#include <string>
#include <math.h>
+#include "../base/simplex.h"
using namespace std;
-// The exact integrals were computed with 20 digits precision using Maple.
-double exact_integral_one_over_r(const unsigned int i,
- const unsigned int j,
- const unsigned int vertex_index);
-
ofstream logfile("output");
int main()
}
}
}
-
-double exact_integral_one_over_r(const unsigned int vertex_index,
- const unsigned int i,
- const unsigned int j)
-{
- Assert(vertex_index < 4, ExcInternalError());
- Assert(i<6, ExcNotImplemented());
- Assert(j<6, ExcNotImplemented());
-
- // The integrals are computed using the following maple snippet of
- // code:
- //
- // sing_int := proc(index, N, M)
- // if index = 0 then
- // return int(int(x^N *y^M/sqrt(x^2+y^2), x=0.0..1.0), y=0.0..1.0);
- // elif index = 1 then
- // return int(int(x^N *y^M/sqrt((x-1)^2+y^2), x=0.0..1.0), y=0.0..1.0);
- // elif index = 2 then
- // return int(int(x^N *y^M/sqrt(x^2+(y-1)^2), x=0.0..1.0), y=0.0..1.0);
- // elif index = 3 then
- // return int(int((1-x)^N *(1-y)^M/sqrt(x^2+y^2), x=0.0..1.0), y=0.0..1.0);
- // end if;
- // end proc;
- // Digits := 20;
- // for i from 3 to 3 do
- // for n from 0 to 5 do
- // for m from 0 to 5 do
- // C( v[i+1][n+1][m+1] = sing_int(i, n, m), resultname="a");
- // end do;
- // end do;
- // end do;
-
- static double v[4][6][6] = {{{0}}};
- if (v[0][0][0] == 0)
- {
- v[0][0][0] = 0.17627471740390860505e1;
- v[0][0][1] = 0.64779357469631903702e0;
- v[0][0][2] = 0.38259785823210634567e0;
- v[0][0][3] = 0.26915893322379450224e0;
- v[0][0][4] = 0.20702239737104695572e0;
- v[0][0][5] = 0.16800109713227567467e0;
- v[0][1][0] = 0.64779357469631903702e0;
- v[0][1][1] = 0.27614237491539669920e0;
- v[0][1][2] = 0.17015838751246776515e0;
- v[0][1][3] = 0.12189514164974600651e0;
- v[0][1][4] = 0.94658660368131133694e-1;
- v[0][1][5] = 0.77263794021029438797e-1;
- v[0][2][0] = 0.38259785823210634567e0;
- v[0][2][1] = 0.17015838751246776515e0;
- v[0][2][2] = 0.10656799507071040471e0;
- v[0][2][3] = 0.76947022258735165920e-1;
- v[0][2][4] = 0.60022626787495395021e-1;
- v[0][2][5] = 0.49131622931360879320e-1;
- v[0][3][0] = 0.26915893322379450224e0;
- v[0][3][1] = 0.12189514164974600651e0;
- v[0][3][2] = 0.76947022258735165919e-1;
- v[0][3][3] = 0.55789184535895709637e-1;
- v[0][3][4] = 0.43625068213915842136e-1;
- v[0][3][5] = 0.35766126849971778500e-1;
- v[0][4][0] = 0.20702239737104695572e0;
- v[0][4][1] = 0.94658660368131133694e-1;
- v[0][4][2] = 0.60022626787495395021e-1;
- v[0][4][3] = 0.43625068213915842137e-1;
- v[0][4][4] = 0.34164088852375945192e-1;
