From a82f2dd13fcfdcf41343e5c72e6321ab21a1c6ca Mon Sep 17 00:00:00 2001 From: treecity Date: Sun, 5 Jun 2011 19:55:24 +0000 Subject: [PATCH] =?utf8?q?[src]=20F=5Fort=20implementiert=20[src]=20test?= =?utf8?q?=20dazu=20geschrieben=20[src]=20build=5FA=20f=C3=BCr=20orthogona?= =?utf8?q?le=20St=C3=BCcke=20erweitert=20[src]=20surfDoubleQuad=20(subopti?= =?utf8?q?mal)=20[src]=20example=203dFichCube=20gebaut=20[-1=201]^3=20[src?= =?utf8?q?]=20code=20jetzt=20auch=20in=20Mayer=20eingebaut...=20(l=C3=A4uf?= =?utf8?q?t=20noch=20nicht)=20[dir]=20recangle=20->=20rectangle=20in=20May?= =?utf8?q?erCode?= MIME-Version: 1.0 Content-Type: text/plain; charset=utf8 Content-Transfer-Encoding: 8bit git-svn-id: https://drops.fb12.tu-berlin.de/svn/bacc/trunk@32 26120e32-c555-405d-b3e1-1f783fb42516 --- src/SLPrecangle.cpp | 261 ++++------- src/SLPrecangle.hpp | 5 +- src/bem3d/src/boundary_mesh/testhilbertmesh | Bin 1283424 -> 1283752 bytes src/bem3d/src/laplace/SLPrecangle.cpp | 357 --------------- src/bem3d/src/laplace/SLPrecangle.hpp | 21 - src/bem3d/src/laplace/SLPrectangle.cpp | 166 +++++++ src/bem3d/src/laplace/SLPrectangle.hpp | 28 ++ .../src/laplace/SimpleLayerPotential.cpp | 410 +++++++++++------- src/bem3d/src/spaces/testP0Space | Bin 1712309 -> 1713189 bytes src/build_A.cpp | 107 +++-- src/exmpl_3DFichCube.mat | Bin 0 -> 322 bytes src/exportCOEL.m | 24 +- src/mex_Fort.cpp | 44 ++ src/mex_Fpar.cpp | 2 +- src/mexit.m | 1 + src/surfDoubleQuad.m | 88 ++-- src/test_Fort.m | 19 + src/test_solveError.m | 4 +- 18 files changed, 728 insertions(+), 809 deletions(-) delete mode 100644 src/bem3d/src/laplace/SLPrecangle.cpp delete mode 100644 src/bem3d/src/laplace/SLPrecangle.hpp create mode 100644 src/bem3d/src/laplace/SLPrectangle.cpp create mode 100644 src/bem3d/src/laplace/SLPrectangle.hpp create mode 100644 src/exmpl_3DFichCube.mat create mode 100644 src/mex_Fort.cpp create mode 100644 src/test_Fort.m diff --git a/src/SLPrecangle.cpp b/src/SLPrecangle.cpp index 42b08e4..a5f3b7e 100644 --- a/src/SLPrecangle.cpp +++ b/src/SLPrecangle.cpp @@ -14,158 +14,14 @@ using namespace std; int sign(double); //double arsinh(double); -/* -void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { - //sicherheitsabfragen zu Datengroessen - if (nrhs != 2) - mexErrMsgTxt("expected (coordinates(Nx3),elements(Mx3))"); - if (nlhs > 1) - mexErrMsgTxt("has only one output argument"); - - int cm = mxGetM(prhs[0]); - int cn = mxGetN(prhs[0]); - - if (cn != 3) - mexErrMsgTxt("expected coordinates (Nx3)"); - int em = mxGetM(prhs[1]); - int en = mxGetN(prhs[1]); - if (en != 3) - mexErrMsgTxt("expected elements (Mx3)"); - //Vorbereitung der Daten - - plhs[0] = mxCreateDoubleMatrix(em, em, mxREAL); - double * A = mxGetPr(plhs[0]); - double * C = mxGetPr(prhs[0]); - double * E = mxGetPr(prhs[1]); - - double * x1 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL)); - double * x2 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL)); - double * x3 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL)); - double * xn = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL)); - - double * y1 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL)); - double * y2 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL)); - double * y3 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL)); - double * yn = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL)); - - double * d = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL)); - - double tmp; - - int rx, ry; - - //Ausrechnen - for (int j = 0; j < em; ++j) { - x1[0] = C[(int) E[j] - 1]; - x1[1] = C[cm + (int) E[j] - 1]; - x1[2] = C[2 * cm + (int) E[j] - 1]; - - x2[0] = C[(int) E[em + j] - 1]; - x2[1] = C[cm + (int) E[em + j] - 1]; - x2[2] = C[2 * cm + (int) E[em + j] - 1]; - - x3[0] = C[(int) E[2 * em + j] - 1]; - x3[1] = C[cm + (int) E[2 * em + j] - 1]; - x3[2] = C[2 * cm + (int) E[2 * em + j] - 1]; - - xn[0] = (x2[1] - x1[1]) * (x3[2] - x1[2]) - (x2[2] - x1[2]) * (x3[1] - - x1[1]); - xn[1] = (x2[2] - x1[2]) * (x3[0] - x1[0]) - (x2[0] - x1[0]) * (x3[2] - - x1[2]); - xn[2] = (x2[0] - x1[0]) * (x3[1] - x1[1]) - (x2[1] - x1[1]) * (x3[0] - - x1[0]); - - //if(xn[0]*xn[0]+xn[1]*xn[1] 0 ? 1 : (x < 0 ? -1 : 0); } /* -double inline arsinh(double x) { - return log(x + sqrt(x * x + 1)); -} -*/ + double inline arsinh(double x) { + return log(x + sqrt(x * x + 1)); + } + */ //y-x muss != 0 sein double g0(double p, double y, double x, double l) { //printf("%.1f | %.1f | %.1f | %.1f +",p,x,y,l); @@ -182,7 +38,7 @@ double g0(double p, double y, double x, double l) { else if (p == -0.5) sol = asinh((y - x) / fabs(l)); else if (p == -1) - sol = atan((y - x) / fabs(l))/l; + sol = atan((y - x) / fabs(l)) / l; else if (p == -1.5) sol = (y - x) / ((l * l) * sqrt((y - x) * (y - x) + l * l)); else @@ -200,9 +56,9 @@ double g0(double p, double y, double x, double l) { double G00(double p, double y1, double y2, double x1, double x2, double l) { // printf("%.1f | %.1f %.1f | %.1f %.1f | %.1f +",p,x1,x2,y1,y2,l); - + double pt = p + 1.5; double sol = 0; - if (p == -1.5) { + if (pt == 0) { if (l == 0) { sol = -sqrt((y1 - x1) * (y1 - x1) + (y2 - x2) * (y2 - x2)) / ((y1 - x1) * (y2 - x2)); @@ -213,7 +69,7 @@ double G00(double p, double y1, double y2, double