#include <algorithm>
+
+
#if deal_II_dimension == 1
template <>
template <>
+inline
double
FELinear<2>::shape_value (const unsigned int i,
const Point<2>& p) const
// x_l(xi_l) = sum_j p_j N_j(xi_l)
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] * shape_value(j, unit_points[l]);
+ q_points[l] += vertices[j] *
+ FELinear<dim>::shape_value(j, unit_points[l]);
};
-
-
-
-#if deal_II_dimension == 1
-
-template <>
-FEQuadraticSub<1>::FEQuadraticSub () :
- FiniteElement<1> (1, 1) {};
-
-
-
-template <>
-void FEQuadraticSub<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
-FEQuadraticSub<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 (1-xi)*(1-2*xi);
- case 1: return xi*(2*xi-1);
- case 2: return 4*xi*(1-xi);
- }
- return 0.;
-}
-
-
-
-template <>
-inline
-Point<1>
-FEQuadraticSub<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>(-3+4*xi);
- case 1: return Point<1>(4*xi-1);
- case 2: return Point<1>(4-8*xi);
- }
- return Point<1>();
-};
-
-
-
-template <>
-void FEQuadraticSub<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 FEQuadraticSub<1>::get_face_ansatz_points (const typename DoFHandler<1>::face_iterator &,
- const Boundary<1> &,
- vector<Point<1> > &) const {
- Assert (false, ExcInternalError());
-};
-
-
-
-template <>
-void FEQuadraticSub<1>::get_face_jacobians (const DoFHandler<1>::face_iterator &,
- const Boundary<1> &,
- const vector<Point<0> > &,
- vector<double> &) const {
- Assert (false, ExcInternalError());
-};
-
-
-
-template <>
-void FEQuadraticSub<1>::get_subface_jacobians (const DoFHandler<1>::face_iterator &,
- const unsigned int ,
- const vector<Point<0> > &,
- vector<double> &) const {
- Assert (false, ExcInternalError());
-};
-
-
-
-template <>
-void FEQuadraticSub<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 FEQuadraticSub<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 FEQuadraticSub<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());
-
- local_mass_matrix(0,0) = local_mass_matrix(1,1) = 2./15.*h;
- local_mass_matrix(0,1) = local_mass_matrix(1,0) = -1./30.*h;
- local_mass_matrix(0,2) = local_mass_matrix(2,0) = 1./15.*h;
- local_mass_matrix(1,2) = local_mass_matrix(2,1) = 1./15.*h;
- local_mass_matrix(2,2) = local_mass_matrix(2,2) = 8./15.*h;
-};
-
-
-#endif
-
-
-#if deal_II_dimension == 2
-
-template <>
-FEQuadraticSub<2>::FEQuadraticSub () :
- 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.;
-
- // still implement restriction
- // and prolongation
- Assert (false, ExcNotImplemented());
-};
-
-
-template <>
-double
-FEQuadraticSub<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-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);
- };
- return 0;
-};
-
-
-
-template <>
-Point<2>
-FEQuadraticSub<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>(-(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);
- };
- return Point<2> ();
-};
-
-
-
-template <>
-void FEQuadraticSub<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));
-
-/* 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),
- 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[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);
-};
-
-
-
-template <>
-void FEQuadraticSub<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));
-
- 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;
-};
-
-
-
-template <>
-void FEQuadraticSub<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] = (ansatz_points[0] + ansatz_points[1]) / 1;
-};
-
-
-
-template <>
-void FEQuadraticSub<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 FEQuadraticSub<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 FEQuadraticSub<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 FEQuadraticSub<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 FEQuadraticSub<dim>::fill_fe_values (const DoFHandler<dim>::cell_iterator &,
- const vector<Point<dim> > &unit_points,
- vector<dFMatrix> &jacobians,
- const bool,
- vector<Point<dim> > &ansatz_points,
- const bool,
- vector<Point<dim> > &q_points,
- const bool,
