices_per_cell; ++s)
+ {
+ // we want the linear transform,
+ // so use that function
+ const Point<dim> gradient = linear_shape_grad (s, unit_points[l]);
+ for (unsigned int i=0; i<dim; ++i)
+ for (unsigned int j=0; j<dim; ++j)
+ M(i,j) += vertices[s](i) * gradient(j);
+ };
+ jacobians[l].invert(M);
+ };
+ };
+
+ // compute ansatz points, which are
+ // the corners for linear elements
+ if (compute_ansatz_points)
+ get_ansatz_points (cell, boundary, ansatz_points);
+};
+
+
+
+
+// explicit instantiations
+
+template class FEQuarticSub<deal_II_dimension>;
+