x1, double x2, double l) { + l * l)) + 1); } - } else if (p == -0.5) { + } else if ((pt > 0) && ((int) pt == pt)) { if (l != 0) sol = 2 * p * l * l * G00(p - 1, y1, y2, x1, x2, l); if ((y1 - x1) != 0) @@ -225,7 +81,7 @@ double G00(double p, double y1, double y2, double x1, double x2, double l) { sol /= 2 * p + 2; } else { sol = NAN; - printf("warning in G00: no case for p defined\n"); + printf("warning in G00: no case for p=%.2f defined\n", p); //mexErrMsgTxt("no case for p defined\n"); } @@ -239,7 +95,7 @@ double F_par(double x1, double x2, double y1, double y2, double d1, double d2, double sol = (x1 - y1 - d1) * (x2 - y2 - d2); if (sol != 0) - sol *= G00(-0.5,x1, x2, y1 + d1, y2 + d2, d3); + sol *= G00(-0.5, x1, x2, y1 + d1, y2 + d2, d3); if ((x1 - y1 - d1) != 0) sol -= (x1 - y1 - d1) * g0(0.5, x1, y1 + d1, @@ -255,43 +111,70 @@ double F_par(double x1, double x2, double y1, double y2, double d1, double d2, return sol; } +double F_ort(double x1, double x2, double y2, double y3, double d1, double d2, + double d3) { + + // printf("%.1f %.1f | %.1f %.1f | %.1f %.1f %.1f",x1,x2,y2,y3,d1,d2,d3); + double sol = -G00(0.5, y3, x1, -d3, d1, x2 - y2 - d2); + + if ((x1 - d1) * (x2 - y2 - d2) != 0) + sol -= (x1 - d1) * (x2 - y2 - d2) * G00(-0.5, x2, y3, y2 + d2, -d3, + x1 - d1); + + if ((x1 - d1) != 0) + sol += (x1 - d1) * g0(0.5, y3, -d3, + sqrt((x1 - d1) * (x1 - d1) + (x2 - y2 - d2) * (x2 - y2 - d2))); + + if ((y3 + d3) * (x2 - y2 - d2) != 0) + sol -= (y3 + d3) * (x2 - y2 - d2) * G00(-0.5, x1, x2, d1, y2 + d2, + -y3 - d3); + + if ((y3 + d3) != 0) + sol += (y3 + d3) * g0(0.5, x1, d1, + sqrt((x2 - y2 - d2) * (x2 - y2 - d2) + (y3 + d3) * (y3 + d3))); + + return sol / 2.; +} + double quadInt( double(*f)(double, double, double, double, double, double, double), - double a, double b, double c, double d, double r, double t, - double u, double v, double d1, double d2, double d3) { - - return f(b,d,t,v,d1,d2,d3)-f(b,d,t,u,d1,d2,d3)-f(b,d,r,v,d1,d2,d3)+f(b,d,r,u,d1,d2,d3) - -f(b,c,t,v,d1,d2,d3)+f(b,c,t,u,d1,d2,d3)+f(b,c,r,v,d1,d2,d3)-f(b,c,r,u,d1,d2,d3) - -f(a,d,t,v,d1,d2,d3)+f(a,d,t,u,d1,d2,d3)+f(a,d,r,v,d1,d2,d3)-f(a,d,r,u,d1,d2,d3) - +f(a,c,t,v,d1,d2,d3)-f(a,c,t,u,d1,d2,d3)-f(a,c,r,v,d1,d2,d3)+f(a,c,r,u,d1,d2,d3); -/* - return f(k1, k2, l1, l2, d1, d2, d3) - f(k1, k2, l1, t2, d1, d2, d3) - f( - k1, k2, t1, l2, d1, d2, d3) + f(k1, k2, t1, t2, d1, d2, d3) - f(k1, - s2, l1, l2, d1, d2, d3) + f(k1, s2, l1, t2, d1, d2, d3) + f(k1, s2, - t1, l2, d1, d2, d3) - f(k1, s2, t1, t2, d1, d2, d3) - f(s1, k2, l1, - l2, d1, d2, d3) + f(s1, k2, l1, t2, d1, d2, d3) + f(s1, k2, t1, l2, - d1, d2, d3) - f(s1, l2, t1, t2, d1, d2, d3) + f(s1, s2, l1, l2, d1, - d2, d3) - f(s1, 0, l1, t2, d1, d2, d3) - f(s1, s2, t1, l2, d1, d2, - d3) + f(s1, s2, t1, t2, d1, d2, d3); - - */ + double a, double b, double c, double d, double r, double t, double u, + double v, double d1, double d2, double d3) { + + return f(b, d, t, v, d1, d2, d3) - f(b, d, t, u, d1, d2, d3) - f(b, d, r, + v, d1, d2, d3) + f(b, d, r, u, d1, d2, d3) - f(b, c, t, v, d1, d2, + d3) + f(b, c, t, u, d1, d2, d3) + f(b, c, r, v, d1, d2, d3) - f(b, + c, r, u, d1, d2, d3) - f(a, d, t, v, d1, d2, d3) + f(a, d, t, u, + d1, d2, d3) + f(a, d, r, v, d1, d2, d3) - f(a, d, r, u, d1, d2, d3) + + f(a, c, t, v, d1, d2, d3) - f(a, c, t, u, d1, d2, d3) - f(a, c, + r, v, d1, d2, d3) + f(a, c, r, u, d1, d2, d3); + /* + return f(k1, k2, l1, l2, d1, d2, d3) - f(k1, k2, l1, t2, d1, d2, d3) - f( + k1, k2, t1, l2, d1, d2, d3) + f(k1, k2, t1, t2, d1, d2, d3) - f(k1, + s2, l1, l2, d1, d2, d3) + f(k1, s2, l1, t2, d1, d2, d3) + f(k1, s2, + t1, l2, d1, d2, d3) - f(k1, s2, t1, t2, d1, d2, d3) - f(s1, k2, l1, + l2, d1, d2, d3) + f(s1, k2, l1, t2, d1, d2, d3) + f(s1, k2, t1, l2, + d1, d2, d3) - f(s1, l2, t1, t2, d1, d2, d3) + f(s1, s2, l1, l2, d1, + d2, d3) - f(s1, 0, l1, t2, d1, d2, d3) - f(s1, s2, t1, l2, d1, d2, + d3) + f(s1, s2, t1, t2, d1, d2, d3); + + */ } double quad0Int( double(*f)(double, double, double, double, double, double, double), double b, double d, double t, double v, double d1, double d2, double d3) { - return f(b,d,t,v,d1,d2,d3)-f(b,d,t,0,d1,d2,d3)-f(b,d,0,v,d1,d2,d3)+f(b,d,0,0,d1,d2,d3) - -f(b,0,t,v,d1,d2,d3)+f(b,0,t,0,d1,d2,d3)+f(b,0,0,v,d1,d2,d3)-f(b,0,0,0,d1,d2,d3) - -f(0,d,t,v,d1,d2,d3)+f(0,d,t,0,d1,d2,d3)+f(0,d,0,v,d1,d2,d3)-f(0,d,0,0,d1,d2,d3) - +f(0,0,t,v,d1,d2,d3)-f(0,0,t,0,d1,d2,d3)-f(0,0,0,v,d1,d2,d3)+f(0,0,0,0,d1,d2,d3); + return f(b, d, t, v, d1, d2, d3) - f(b, d, t, 0, d1, d2, d3) - f(b, d, 0, + v, d1, d2, d3) + f(b, d, 0, 0, d1, d2, d3) - f(b, 0, t, v, d1, d2, + d3) + f(b, 0, t, 0, d1, d2, d3) + f(b, 0, 0, v, d1, d2, d3) - f(b, + 0, 0, 0, d1, d2, d3) - f(0, d, t, v, d1, d2, d3) + f(0, d, t, 0, + d1, d2, d3) + f(0, d, 0, v, d1, d2, d3) - f(0, d, 0, 0, d1, d2, d3) + + f(0, 0, t, v, d1, d2, d3) - f(0, 0, t, 0, d1, d2, d3) - f(0, 0, + 0, v, d1, d2, d3) + f(0, 0, 0, 0, d1, d2, d3); } - - - - double slpADLO(double y1, double y2, double x1, double x2, double a) { double G3 = 0; double gL = 0; @@ -354,7 +237,7 @@ double compute_g0(double p, double y, double x, double a) { return (y - x) * pow((x * x + y * y + a * a - 2 * x * y), -0.5) / (a * a); default: - printf("p must be either 0, -1/2, -1 or -3/2."); + printf("p must be