- v[0][4][5] = 0.28037139560980277614e-1;
- v[0][5][0] = 0.16800109713227567467e0;
- v[0][5][1] = 0.77263794021029438797e-1;
- v[0][5][2] = 0.49131622931360879320e-1;
- v[0][5][3] = 0.35766126849971778501e-1;
- v[0][5][4] = 0.28037139560980277614e-1;
- v[0][5][5] = 0.23024181049838367777e-1;
- v[1][0][0] = 0.17627471740390860505e1;
- v[1][0][1] = 0.64779357469631903702e0;
- v[1][0][2] = 0.38259785823210634567e0;
- v[1][0][3] = 0.26915893322379450224e0;
- v[1][0][4] = 0.20702239737104695572e0;
- v[1][0][5] = 0.16800109713227567467e0;
- v[1][1][0] = 0.11149535993427670134e1;
- v[1][1][1] = 0.37165119978092233782e0;
- v[1][1][2] = 0.21243947071963858053e0;
- v[1][1][3] = 0.14726379157404849573e0;
- v[1][1][4] = 0.11236373700291582202e0;
- v[1][1][5] = 0.90737303111246235871e-1;
- v[1][2][0] = 0.84975788287855432210e0;
- v[1][2][1] = 0.26566721237799340376e0;
- v[1][2][2] = 0.14884907827788122009e0;
- v[1][2][3] = 0.10231567218303765515e0;
- v[1][2][4] = 0.77727703422280083352e-1;
- v[1][2][5] = 0.62605132021577676395e-1;
- v[1][3][0] = 0.69800109142265347423e0;
- v[1][3][1] = 0.20794647083778622837e0;
- v[1][3][2] = 0.11487965864809909847e0;
- v[1][3][3] = 0.78525390514866270852e-1;
- v[1][3][4] = 0.59489228415223897572e-1;
- v[1][3][5] = 0.47838457013298217744e-1;
- v[1][4][0] = 0.59754668912231692323e0;
- v[1][4][1] = 0.17125249387868593878e0;
- v[1][4][2] = 0.93606816359052444729e-1;
- v[1][4][3] = 0.63728830247554475330e-1;
- v[1][4][4] = 0.48187332620207367724e-1;
- v[1][4][5] = 0.38708290797416359020e-1;
- v[1][5][0] = 0.52527944036356840363e0;
- v[1][5][1] = 0.14574366656617935708e0;
- v[1][5][2] = 0.78997159795636003667e-1;
- v[1][5][3] = 0.53620816423066464705e-1;
- v[1][5][4] = 0.40487985967086264433e-1;
- v[1][5][5] = 0.32498604596082509165e-1;
- v[2][0][0] = 0.17627471740390860505e1;
- v[2][0][1] = 0.11149535993427670134e1;
- v[2][0][2] = 0.84975788287855432210e0;
- v[2][0][3] = 0.69800109142265347419e0;
- v[2][0][4] = 0.59754668912231692318e0;
- v[2][0][5] = 0.52527944036356840362e0;
- v[2][1][0] = 0.64779357469631903702e0;
- v[2][1][1] = 0.37165119978092233782e0;
- v[2][1][2] = 0.26566721237799340376e0;
- v[2][1][3] = 0.20794647083778622835e0;
- v[2][1][4] = 0.17125249387868593876e0;
- v[2][1][5] = 0.14574366656617935708e0;
- v[2][2][0] = 0.38259785823210634567e0;
- v[2][2][1] = 0.21243947071963858053e0;
- v[2][2][2] = 0.14884907827788122009e0;
- v[2][2][3] = 0.11487965864809909845e0;
- v[2][2][4] = 0.93606816359052444712e-1;
- v[2][2][5] = 0.78997159795636003667e-1;
- v[2][3][0] = 0.26915893322379450223e0;