- const Boundary<dim> &) 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));
-
- Assert (false, ExcNotImplemented());
-};
-
-
-
-
-
-
-#if deal_II_dimension == 1
-
-template <>
-FECubic<1>::FECubic () :
- FiniteElement<1> (1, 2) {};
-
-
-
-template <>
-void FECubic<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 <>
-void FECubic<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 FECubic<1>::get_face_ansatz_points (const typename DoFHandler<1>::face_iterator &,
- const Boundary<1> &,
- vector<Point<1> > &) const {
- Assert (false, ExcInternalError());
-};
-
-
-
-template <>
-void FECubic<1>::get_face_jacobians (const DoFHandler<1>::face_iterator &,
- const Boundary<1> &,
- const vector<Point<0> > &,
- vector<double> &) const {
- Assert (false, ExcInternalError());
-};
-
-
-
-template <>
-void FECubic<1>::get_subface_jacobians (const DoFHandler<1>::face_iterator &,
- const unsigned int ,
- const vector<Point<0> > &,
- vector<double> &) const {
- Assert (false, ExcInternalError());
-};
-
-
-
-template <>
-void FECubic<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 FECubic<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());
-};
-
-#endif
-
-
-
-#if deal_II_dimension == 2
-
-template <>
-FECubic<2>::FECubic () :
- FiniteElement<2> (1, 2, 4) {};
-
-#endif
-
-
-
-template <int dim>
-double
-FECubic<dim>::shape_value (const unsigned int i,
- const Point<dim> &) const
-{
- Assert (i<total_dofs, typename FiniteElementBase<dim>::ExcInvalidIndex(i));
- Assert (false, ExcNotImplemented());
- return 0.;
-};
-
-
-
-template <int dim>
-Point<dim>
-FECubic<dim>::shape_grad (const unsigned int i,
- const Point<dim> &) const
-{
- Assert (i<total_dofs, typename FiniteElementBase<dim>::ExcInvalidIndex(i));
- Assert (false, ExcNotImplemented());
- return Point<dim> ();
-};
-
-
-
-template <int dim>
-void FECubic<dim>::fill_fe_values (const DoFHandler<dim>::cell_iterator &,
- const vector<Point<dim> > &unit_points,
- vector<dFMatrix> &jacobians,
- const bool,
- vector<Point<dim> > &ansatz_points,
- const bool,
- vector<Point<dim> > &q_points,
- const bool,
- const Boundary<dim> &) 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));
-
- Assert (false, ExcNotImplemented());
-};
-
-
-
-template <int dim>
-void FECubic<dim>::get_ansatz_points (const typename DoFHandler<dim>::cell_iterator &,
- const Boundary<dim> &,
- vector<Point<dim> > &) const {
- Assert (false, ExcNotImplemented());
-};
-
-
-
-template <int dim>
-void FECubic<dim>::get_face_ansatz_points (const typename DoFHandler<dim>::face_iterator &,
- const Boundary<dim> &,
- vector<Point<dim> > &) const {
- Assert (false, ExcNotImplemented());
-};
-
-
-
-template <int dim>
-void FECubic<dim>::get_face_jacobians (const DoFHandler<dim>::face_iterator &,
- const Boundary<dim> &,
- const vector<Point<dim-1> > &,
- vector<double> &) const {
- Assert (false, ExcNotImplemented());
-};
-
-
-
-template <int dim>
-void FECubic<dim>::get_subface_jacobians (const DoFHandler<dim>::face_iterator &face,
- const unsigned int ,
- const vector<Point<dim-1> > &,
- vector<double> &) const {
- Assert (face->at_boundary() == false,
- ExcBoundaryFaceUsed ());
-
- Assert (false, ExcNotImplemented());
-};
-
-
-
-template <int dim>
-void FECubic<dim>::get_normal_vectors (const DoFHandler<dim>::cell_iterator &,
- const unsigned int,
- const Boundary<dim> &,
- const vector<Point<dim-1> > &,
- vector<Point<dim> > &) const {
- Assert (false, ExcNotImplemented());
-};
-
-
-
-template <int dim>
-void FECubic<dim>::get_normal_vectors (const DoFHandler<dim>::cell_iterator &cell,
- const unsigned int face_no,
- const unsigned int ,
- const vector<Point<dim-1> > &,
- vector<Point<dim> > &) const {
- Assert (cell->face(face_no)->at_boundary() == false,
- ExcBoundaryFaceUsed ());
-
- Assert (false, ExcNotImplemented());
-};
-
-
-
-template <int dim>
-void FECubic<dim>::get_local_mass_matrix (const DoFHandler<dim>::cell_iterator &,
- const Boundary<dim> &,
- dFMatrix &) const {
- Assert (false, ExcNotImplemented());