either 0, -1/2, -1 or -3/2. (%.2f)\n", p); return NAN; } } @@ -375,3 +258,19 @@ double FLO_plane(double x1, double x2, double y1, double y2, double delta1, x1, yd1, tmp3) - tmp2 * compute_g0(-0.5, x2, yd2, tmp4) + tmp5 / 3.; return rval; } + +double FLO_perp(double x1, double x2, double y2, double y3, double delta1, + double delta2, double a) { + double xd1 = x1 - delta1; + double xd2 = x2 - delta2; + double yd2 = y2 - delta2; + double yd3 = y3 - a; + double tmp2 = x2 - y2 - delta2; + double rval = 0; + + rval = xd1 * compute_g0(y3, a, sqrt(xd1 * xd1 + tmp2 * tmp2), -0.5) + yd3 + * compute_g0(x1, delta1, sqrt(tmp2 * tmp2 + yd3 * yd3), -0.5) - xd1 + * tmp2 * slpADLO(x2, y3, yd2, a, xd1) - yd3 * tmp2 * slpADLO(x1, + x2, delta1, yd2, -y3 - a) - slpADLO(y3, x1, -a, delta1, tmp2); + return rval; +} diff --git a/src/SLPrecangle.hpp b/src/SLPrecangle.hpp index 418bf5e..d801cfe 100644 --- a/src/SLPrecangle.hpp +++ b/src/SLPrecangle.hpp @@ -10,13 +10,14 @@ double g0(double, double, double, double); double G00(double, double, double, double, double, double); // sol = F_par(x1,x2,y1,y2,d1,d2,d3); double F_par(double, double, double, double, double, double, double); -// sol = F_ort(x1,x2,y1,y2,d1,d2,d3); -//double F_ort(double, double, double, double, double, double, double); +// sol = F_ort(x1,x2,y2,y3,d1,d2,d3); +double F_ort(double, double, double, double, double, double, double); double slpADLO(double, double, double, double, double); double compute_g0(double, double, double, double); double FLO_plane(double, double, double, double, double, double, double); +double FLO_perp(double, double, double, double, double, double, double); // sol = quadInt((F_par/F_ort),a,b,c,d,r,t,u,v,d1,d2,d3); double quadInt( diff --git a/src/bem3d/src/boundary_mesh/testhilbertmesh b/src/bem3d/src/boundary_mesh/testhilbertmesh index 51b8ad865cc8f68da30537b42ad4f459db86a9ae..d49c645eb0368dc4ee4a55e8080a16ea7c9da947 100755 GIT binary patch delta 259550 zcmcG1c|cUv+y7Zc7#YDCfnnbqKtw@sLB)OFP%-xv5K&Ov5O;G>({eXUPo<`rmRY7& 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+0,0 @@ -#include -#include -#include -#include - -#include "SLPrecangle.hpp" - -#define my_PI 3.141592653589793 -#define EPS 0.02 - -using namespace std; - -int sign(double); -double arsinh(double); - -// sol = quadInt((F_par/F_ort),s1,s2,k1,k2,t1,t2,l1,l2,d1,d2,d3); -double quadInt( - double(*)(double, double, double, double, double, double, double), - double, double, double, double, double, double, double, double, double, - double, double); - -void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { - //sicherheitsabfragen zu Datengroessen - if (nrhs != 2) - mexErrMsgTxt("expected (coordinates(Nx3),elements(Mx3))"); - if (nlhs > 1) - mexErrMsgTxt("has only one output argument"); - - int cm = mxGetM(prhs[0]); - int cn = mxGetN(prhs[0]); - - if (cn != 3) - mexErrMsgTxt("expected coordinates (Nx3)"); - int em = mxGetM(prhs[1]); - int en = mxGetN(prhs[1]); - if (en != 3) - mexErrMsgTxt("expected elements (Mx3)"); - //Vorbereitung der Daten - - plhs[0] = mxCreateDoubleMatrix(em, em, mxREAL); - double * A = mxGetPr(plhs[0]); - double * C = mxGetPr(prhs[0]); - double * E = mxGetPr(prhs[1]); - - double * x1 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL)); - double * x2 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL)); - double * x3 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL)); - double * xn = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL)); - - double * y1 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL)); - double * y2 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL)); - double * y3 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL)); - double * yn = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL)); - - double * d = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL)); - - double tmp; - - int rx, ry; - - //Ausrechnen - for (int j = 0; j < em; ++j) { - x1[0] = C[(int) E[j] - 1]; - x1[1] = C[cm + (int) E[j] - 1]; - x1[2] = C[2 * cm + (int) E[j] - 1]; - - x2[0] = C[(int) E[em + j] - 1]; - x2[1] = C[cm + (int) E[em + j] - 1]; - x2[2] = C[2 * cm + (int) E[em + j] - 1]; - - x3[0] = C[(int) E[2 * em + j] - 1]; - x3[1] = C[cm + (int) E[2 * em + j] - 1]; - x3[2] = C[2 * cm + (int) E[2 * em + j] - 1]; - - xn[0] = (x2[1] - x1[1]) * (x3[2] - x1[2]) - (x2[2] - x1[2]) * (x3[1] - - x1[1]); - xn[1] = (x2[2] - x1[2]) * (x3[0] - x1[0]) - (x2[0] - x1[0]) * (x3[2] - - x1[2]); - xn[2] = (x2[0] - x1[0]) * (x3[1] - x1[1]) - (x2[1] - x1[1]) * (x3[0] - - x1[0]); - - //if(xn[0]*xn[0]+xn[1]*xn[1] 0 ? 