- v[2][3][1] = 0.14726379157404849572e0;
- v[2][3][2] = 0.10231567218303765514e0;
- v[2][3][3] = 0.78525390514866270835e-1;
- v[2][3][4] = 0.63728830247554475311e-1;
- v[2][3][5] = 0.53620816423066464702e-1;
- v[2][4][0] = 0.20702239737104695572e0;
- v[2][4][1] = 0.11236373700291582202e0;
- v[2][4][2] = 0.77727703422280083352e-1;
- v[2][4][3] = 0.59489228415223897563e-1;
- v[2][4][4] = 0.48187332620207367713e-1;
- v[2][4][5] = 0.40487985967086264434e-1;
- v[2][5][0] = 0.16800109713227567468e0;
- v[2][5][1] = 0.90737303111246235879e-1;
- v[2][5][2] = 0.62605132021577676399e-1;
- v[2][5][3] = 0.47838457013298217740e-1;
- v[2][5][4] = 0.38708290797416359014e-1;
- v[2][5][5] = 0.32498604596082509169e-1;
- v[3][0][0] = 0.17627471740390860505e1;
- v[3][0][1] = 0.11149535993427670134e1;
- v[3][0][2] = 0.84975788287855432210e0;
- v[3][0][3] = 0.69800109142265347419e0;
- v[3][0][4] = 0.59754668912231692318e0;
- v[3][0][5] = 0.52527944036356840362e0;
- v[3][1][0] = 0.11149535993427670134e1;
- v[3][1][1] = 0.74330239956184467563e0;
- v[3][1][2] = 0.58409067050056091834e0;
- v[3][1][3] = 0.49005462058486724584e0;
- v[3][1][4] = 0.42629419524363098443e0;
- v[3][1][5] = 0.37953577379738904654e0;
- v[3][2][0] = 0.84975788287855432210e0;
- v[3][2][1] = 0.58409067050056091834e0;
- v[3][2][2] = 0.46727253640044873467e0;
- v[3][2][3] = 0.39698780839518011595e0;
- v[3][2][4] = 0.34864851772399749038e0;
- v[3][2][5] = 0.31278926702684569312e0;
- v[3][3][0] = 0.69800109142265347423e0;
- v[3][3][1] = 0.49005462058486724586e0;
- v[3][3][2] = 0.39698780839518011599e0;
- v[3][3][3] = 0.34027526433872581371e0;
- v[3][3][4] = 0.30088082631586196583e0;
- v[3][3][5] = 0.27141910362887187844e0;
- v[3][4][0] = 0.59754668912231692323e0;
- v[3][4][1] = 0.42629419524363098445e0;
- v[3][4][2] = 0.34864851772399749044e0;
- v[3][4][3] = 0.30088082631586196576e0;
- v[3][4][4] = 0.26744962339187730308e0;
- v[3][4][5] = 0.24229245314748740295e0;
- v[3][5][0] = 0.52527944036356840363e0;
- v[3][5][1] = 0.37953577379738904655e0;
- v[3][5][2] = 0.31278926702684569301e0;
- v[3][5][3] = 0.27141910362887187862e0;
- v[3][5][4] = 0.24229245314748740263e0;
- v[3][5][5] = 0.22026586649771582089e0;
- }
- return v[vertex_index][i][j];
-}
#include <deal.II/base/quadrature_lib.h>
#include <deal.II/base/geometry_info.h>
#include <deal.II/fe/fe_q.h>
+#include "../base/simplex.h"
#include <string>
using namespace std;
using namespace dealii;
-// We test the integration of singular kernels with a singularity of kind 1/R
-// We multiply this function with a polynomial up to degree 6.