-};
-
-
-
-
// explicit instantiations
template class FELinear<deal_II_dimension>;
-template class FEQuadraticSub<deal_II_dimension>;
-template class FECubic<deal_II_dimension>;
-
--- /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>
+
+
+
+
+
+
+#if deal_II_dimension == 1
+
+template <>
+FEQuadraticSub<1>::FEQuadraticSub () :
+ FiniteElement<1> (1, 1) {};
+
+
+
+template <>
+void FEQuadraticSub<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
+FEQuadraticSub<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 (1-xi)*(1-2*xi);
+ case 1: return xi*(2*xi-1);
+ case 2: return 4*xi*(1-xi);
+ }
+ return 0.;
+}
+
+
+
+template <>
+inline
+Point<1>
+FEQuadraticSub<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>(-3+4*xi);
+ case 1: return Point<1>(4*xi-1);
+ case 2: return Point<1>(4-8*xi);
+ }
+ return Point<1>();
+};
+
+
+
+template <>
+void FEQuadraticSub<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 FEQuadraticSub<1>::get_face_ansatz_points (const typename DoFHandler<1>::face_iterator &,
+ const Boundary<1> &,
+ vector<Point<1> > &) const {
+ Assert (false, ExcInternalError());
+};
+
+
+
+template <>
+void FEQuadraticSub<1>::get_face_jacobians (const DoFHandler<1>::face_iterator &,
+ const Boundary<1> &,
+ const vector<Point<0> > &,
+ vector<double> &) const {
+ Assert (false, ExcInternalError());
+};
+
+
+
+template <>
+void FEQuadraticSub<1>::get_subface_jacobians (const DoFHandler<1>::face_iterator &,
+ const unsigned int ,
+ const vector<Point<0> > &,
+ vector<double> &) const {
+ Assert (false, ExcInternalError());
+};
+
+
+
+template <>
+void FEQuadraticSub<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 FEQuadraticSub<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 FEQuadraticSub<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());
+
+ local_mass_matrix(0,0) = local_mass_matrix(1,1) = 2./15.*h;
+ local_mass_matrix(0,1) = local_mass_matrix(1,0) = -1./30.*h;
+ local_mass_matrix(0,2) = local_mass_matrix(2,0) = 1./15.*h;
+ local_mass_matrix(1,2) = local_mass_matrix(2,1) = 1./15.*h;
+ local_mass_matrix(2,2) = local_mass_matrix(2,2) = 8./15.*h;
+};
+
+
+#endif
+
+
+#if deal_II_dimension == 2
+
+template <>
+FEQuadraticSub<2>::FEQuadraticSub () :
+ 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.;
+
+ // still implement restriction
+ // and prolongation
+ Assert (false, ExcNotImplemented());
+};
+
+
+template <>
+double
+FEQuadraticSub<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-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);
+ };
+ return 0;
+};
+
+
+
+template <>
+Point<2>
+FEQuadraticSub<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>(-(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);
+ };
+ return Point<2> ();
+};
+
+
+
+template <>
+void FEQuadraticSub<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));
+
+/* 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),
+ 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[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);
+};
+
+
+
+template <>
+void FEQuadraticSub<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));
+
+ 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;
+};
+
+
+
+template <>
+void FEQuadraticSub<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] = (ansatz_points[0] + ansatz_points[1]) / 1;
+};
+
+
+
+template <>
+void FEQuadraticSub<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 FEQuadraticSub<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 FEQuadraticSub<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 FEQuadraticSub<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 FEQuadraticSub<dim>::fill_fe_values (const DoFHandler<dim>::cell_iterator &,
+ const vector<Point<dim> > &unit_points,
+ vector<dFMatrix> &jacobians,
+ const bool,
+ vector<Point<dim> > &ansatz_points,
+ const bool,
+ vector<Point<dim> > &q_points,
+ const bool,
+ const Boundary<dim> &) 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));
+