1 : (x < 0 ? -1 : 0); -} - -double inline arsinh(double x) { - return log(x + sqrt(x * x + 1)); -} - -//y-x muss != 0 sein -double g0(double p, double y, double x, double l) { - //printf("%.1f | %.1f | %.1f | %.1f +",p,x,y,l); - - double sol = 0; - - if (l != 0) { - if (p == 0.5) { - sol = (y - x) / 2 * sqrt((y - x) * (y - x) + l * l) + l * l / 2 - * arsinh((y - x) / fabs(l)); - // printf("%.2f |",sol); - } else if (p == 0) - sol = y - x; - else if (p == -0.5) - sol = asinh((y - x) / fabs(l)); - else if (p == -1) - sol = atan((y - x) / fabs(l)); - else if (p == -1.5) - sol = (y - x) / ((l * l) * sqrt((y - x) * (y - x) + l * l)); - else - sol = (y - x) * pow((y - x) * (y - x) + l * l, p) + 2 * p * l * l - * g0(p - 1, y, x, l) / (2 * p + 1); - } else { - if (p == -0.5) - sol = sign(y - x) * log(fabs(y - x)); - else - sol = (y - x) * pow(fabs(y - x), 2 * p) / (2 * p + 1); - } - - return sol; -} - -double G00(double p, double y1, double y2, double x1, double x2, double l) { - // printf("%.1f | %.1f %.1f | %.1f %.1f | %.1f +",p,x1,x2,y1,y2,l); - - double sol = 0; - if (p == -1.5) { - if (l == 0) { - sol = -sqrt((y1 - x1) * (y1 - x1) + (y2 - x2) * (y2 - x2)) / ((y1 - - x1) * (y2 - x2)); - } else { - sol = sign((y1 - x1) * (y2 - x2)) / (2 * fabs(l)) * acos( - -2 * (y1 - x1) * (y1 - x1) * (y2 - x2) * (y2 - x2) / (((y1 - - x1) * (y1 - x1) + l * l) * ((y2 - x2) * (y2 - x2) - + l * l)) + 1); - } - - } else if (p == -0.5) { - if (l != 0) - sol = 2 * p * l * l * G00(p - 1, y1, y2, x1, x2, l); - if ((y1 - x1) != 0) - sol += (y1 - x1) * g0(p, y2, x2, - sqrt((y1 - x1) * (y1 - x1) + l * l)); - if ((y2 - x2) != 0) - sol += (y2 - x2) * g0(p, y1, x1, - sqrt((y2 - x2) * (y2 - x2) + l * l)); - sol /= 2 * p + 2; - } else { - mexErrMsgTxt("no case for p defined"); - } - - return sol; -} - -double F_par(double x1, double x2, double y1, double y2, double d1, double d2, - double d3) { - - // printf("%.1f %.1f | %.1f %.1f | %.1f %.1f %.1f",x1,x2,y1,y2,d1,d2,d3); - double sol = (x1 - y1 - d1) * (x2 - y2 - d2); - - if (sol != 0) - sol *= slpADLO(x1, x2, y1 + d1, y2 + d2, d3); - - if ((x1 - y1 - d1) != 0) - sol -= (x1 - y1 - d1) * compute_g0(0.5, x1, y1 + d1, - sqrt((x2 - y2 - d2) * (x2 - y2 - d2) + d3 * d3)); - - if ((x2 - y2 - d2) != 0) - sol -= (x2 - y2 - d2) * compute_g0(0.5, x2, y2 + d2, - sqrt((x1 - y1 - d1) * (x1 - y1 - d1) + d3 * d3)); - - double hlp = ((x1 - y1 - d1) * (x1 - y1 - d1) + (x2 - y2 - d2) * (x2 - y2 - - d2) + d3 * d3); - sol += 1. / 3 * hlp * sqrt(hlp); - return sol; -} - -double inline quadInt( - double(*f)(double, double, double, double, double, double, double), - double s1, double s2, double k1, double k2, double t1, double t2, - double l1, double l2, double d1, double d2, double d3) { - - return f(k1, k2, l1, l2, d1, d2, d3) - f(k1, k2, l1, t2, d1, d2, d3) - f( - k1, k2, t1, l2, d1, d2, d3) + f(k1, k2, t1, t2, d1, d2, d3) - f(k1, - s2, l1, l2, d1, d2, d3) + f(k1, s2, l1, t2, d1, d2, d3) + f(k1, s2, - t1, l2, d1, d2, d3) - f(k1, s2, t1, t2, d1, d2, d3) - f(s1, k2, l1, - l2, d1, d2, d3) + f(s1, k2, l1, t2, d1, d2, d3) + f(s1, k2, t1, l2, - d1, d2, d3) - f(s1, l2, t1, t2, d1, d2, d3) + f(s1, s2, l1, l2, d1, - d2, d3) - f(s1, 0, l1, t2, d1, d2, d3) - f(s1, s2, t1, l2, d1, d2, - d3) + f(s1, s2, t1, t2, d1, d2, d3); -} - -double slpADLO(double y1, double y2, double x1, double x2, double a) { - double G3 = 0; - double gL = 0; - double gK = 0; - double tmp; - - tmp = y1 - x1; - if (fabs(tmp) >= EPS * y1) { - tmp = sqrt(y1 * y1 + x1 * x1 + a * a - 2 * y1 * x1); - gL = compute_g0(-0.5, y2, x2, tmp); - } - tmp = y2 - x2; - if (fabs(tmp) >= EPS * y2) { - tmp = sqrt(y2 * y2 + x2 * x2 + a * a - 2 * y2 * x2); - gK = compute_g0(-0.5, y1, x1, tmp); - } - if (fabs(a * a) > EPS) { - if ((y1 - x1) * (y2 - x2) * a >= 0) - tmp = 1.; - else - tmp = -1.; - - G3 = tmp * acos( - (-2. * (y1 - x1) * (y1 - x1) * (y2 - x2) * (y2 - x2)) / (((y1 - - x1) * (y1 - x1) + a * a) * ((y2 - x2) * (y2 - x2) + a - * a)) + 1.) / (2. * a); - } - - return (y1 - x1) * gL + (y2 - x2) * gK - a * a * G3; -} - -double compute_g0(double p, double y, double x, double a) { - int sp = (int) 2 * (p - EPS); // MK (p-EPS) instead of (p+EPS) - //printf("\n compute_g0, p = %lf, sp = %d\n",p,sp); - assert( - p == 0 || (p == -0.5) || (p == -1) || (p == -1.5) || (fabs(a) - <= EPS)); - if (fabs(a) <= EPS) { - // printf("\n a < eps\n"); - switch (sp) { - case 0: - return y - x; - case -1: - return log(fabs(x - y)) * (y - x) / fabs(y - x); - case -2: - return -(y - x) / fabs(y - x) / fabs(y - x); - case -3: - return -0.5 * (y - x) / fabs(y - x) / fabs(y - x) / fabs(y - x); - } - } else { - // printf("\n a > eps\n"); - switch (sp) { - case 0: - return y - x; - case -1: - return asinh((y - x) / fabs(a)); - case -2: - return atan((y - x) / fabs(a)); - case -3: - return (y - x) * pow((x * x + y * y + a * a - 2 * x * y), -0.5) - / (a * a); - default: - printf("p must be either 0, -1/2, -1 or -3/2."); - return NAN; - } - } -} - -double FLO_plane(double x1, double x2, double y1, double y2, double delta1, - double delta2, double a) { - double yd1 = y1 + delta1; - double yd2 = y2 + delta2; - double tmp1 = x1 - y1 - delta1; - double tmp2 = x2 - y2 - delta2; - double tmp3 = sqrt(tmp2 * tmp2 + a * a); - double tmp4 = sqrt(tmp1 * tmp1 + a * a); - double tmp5 = pow(tmp1 * tmp1 + tmp2 * tmp2 + a * a, 3. / 2.); - double rval = 0; - - rval = tmp1 * tmp2 * slpADLO(x1, x2, yd1, yd2, a) - tmp1 * compute_g0(-0.5, - x1, yd1, tmp3) - tmp2 * compute_g0(-0.5, x2, yd2, tmp4) + tmp5 / 3.; - return rval; -} diff --git a/src/bem3d/src/laplace/SLPrecangle.hpp b/src/bem3d/src/laplace/SLPrecangle.hpp deleted file mode 100644 index 6f80150..0000000 --- a/src/bem3d/src/laplace/SLPrecangle.hpp +++ /dev/null @@ -1,21 +0,0 @@ -#ifndef HILBERT3D_LAPLACE_SLPRECTANGLE_HPP_GUARD_ -#define HILBERT3D_LAPLACE_SLPRECTANGLE_HPP_GUARD_ - -int sign(double); -double arsinh(double); - -// sol = g0(p,y,x,l); -double