-
-double
-exact_integral_one_over_r (
- const unsigned int i, const unsigned int j,
- const unsigned int vertex_index);
-
int
main ()
{
}
}
}
-
-double exact_integral_one_over_r(const unsigned int vertex_index,
- const unsigned int i,
- const unsigned int j)
-{
- Assert(vertex_index < 4, ExcInternalError());
- Assert(i<6, ExcNotImplemented());
- Assert(j<6, ExcNotImplemented());
-
-// The integrals are computed using the following maple snippet of
-// code:
-//
-// singint := proc(index, N, M)
-// if index = 0 then
-// return int(int(x^N *y^M/sqrt(x^2+y^2), x=0.0..1.0), y=0.0..1.0);
-// elif index = 1 then
-// return int(int(x^N *y^M/sqrt((x-1)^2+y^2), x=0.0..1.0), y=0.0..1.0);
-// elif index = 2 then
-// return int(int(x^N *y^M/sqrt(x^2+(y-1)^2), x=0.0..1.0), y=0.0..1.0);
-// elif index = 3 then
-// return int(int((1-x)^N *(1-y)^M/sqrt(x^2+y^2), x=0.0..1.0), y=0.0..1.0);
-// end if;
-// end proc;
-// Digits := 20;
-// for i from 3 to 3 do
-// for n from 0 to 5 do
-// for m from 0 to 5 do
-// v[i+1][n+1][m+1] = sing_int(i, n, m);
-// end do;
-// end do;
-// end do;
-// C(v)
-
- static double v[4][6][6] =
- {
- {
- { 0}
- }
- };
- if (v[0][0][0] == 0)
- {
- v[0][0][0] = 0.17627471740390860505e1;
- v[0][0][1] = 0.64779357469631903702e0;
- v[0][0][2] = 0.38259785823210634567e0;
- v[0][0][3] = 0.26915893322379450224e0;
- v[0][0][4] = 0.20702239737104695572e0;
- v[0][0][5] = 0.16800109713227567467e0;
- v[0][1][0] = 0.64779357469631903702e0;
- v[0][1][1] = 0.27614237491539669920e0;
- v[0][1][2] = 0.17015838751246776515e0;
- v[0][1][3] = 0.12189514164974600651e0;
- v[0][1][4] = 0.94658660368131133694e-1;
- v[0][1][5] = 0.77263794021029438797e-1;
- v[0][2][0] = 0.38259785823210634567e0;
- v[0][2][1] = 0.17015838751246776515e0;
- v[0][2][2] = 0.10656799507071040471e0;
- v[0][2][3] = 0.76947022258735165920e-1;
- v[0][2][4] = 0.60022626787495395021e-1;
- v[0][2][5] = 0.49131622931360879320e-1;
- v[0][3][0] = 0.26915893322379450224e0;
- v[0][3][1] = 0.12189514164974600651e0;
- v[0][3][2] = 0.76947022258735165919e-1;
- v[0][3][3] = 0.55789184535895709637e-1;
- v[0][3][4] = 0.43625068213915842136e-1;
- v[0][3][5] = 0.35766126849971778500e-1;
- v[0][4][0] = 0.20702239737104695572e0;
- v[0][4][1] = 0.94658660368131133694e-1;
- v[0][4][2] = 0.60022626787495395021e-1;
- v[0][4][3] = 0.43625068213915842137e-1;
- v[0][4][4] = 0.34164088852375945192e-1;
- v[0][4][5] = 0.28037139560980277614e-1;
- v[0][5][0] = 0.16800109713227567467e0;
- v[0][5][1] = 0.77263794021029438797e-1;
- v[0][5][2] = 0.49131622931360879320e-1;
- v[0][5][3] = 0.35766126849971778501e-1;
- v[0][5][4] = 0.28037139560980277614e-1;
- v[0][5][5] = 0.23024181049838367777e-1;
- v[1][0][0] = 0.17627471740390860505e1;
- v[1][0][1] = 0.64779357469631903702e0;
- v[1][0][2] = 0.38259785823210634567e0;
- v[1][0][3] = 0.26915893322379450224e0;
- v[1][0][4] = 0.20702239737104695572e0;
- v[1][0][5] = 0.16800109713227567467e0;
- v[1][1][0] = 0.11149535993427670134e1;