+ Assert (false, ExcNotImplemented());
+};
+
+
+
+
+
+
+#if deal_II_dimension == 1
+
+template <>
+FECubic<1>::FECubic () :
+ FiniteElement<1> (1, 2) {};
+
+
+
+template <>
+void FECubic<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 <>
+void FECubic<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 FECubic<1>::get_face_ansatz_points (const typename DoFHandler<1>::face_iterator &,
+ const Boundary<1> &,
+ vector<Point<1> > &) const {
+ Assert (false, ExcInternalError());
+};
+
+
+
+template <>
+void FECubic<1>::get_face_jacobians (const DoFHandler<1>::face_iterator &,
+ const Boundary<1> &,
+ const vector<Point<0> > &,
+ vector<double> &) const {
+ Assert (false, ExcInternalError());
+};
+
+
+
+template <>
+void FECubic<1>::get_subface_jacobians (const DoFHandler<1>::face_iterator &,
+ const unsigned int ,
+ const vector<Point<0> > &,
+ vector<double> &) const {
+ Assert (false, ExcInternalError());
+};
+
+
+
+template <>
+void FECubic<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 FECubic<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());
+};
+
+#endif
+
+
+
+#if deal_II_dimension == 2
+
+template <>
+FECubic<2>::FECubic () :
+ FiniteElement<2> (1, 2, 4) {};
+
+#endif
+
+
+
+template <int dim>
+double
+FECubic<dim>::shape_value (const unsigned int i,
+ const Point<dim> &) const
+{
+ Assert (i<total_dofs, typename FiniteElementBase<dim>::ExcInvalidIndex(i));
+ Assert (false, ExcNotImplemented());
+ return 0.;
+};
+
+
+
+template <int dim>
+Point<dim>
+FECubic<dim>::shape_grad (const unsigned int i,
+ const Point<dim> &) const
+{
+ Assert (i<total_dofs, typename FiniteElementBase<dim>::ExcInvalidIndex(i));
+ Assert (false, ExcNotImplemented());
+ return Point<dim> ();
+};
+
+
+
+template <int dim>
+void FECubic<dim>::fill_fe_values (const DoFHandler<dim>::cell_iterator &,
+ const vector<Point<dim> > &unit_points,
+ vector<dFMatrix> &jacobians,
+ const bool,
+ vector<Point<dim> > &ansatz_points,
+ const bool,
+ vector<Point<dim> > &q_points,
+ const bool,
+ const Boundary<dim> &) 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));
+
+ Assert (false, ExcNotImplemented());
+};
+
+
+
+template <int dim>
+void FECubic<dim>::get_ansatz_points (const typename DoFHandler<dim>::cell_iterator &,
+ const Boundary<dim> &,
+ vector<Point<dim> > &) const {
+ Assert (false, ExcNotImplemented());
+};
+
+
+
+template <int dim>
+void FECubic<dim>::get_face_ansatz_points (const typename DoFHandler<dim>::face_iterator &,
+ const Boundary<dim> &,
+ vector<Point<dim> > &) const {
+ Assert (false, ExcNotImplemented());
+};
+
+
+
+template <int dim>
+void FECubic<dim>::get_face_jacobians (const DoFHandler<dim>::face_iterator &,
+ const Boundary<dim> &,
+ const vector<Point<dim-1> > &,
+ vector<double> &) const {
+ Assert (false, ExcNotImplemented());
+};
+
+
+
+template <int dim>
+void FECubic<dim>::get_subface_jacobians (const DoFHandler<dim>::face_iterator &face,
+ const unsigned int ,
+ const vector<Point<dim-1> > &,
+ vector<double> &) const {
+ Assert (face->at_boundary() == false,
+ ExcBoundaryFaceUsed ());
+
+ Assert (false, ExcNotImplemented());
+};
+
+
+
+template <int dim>
+void FECubic<dim>::get_normal_vectors (const DoFHandler<dim>::cell_iterator &,
+ const unsigned int,
+ const Boundary<dim> &,
+ const vector<Point<dim-1> > &,
+ vector<Point<dim> > &) const {
+ Assert (false, ExcNotImplemented());
+};
+
+
+
+template <int dim>
+void FECubic<dim>::get_normal_vectors (const DoFHandler<dim>::cell_iterator &cell,
+ const unsigned int face_no,
+ const unsigned int ,
+ const vector<Point<dim-1> > &,
+ vector<Point<dim> > &) const {
+ Assert (cell->face(face_no)->at_boundary() == false,
+ ExcBoundaryFaceUsed ());
+
+ Assert (false, ExcNotImplemented());
+};
+
+
+
+template <int dim>
+void FECubic<dim>::get_local_mass_matrix (const DoFHandler<dim>::cell_iterator &,
+ const Boundary<dim> &,
+ dFMatrix &) const {
+ Assert (false, ExcNotImplemented());
+};
+
+
+
+
+// explicit instantiations
+
+template class FEQuadraticSub<deal_II_dimension>;
+