g0(double, double, double, double); -// sol = G00(p,y1,y2,x1,x2,l); -double G00(double, double, double, double, double, double); -// sol = F_par(x1,x2,y1,y2,d1,d2,d3); -double F_par(double, double, double, double, double, double, double); -// sol = F_ort(x1,x2,y1,y2,d1,d2,d3); -//double F_ort(double, double, double, double, double, double, double); - - -double slpADLO(double, double, double, double, double); -double compute_g0(double, double, double, double); -double FLO_plane(double, double, double, double, double, double, double); - -#endif diff --git a/src/bem3d/src/laplace/SLPrectangle.cpp b/src/bem3d/src/laplace/SLPrectangle.cpp new file mode 100644 index 0000000..26db04b --- /dev/null +++ b/src/bem3d/src/laplace/SLPrectangle.cpp @@ -0,0 +1,166 @@ +#include +#include +#include +#include + +#include "SLPrectangle.hpp" + +#define my_PI 3.141592653589793 +#define EPS 0.00001 + +using namespace std; + +int sign(double); +//double arsinh(double); + + +int inline sign(double x) { + return x > 0 ? 1 : (x < 0 ? -1 : 0); +} +/* + double inline arsinh(double x) { + return log(x + sqrt(x * x + 1)); + } + */ + +//y-x muss != 0 sein +double g0(double p, double y, double x, double l) { + //printf("%.1f | %.1f | %.1f | %.1f +",p,x,y,l); + + double sol = 0; + + if (l != 0) { + if (p == 0.5) { + sol = (y - x) / 2 * sqrt((y - x) * (y - x) + l * l) + l * l / 2 + * asinh((y - x) / fabs(l)); + // printf("%.2f |",sol); + } else if (p == 0) + sol = y - x; + else if (p == -0.5) + sol = asinh((y - x) / fabs(l)); + else if (p == -1) + sol = atan((y - x) / fabs(l)) / l; + else if (p == -1.5) + sol = (y - x) / ((l * l) * sqrt((y - x) * (y - x) + l * l)); + else + sol = (y - x) * pow((y - x) * (y - x) + l * l, p) + 2 * p * l * l + * g0(p - 1, y, x, l) / (2 * p + 1); + } else { + if (p == -0.5) + sol = sign(y - x) * log(fabs(y - x)); + else + sol = (y - x) * pow(fabs(y - x), 2 * p) / (2 * p + 1); + } + + return sol; +} + +double G00(double p, double y1, double y2, double x1, double x2, double l) { + // printf("%.1f | %.1f %.1f | %.1f %.1f | %.1f +",p,x1,x2,y1,y2,l); + + double sol = 0; + if (p == -1.5) { + if (l == 0) { + sol = -sqrt((y1 - x1) * (y1 - x1) + (y2 - x2) * (y2 - x2)) / ((y1 + - x1) * (y2 - x2)); + } else { + sol = sign((y1 - x1) * (y2 - x2)) / (2 * fabs(l)) * acos( + -2 * (y1 - x1) * (y1 - x1) * (y2 - x2) * (y2 - x2) / (((y1 + - x1) * (y1 - x1) + l * l) * ((y2 - x2) * (y2 - x2) + + l * l)) + 1); + } + + } else if ((pt > 0) && ((int) pt == pt)) { + if (l != 0) + sol = 2 * p * l * l * G00(p - 1, y1, y2, x1, x2, l); + if ((y1 - x1) != 0) + sol += (y1 - x1) * g0(p, y2, x2, + sqrt((y1 - x1) * (y1 - x1) + l * l)); + if ((y2 - x2) != 0) + sol += (y2 - x2) * g0(p, y1, x1, + sqrt((y2 - x2) * (y2 - x2) + l * l)); + sol /= 2 * p + 2; + } else { + sol = NAN; + printf("warning in G00: no case for p=%.2f defined\n", p); + } + + return sol; +} + +double F_par(double x1, double x2, double y1, double y2, double d1, double d2, + double d3) { + + // printf("%.1f %.1f | %.1f %.1f | %.1f %.1f %.1f",x1,x2,y1,y2,d1,d2,d3); + double sol = (x1 - y1 - d1) * (x2 - y2 - d2); + + if (sol != 0) + sol *= G00(-0.5, x1, x2, y1 + d1, y2 + d2, d3); + + if ((x1 - y1 - d1) != 0) + sol -= (x1 - y1 - d1) * g0(0.5, x1, y1 + d1, + sqrt((x2 - y2 - d2) * (x2 - y2 - d2) + d3 * d3)); + + if ((x2 - y2 - d2) != 0) + sol -= (x2 - y2 - d2) * g0(0.5, x2, y2 + d2, + sqrt((x1 - y1 - d1) * (x1 - y1 - d1) + d3 * d3)); + + double hlp = ((x1 - y1 - d1) * (x1 - y1 - d1) + (x2 - y2 - d2) * (x2 - y2 + - d2) + d3 * d3); + sol += 1. / 3 * hlp * sqrt(hlp); + return sol; +} + +double F_ort(double x1, double x2, double y2, double y3, double d1, double d2, + double d3) { + + // printf("%.1f %.1f | %.1f %.1f | %.1f %.1f %.1f",x1,x2,y2,y3,d1,d2,d3); + double sol = -G00(0.5, y3, x1, -d3, d1, x2 - y2 - d2); + + if ((x1 - d1) * (x2 - y2 - d2) != 0) + sol -= (x1 - d1) * (x2 - y2 - d2) * G00(-0.5, x2, y3, y2 + d2, -d3, + x1 - d1); + + if ((x1 - d1) != 0) + sol += (x1 - d1) * g0(0.5, y3, -d3, + sqrt((x1 - d1) * (x1 - d1) + (x2 - y2 - d2) * (x2 - y2 - d2))); + + if ((y3 + d3) * (x2 - y2 - d2) != 0) + sol -= (y3 + d3) * (x2 - y2 - d2) * G00(-0.5, x1, x2, d1, y2 + d2, + -y3 - d3); + + if ((y3 + d3) != 0) + sol += (y3 + d3) * g0(0.5, x1, d1, + sqrt((x2 - y2 - d2) * (x2 - y2 - d2) + (y3 + d3) * (y3 + d3))); + + return sol / 2.; +} + +double quadInt( + double(*f)(double, double, double, double, double, double, double), + double a, double b, double c, double d, double r, double t, double u, + double v, double d1, double d2, double d3) { + + return f(b, d, t, v, d1, d2, d3) - f(b, d, t, u, d1, d2, d3) - f(b, d, r, + v, d1, d2, d3) + f(b, d, r, u, d1, d2, d3) - f(b, c, t, v, d1, d2, + d3) + f(b, c, t, u, d1, d2, d3) + f(b, c, r, v, d1, d2, d3) - f(b, + c, r, u, d1, d2, d3) - f(a, d, t, v, d1, d2, d3) + f(a, d, t, u, + d1, d2, d3) + f(a, d, r, v, d1, d2, d3) - f(a, d, r, u, d1, d2, d3) + + f(a, c, t, v, d1, d2, d3) - f(a, c, t, u, d1, d2, d3) - f(a, c, + r, v, d1, d2, d3) + f(a, c, r, u, d1, d2, d3); +} + +double quad0Int( + double(*f)(double, double, double, double, double, double, double), + double b, double d, double t, double v, double d1, double d2, double d3) { + + return f(b, d, t, v, d1, d2, d3) - f(b, d, t, 0, d1, d2, d3) - f(b, d, 