- v[1][1][1] = 0.37165119978092233782e0;
- v[1][1][2] = 0.21243947071963858053e0;
- v[1][1][3] = 0.14726379157404849573e0;
- v[1][1][4] = 0.11236373700291582202e0;
- v[1][1][5] = 0.90737303111246235871e-1;
- v[1][2][0] = 0.84975788287855432210e0;
- v[1][2][1] = 0.26566721237799340376e0;
- v[1][2][2] = 0.14884907827788122009e0;
- v[1][2][3] = 0.10231567218303765515e0;
- v[1][2][4] = 0.77727703422280083352e-1;
- v[1][2][5] = 0.62605132021577676395e-1;
- v[1][3][0] = 0.69800109142265347423e0;
- v[1][3][1] = 0.20794647083778622837e0;
- v[1][3][2] = 0.11487965864809909847e0;
- v[1][3][3] = 0.78525390514866270852e-1;
- v[1][3][4] = 0.59489228415223897572e-1;
- v[1][3][5] = 0.47838457013298217744e-1;
- v[1][4][0] = 0.59754668912231692323e0;
- v[1][4][1] = 0.17125249387868593878e0;
- v[1][4][2] = 0.93606816359052444729e-1;
- v[1][4][3] = 0.63728830247554475330e-1;
- v[1][4][4] = 0.48187332620207367724e-1;
- v[1][4][5] = 0.38708290797416359020e-1;
- v[1][5][0] = 0.52527944036356840363e0;
- v[1][5][1] = 0.14574366656617935708e0;
- v[1][5][2] = 0.78997159795636003667e-1;
- v[1][5][3] = 0.53620816423066464705e-1;
- v[1][5][4] = 0.40487985967086264433e-1;
- v[1][5][5] = 0.32498604596082509165e-1;
- v[2][0][0] = 0.17627471740390860505e1;
- v[2][0][1] = 0.11149535993427670134e1;
- v[2][0][2] = 0.84975788287855432210e0;
- v[2][0][3] = 0.69800109142265347419e0;
- v[2][0][4] = 0.59754668912231692318e0;
- v[2][0][5] = 0.52527944036356840362e0;
- v[2][1][0] = 0.64779357469631903702e0;
- v[2][1][1] = 0.37165119978092233782e0;
- v[2][1][2] = 0.26566721237799340376e0;
- v[2][1][3] = 0.20794647083778622835e0;
- v[2][1][4] = 0.17125249387868593876e0;
- v[2][1][5] = 0.14574366656617935708e0;
- v[2][2][0] = 0.38259785823210634567e0;
- v[2][2][1] = 0.21243947071963858053e0;
- v[2][2][2] = 0.14884907827788122009e0;
- v[2][2][3] = 0.11487965864809909845e0;
- v[2][2][4] = 0.93606816359052444712e-1;
- v[2][2][5] = 0.78997159795636003667e-1;
- v[2][3][0] = 0.26915893322379450223e0;
- v[2][3][1] = 0.14726379157404849572e0;
- v[2][3][2] = 0.10231567218303765514e0;
- v[2][3][3] = 0.78525390514866270835e-1;
- v[2][3][4] = 0.63728830247554475311e-1;
- v[2][3][5] = 0.53620816423066464702e-1;
- v[2][4][0] = 0.20702239737104695572e0;
- v[2][4][1] = 0.11236373700291582202e0;
- v[2][4][2] = 0.77727703422280083352e-1;
- v[2][4][3] = 0.59489228415223897563e-1;
- v[2][4][4] = 0.48187332620207367713e-1;
- v[2][4][5] = 0.40487985967086264434e-1;
- v[2][5][0] = 0.16800109713227567468e0;
- v[2][5][1] = 0.90737303111246235879e-1;
- v[2][5][2] = 0.62605132021577676399e-1;
- v[2][5][3] = 0.47838457013298217740e-1;
- v[2][5][4] = 0.38708290797416359014e-1;
- v[2][5][5] = 0.32498604596082509169e-1;
- v[3][0][0] = 0.17627471740390860505e1;
- v[3][0][1] = 0.11149535993427670134e1;
- v[3][0][2] = 0.84975788287855432210e0;
- v[3][0][3] = 0.69800109142265347419e0;
- v[3][0][4] = 0.59754668912231692318e0;
- v[3][0][5] = 0.52527944036356840362e0;
- v[3][1][0] = 0.11149535993427670134e1;