0, + v, d1, d2, d3) + f(b, d, 0, 0, d1, d2, d3) - f(b, 0, t, v, d1, d2, + d3) + f(b, 0, t, 0, d1, d2, d3) + f(b, 0, 0, v, d1, d2, d3) - f(b, + 0, 0, 0, d1, d2, d3) - f(0, d, t, v, d1, d2, d3) + f(0, d, t, 0, + d1, d2, d3) + f(0, d, 0, v, d1, d2, d3) - f(0, d, 0, 0, d1, d2, d3) + + f(0, 0, t, v, d1, d2, d3) - f(0, 0, t, 0, d1, d2, d3) - f(0, 0, + 0, v, d1, d2, d3) + f(0, 0, 0, 0, d1, d2, d3); + +} + diff --git a/src/bem3d/src/laplace/SLPrectangle.hpp b/src/bem3d/src/laplace/SLPrectangle.hpp new file mode 100644 index 0000000..eaff0f0 --- /dev/null +++ b/src/bem3d/src/laplace/SLPrectangle.hpp @@ -0,0 +1,28 @@ +#ifndef HILBERT3D_LAPLACE_SLPRECTANGLE_HPP_GUARD_ +#define HILBERT3D_LAPLACE_SLPRECTANGLE_HPP_GUARD_ + +//int sign(double); +//double arsinh(double); + +// sol = g0(p,y,x,l); +double g0(double, double, double, double); +// sol = G00(p,y1,y2,x1,x2,l); +double G00(double, double, double, double, double, double); +// sol = F_par(x1,x2,y1,y2,d1,d2,d3); +double F_par(double, double, double, double, double, double, double); +// sol = F_ort(x1,x2,y2,y3,d1,d2,d3); +double F_ort(double, double, double, double, double, double, double); + +// sol = quadInt((F_par/F_ort),a,b,c,d,r,t,u,v,d1,d2,d3); +double quadInt( + double(*)(double, double, double, double, double, double, double), + double, double, double, double, double, double, double, double, double, + double, double); + +// sol = quad0Int((F_par/F_ort),b,d,t,v,d1,d2,d3); +double quad0Int( + double(*)(double, double, double, double, double, double, double), + double, double, double, double, double, double, double); + + +#endif diff --git a/src/bem3d/src/laplace/SimpleLayerPotential.cpp b/src/bem3d/src/laplace/SimpleLayerPotential.cpp index c5e299a..8fd3573 100644 --- a/src/bem3d/src/laplace/SimpleLayerPotential.cpp +++ b/src/bem3d/src/laplace/SimpleLayerPotential.cpp @@ -3,174 +3,284 @@ #include "../spaces/P0Space.hpp" #include "TriangleIntegrator.hpp" -#include "SLPrecangle.hpp" - +#include "SLPrectangle.hpp" // Bibliothek fuer achsenorientierte Rechtecke #include using namespace laplace; -SimpleLayerPotential::SimpleLayerPotential(const space::P0Space& space) - : HLibOperator< space::P0Space, space::P0Space, SymmetricMatrix >( - space, space, SimpleLayerPotential::computeEntry) -{ +SimpleLayerPotential::SimpleLayerPotential(const space::P0Space& space) : + HLibOperator ( + space, space, SimpleLayerPotential::computeEntry) { } -SimpleLayerPotential::~SimpleLayerPotential() -{ +SimpleLayerPotential::~SimpleLayerPotential() { } -template < class TMesh > -double ComputeSimpleLayerPotentialEntry< TMesh >::exec( - const typename TMesh::Prop::Triangle& f1, - const typename TMesh::Prop::Triangle& f2) const -{ - TriangleIntegrator integrator = TriangleIntegrator(); - - if ( f1.computeArea() < f2.computeArea() ) - { - return integrator.integrate( f1, f2, - computeInnerIntegralForTriangles); - } - else - { - return integrator.integrate( f2, f1, - computeInnerIntegralForTriangles); - } +template +double ComputeSimpleLayerPotentialEntry::exec( + const typename TMesh::Prop::Triangle& f1, + const typename TMesh::Prop::Triangle& f2) const { + TriangleIntegrator integrator = TriangleIntegrator(); + + if (f1.computeArea() < f2.computeArea()) { + return integrator.integrate(f1, f2, computeInnerIntegralForTriangles); + } else { + return integrator.integrate(f2, f1, computeInnerIntegralForTriangles); + } } -template < class TMesh > -double ComputeSimpleLayerPotentialEntry< TMesh >::exec( - const typename TMesh::Prop::Parallelogram& f1, - const typename TMesh::Prop::Parallelogram& f2) const -{ - - const typename TMesh::Vertex& a1 = f1.getA(); - const typename TMesh::Vertex& a2 = f2.getA(); - - - - - return NAN; +template +double ComputeSimpleLayerPotentialEntry::exec( + const typename TMesh::Prop::Parallelogram& f1, + const typename TMesh::Prop::Parallelogram& f2) const { + + // Zwischenvariable fuer die Loesung (kann fuer geschwindigkeit entfernt werden) + double sol = NAN; + + // Flaechenstueck 1 + const typename TMesh::Vertex& xa = f1.getA() - f1.getB(); + const typename TMesh::Vertex& xb = f1.getA() - f1.getD(); + const typename TMesh::Vertex& xn = f1.getA() * f1.getD(); //todo Kreuzprodukt!? + + // Flaechenstueck 2 + const typename TMesh::Vertex& ya = f2.getA() - f1.getB(); + const typename TMesh::Vertex& yb = f2.getA() - f1.getD(); + const typename TMesh::Vertex& yn = f2.getA() * f2.getD(); //todo Kreuzprodukt!? + + // Abstand zwischen den Stuecken (Achtung) abstand von den beiden "kleinsten" Ecken + const typename TMesh::Vertex& d = NULL; //todo new??? + + //Variablen fuer LageInformationen + int rx, rxa, rxb, ry, rya, ryb; + + // Lage des ersten Elements ermitteln + if (xn[2] != 0) + rx = 2; + else if (xn[1] != 0) + rx = 1; + else + rx = 0; + + if (xa[2] != 0) + rxa = 2; + else if (xa[1] != 0) + rxa = 1; + else + rxa = 0; + + if (xb[2] != 0) + rxb = 2; + else if (xb[1] != 0) + rxb = 1; + else + rxb = 0; + + //kleinste Ecke finden und fuer \delta verwenden + if (xa[rxa] > 0) { + if (xb[rxb] > 0) { + d = -f1.getA; + } else { + d = -f1.getD; + } + } else { + if (xb[rxb] > 0) { + d = -f1.getB; + } else { + d = -f1.getC; + } + } + + // Lage des zweiten Elements ermitteln + if (yn[2] != 0) + ry = 2; + else