- v[3][1][1] = 0.74330239956184467563e0;
- v[3][1][2] = 0.58409067050056091834e0;
- v[3][1][3] = 0.49005462058486724584e0;
- v[3][1][4] = 0.42629419524363098443e0;
- v[3][1][5] = 0.37953577379738904654e0;
- v[3][2][0] = 0.84975788287855432210e0;
- v[3][2][1] = 0.58409067050056091834e0;
- v[3][2][2] = 0.46727253640044873467e0;
- v[3][2][3] = 0.39698780839518011595e0;
- v[3][2][4] = 0.34864851772399749038e0;
- v[3][2][5] = 0.31278926702684569312e0;
- v[3][3][0] = 0.69800109142265347423e0;
- v[3][3][1] = 0.49005462058486724586e0;
- v[3][3][2] = 0.39698780839518011599e0;
- v[3][3][3] = 0.34027526433872581371e0;
- v[3][3][4] = 0.30088082631586196583e0;
- v[3][3][5] = 0.27141910362887187844e0;
- v[3][4][0] = 0.59754668912231692323e0;
- v[3][4][1] = 0.42629419524363098445e0;
- v[3][4][2] = 0.34864851772399749044e0;
- v[3][4][3] = 0.30088082631586196576e0;
- v[3][4][4] = 0.26744962339187730308e0;
- v[3][4][5] = 0.24229245314748740295e0;
- v[3][5][0] = 0.52527944036356840363e0;
- v[3][5][1] = 0.37953577379738904655e0;
- v[3][5][2] = 0.31278926702684569301e0;
- v[3][5][3] = 0.27141910362887187862e0;
- v[3][5][4] = 0.24229245314748740263e0;
- v[3][5][5] = 0.22026586649771582089e0;
- }
- return v[vertex_index][i][j];
-}
#include <deal.II/base/quadrature_lib.h>
#include <deal.II/base/geometry_info.h>
#include <deal.II/fe/fe_q.h>
+#include "../base/simplex.h"
#include <string>
// We test the integration of singular kernels with a singularity of kind 1/R
// We multiply this function with a polynomial up to degree 6.
-double
-exact_integral_one_over_r_middle (
- const unsigned int i, const unsigned int j);
-
int
main ()
{
}
}
}
-
-double exact_integral_one_over_r_middle(const unsigned int i,
- const unsigned int j)
-{
- Assert(i<6, ExcNotImplemented());
- Assert(j<6, ExcNotImplemented());
-
-// The integrals are computed using the following Mathematica snippet of
-// code:
-//
-// x0 = 0.5
-// y0 = 0.5
-// Do[Do[Print["v[0][", n, "][", m, "]=",
-// NumberForm[
-// NIntegrate[
-// x^n*y^m/Sqrt[(x - x0)^2 + (y - y0)^2], {x, 0, 1}, {y, 0, 1},
-// MaxRecursion -> 10000, PrecisionGoal -> 9], 9], ";"], {n, 0,
-// 4}], {m, 0, 4}]
-
-
- static double v[1][6][6] =
- {
- {
- { 0}
- }
- };
- if (v[0][0][0] == 0)
- {
- v[0][0][0] = 3.52549435;;
- v[0][1][0] = 1.76274717;
- v[0][2][0]=1.07267252;
- v[0][3][0]=0.727635187;
- v[0][4][0]=0.53316959;
- v[0][0][1]=1.76274717;
- v[0][1][1]=0.881373587;
- v[0][2][1]=0.536336258;
- v[0][3][1]=0.363817594;
- v[0][4][1]=0.266584795;
- v[0][0][2]=1.07267252;
- v[0][1][2]=0.536336258;
- v[0][2][2]=0.329313861;
- v[0][3][2]=0.225802662;
- v[0][4][2]=0.167105787;
- v[0][0][3]=0.727635187;
- v[0][1][3]=0.363817594;
- v[0][2][3]=0.225802662;
- v[0][3][3]=0.156795196;
- v[0][4][3]=0.117366283;
- v[0][0][4]=0.53316959;
- v[0][1][4]=0.266584795;
- v[0][2][4]=0.167105787;
- v[0][3][4]=0.117366283;
- v[0][4][4]=0.0887410133;
- }
- return v[0][i][j];
-}
projects / dealii.git / commitdiff