if (yn[1] != 0) + ry = 1; + else + ry = 0; + + if (ya[2] != 0) + rya = 2; + else if (ya[1] != 0) + rya = 1; + else + rya = 0; + + if (yb[2] != 0) + ryb = 2; + else if (yb[1] != 0) + ryb = 1; + else + ryb = 0; + + //kleinste Ecke finden und fuer \delta verwenden + if (ya[rya] > 0) { + if (yb[ryb] > 0) { + d += f2.getA; //todo += definiert??? sonst d = d + ... + } else { + d += f2.getD; //todo += definiert??? sonst d = d + ... + } + } else { + if (yb[ryb] > 0) { + d += f2.getB; //todo += definiert??? sonst d = d + ... + } else { + d += f2.getC; //todo += definiert??? sonst d = d + ... + } + } + + if (rx == ry) { // Flaechen sind parallel + if (rxa == rya) { // Elemente zeigen in gleiche Richtung + sol = quad0Int(F_par, fabs(xa[rxa]), fabs(xb[rxb]), fabs(ya[rxa]), + fabs(yb[rxb]), d[rxa], d[rxb], d[rx]); + } else { // Elemente zeigen nicht in gleiche Richtung + sol = quad0Int(F_par, fabs(xa[rxa]), fabs(xb[rxb]), fabs(yb[rxa]), + fabs(ya[rxb]), d[rxa], d[rxb], d[rx]); + } + } else { // Flaechen sind orthogonal + if (rxa == rya) { //Elmente richtig zuordnen + sol = quad0Int(F_ort, fabs(xb[rxb]), fabs(xa[rxa]), fabs(ya[rya]), + fabs(yb[ryb]), d[rxb], d[rxa], d[rx]); + } else if (rxa == ryb) { + sol = quad0Int(F_ort, fabs(xb[rxb]), fabs(xa[rxa]), fabs(yb[ryb]), + fabs(ya[rya]), d[rxb], d[rxa], d[rx]); + } else if (rxb == rya) { + sol = quad0Int(F_ort, fabs(xa[rxa]), fabs(xb[rxb]), fabs(ya[rya]), + fabs(yb[ryb]), d[rxa], d[rxb], d[rx]); + } else { + sol = quad0Int(F_ort, fabs(xa[rxa]), fabs(xb[rxb]), fabs(yb[ryb]), + fabs(ya[rya]), d[rxa], d[rxb], d[rx]); + } + sol /= 2.; + } + + return sol / (4. * PI); } -double SimpleLayerPotential::computeEntry( - const space::P0Space::Element &e1, - const space::P0Space::Element &e2) -{ - typedef boundary_mesh::DoubleFaceDispatcher< - ComputeSimpleLayerPotentialEntry< BoundaryMesh >, BoundaryMesh, double > - ComputeEntry; +double SimpleLayerPotential::computeEntry(const space::P0Space::Element &e1, + const space::P0Space::Element &e2) { + typedef boundary_mesh::DoubleFaceDispatcher< + ComputeSimpleLayerPotentialEntry , BoundaryMesh, + double> ComputeEntry; - return ComputeEntry::Exec( e1.getSupport(), e2.getSupport(), - ComputeSimpleLayerPotentialEntry< BoundaryMesh >() ); + return ComputeEntry::Exec(e1.getSupport(), e2.getSupport(), + ComputeSimpleLayerPotentialEntry ()); } -template < class TMesh > -double -ComputeSimpleLayerPotentialEntry< TMesh >::computeInnerIntegralForTriangles( - const typename TMesh::Prop::Triangle& tau, - const typename TMesh::UVertex& x) -{ - BoundaryMesh::Face::ConstVertexIterator vIt = tau.begin_v(); - const BoundaryMesh::UVertex& x1 = *vIt; ++vIt; - const BoundaryMesh::UVertex& x2 = *vIt; ++vIt; - const BoundaryMesh::UVertex& x3 = *vIt; ++vIt; - - // determine a local orthogonal coordinate system (r1,r2,n) on the triangle tau - double t_tau = (x3-x2).norm(); - BoundaryMesh::UVertex r2 = (x3-x2)/t_tau; - double t_star=(x1-x2)*r2; - - BoundaryMesh::UVertex r1 = (x2+t_star*r2-x1); - double s_tau = r1.norm(); - r1 = r1 / s_tau; - - BoundaryMesh::UVertex n = BoundaryMesh::Vertex::crossProduct(r1,r2); - - // determine necessary information - double sx = (x-x1)*r1; - double tx = (x-x1)*r2; - double ux = (x-x1)*n; - double a1 = -t_star/s_tau; - double a2 = (t_tau-t_star)/s_tau; - - // analytic computation of inner integral - return 0.25*(F(s_tau,a2,sx,tx,ux) - F(0,a2,sx,tx,ux) - F(s_tau,a1,sx,tx,ux) + F(0,a1,sx,tx,ux))/M_PI; +template +double ComputeSimpleLayerPotentialEntry::computeInnerIntegralForTriangles( + const typename TMesh::Prop::Triangle& tau, + const typename TMesh::UVertex& x) { + BoundaryMesh::Face::ConstVertexIterator vIt = tau.begin_v(); + const BoundaryMesh::UVertex& x1 = *vIt; + ++vIt; + const BoundaryMesh::UVertex& x2 = *vIt; + ++vIt; + const BoundaryMesh::UVertex& x3 = *vIt; + ++vIt; + + // determine a local orthogonal coordinate system (r1,r2,n) on the triangle tau + double t_tau = (x3 - x2).norm(); + BoundaryMesh::UVertex r2 = (x3 - x2) / t_tau; + double t_star = (x1 - x2) * r2; + + BoundaryMesh::UVertex r1 = (x2 + t_star * r2 - x1); + double s_tau = r1.norm(); + r1 = r1 / s_tau; + + BoundaryMesh::UVertex n = BoundaryMesh::Vertex::crossProduct(r1, r2); + + // determine necessary information + double sx = (x - x1) * r1; + double tx = (x - x1) * r2; + double ux = (x - x1) * n; + double a1 = -t_star / s_tau; + double a2 = (t_tau - t_star) / s_tau; + + // analytic computation of inner integral + return 0.25 * (F(s_tau, a2, sx, tx, ux) - F(0, a2, sx, tx, ux) - F(s_tau, + a1, sx, tx, ux) + F(0, a1, sx, tx, ux)) / M_PI; } -template < class TMesh > -double -ComputeSimpleLayerPotentialEntry< TMesh >::F( - double s, double a, double sx, double tx, double ux) -{ - double p = (a*tx+sx)/(1+a*a); - double q = ux*ux + (tx-a*sx)*(tx-a*sx)/(1+a*a); - - return (s-sx)*log(a*s - tx + sqrt((s-sx)*(s-sx) + (a*s-tx)*(a*s-tx) + ux*ux)) - s - + (a*sx-tx)*log(sqrt(1+a*a)*(s-p)+sqrt((1+a*a)*(s-p)*(s-p) + q*q))/sqrt(q+a*a) - + 2*ux*atan(((q-(a*sx-tx)/(1+a*a))*sqrt((1+a*a)*(s-p)*(s-p)+q*q) + (a*s-tx-q)*q)/((s-p)*ux)); +template +double ComputeSimpleLayerPotentialEntry::F(double s, double a, + double sx, double tx, double ux) { + double p = (a * tx + sx) / (1 + a * a); + double q = ux * ux + (tx - a * sx) * (tx - a * sx) / (1 + a * a); + + return (s - sx) * log( + a * s - tx + + sqrt( + (s - sx) * (s - sx) + (a * s - tx) * (a * s - tx) + + ux * ux)) - s + (a * sx - tx) * log( + sqrt(1 + a * a) * (s - p) + sqrt( + (1 + a * a) * (s - p) * (s - p) + q * q)) / sqrt(q + a * a) + + 2 * ux * atan( + ((q - (a * sx - tx) / (1 + a * a)) * sqrt( + (1 + a * a) * (s - p) * (s - p) + q * q) + (a * s + - tx - q) * q) / ((s - p) * ux)); } -void fill_supermatrix_aca_OLD(supermatrix* A, const cluster* row, const cluster* col, void *data, - double (*compute_entry)(int i, int j, void* data), double aca_eps) -{ -// std::cerr << "*** fill_supermatrix_aca" << std::endl; - - fullmatrix* f = A->f; - rkmatrix* r = A->r; - int i, j; - int rank; - - if ( f!= NULL ) { // fill fullmatrix block -// std::cerr << "*** full matrix block" << std::endl; - for ( i=0; isize; i++ ){ - for ( j=0; jsize; j++ ) - f->e[i+j*row->size] = compute_entry(row->start+i,col->start+j, data); - } - - return; - } - - if ( r!= NULL ) { // fill rk-block with aca -// std::cerr << "*** rank k matrix block" << std::endl; - if ( r->rows > r-> cols ) - rank = r->cols; - else - rank = r->rows; - - if ( rank > ACA_KMAX ) - rank = ACA_KMAX; - - r->k = rank; - r->a = allocate_matrix(r->rows,rank); - r->b = allocate_matrix(r->cols,rank); - - r->kt = newaca_fill_block(r->a, r->b, r->rows, r->cols, - row->start, col->start, - compute_entry, data, - rank, aca_eps, ACA_STRATEGY); - - r->a = (double*) realloc(r->a,r->rows*r->kt*sizeof(double)); - r->b = (double*) realloc(r->b,r->cols*r->kt*sizeof(double)); - r->k = r->kt; - - return; - } - - if(row->sons>0) { - if(col->sons>0) { - for(int i=0;isons;++i) - for(int j=0;jsons;++j) { - int s=i+j*row->sons; - fill_supermatrix_aca_OLD(A->s[s],row->son[i],col->son[j],data,compute_entry,aca_eps); - } - } else { - for(int i=0;isons;++i) - fill_supermatrix_aca_OLD(A->s[i],row->son[i],col,data,compute_entry,aca_eps); - } - } else { - for(int i=0;isons;++i) - fill_supermatrix_aca_OLD(A->s[i],row,col->son[i],data,compute_entry,aca_eps); - } +void fill_supermatrix_aca_OLD(supermatrix* A, const cluster* row, + const cluster* col, void *data, + double(*compute_entry)(int i, int j, void* data), double aca_eps) { + // std::cerr << "*** fill_supermatrix_aca" << std::endl; + + fullmatrix* f = A->f; + rkmatrix* r = A->r; + int i, j; + int rank; + + if (f != NULL) { // fill fullmatrix block + // std::cerr << "*** full matrix block" << std::endl; + for (i = 0; i < row->size; i++) { + for (j = 0; j < col->size; j++) + f->e[i + j * row->size] = compute_entry(row->start + i, + col->start + j, data); + } + + return; + } + + if (r != NULL) { // fill rk-block with aca + // std::cerr << "*** rank k matrix block" << std::endl; + if (r->rows > r-> cols) + rank = r->cols; + else + rank = r->rows; + + if (rank > ACA_KMAX) + rank = ACA_KMAX; + + r->k = rank; + r->a = allocate_matrix(r->rows, rank); + r->b = allocate_matrix(r->cols, rank); + + r->kt = newaca_fill_block(r->a, r->b, r->rows, r->cols, row->start, + col->start, compute_entry, data, rank, aca_eps, ACA_STRATEGY); + + r->a = (double*) realloc(r->a, r->rows * r->kt * sizeof(double)); + r->b = (double*) realloc(r->b, r->cols * r->kt * sizeof(double)); + r->k = r->kt; + + return; + } + + if (row->sons > 0) { + if (col->sons > 0) { + for (int i = 0; i < row->sons; ++i) + for (int j = 0; j < col->sons; ++j) { + int s = i + j * row->sons; + fill_supermatrix_aca_OLD(A->s[s], row->son[i], col->son[j], + data, compute_entry, aca_eps); + } + } else { + for (int i = 0; i < row->sons; ++i) + fill_supermatrix_aca_OLD(A->s[i], row->son[i], col, data, + compute_entry, aca_eps); + } + } else { + for (int i = 0; i < col->sons; ++i) + fill_supermatrix_aca_OLD(A->s[i], row, col->son[i], data, + compute_entry, aca_eps); + } } diff --git 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nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { - int i,j,k; + int i, j, k; //sicherheitsabfragen zu Datengroessen if (nrhs != 2) @@ -82,10 +82,10 @@ void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { x3[1] = C[cm + (int) E[3 * em + j] - 1]; x3[2] = C[2 * cm + (int) E[3 * em + j] - 1]; - for (i = 0; i<3;++i) + for (i = 0; i < 3; ++i) xa[i] = x1[i] - x0[i]; - for (i = 0; i<3;++i) + for (i = 0; i < 3; ++i) xb[i] = x3[i] - x0[i]; //Kreuzprodukt @@ -93,7 +93,6 @@ void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { xn[1] = (xa[2]) * (xb[0]) - (xa[0]) * (xb[2]); xn[2] = (xa[0]) * (xb[1]) - (xa[1]) * (xb[0]); - // Lageeigenschaften des Flaechenstuecks //if(xn[0]*xn[0]+xn[1]*xn[1]0){ - if(xb[rxb]>0){ - for (i = 0; i<3;++i) - dt[i] = - x0[i]; - }else{ - for (i = 0; i<3;++i) - dt[i] = - x3[i]; + if (xa[rxa] > 0) { + if (xb[rxb] > 0) { + for (i = 0; i < 3; ++i) + dt[i] = -x0[i]; + } else { + for (i = 0; i < 3; ++i) + dt[i] = -x3[i]; } - }else{ - if(xb[rxb]>0){ - for (i = 0; i<3;++i) - dt[i] = - x1[i]; - }else{ - for (i = 0; i<3;++i) - dt[i] = - x2[i]; + } else { + if (xb[rxb] > 0) { + for (i = 0; i < 3; ++i) + dt[i] = -x1[i]; + } else { + for (i = 0; i < 3; ++i) + dt[i] = -x2[i]; //printf("Error! Daten existieren nicht. Zugriff auf vierten punkt"); } } @@ -161,10 +160,10 @@ void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { y3[1] = C[cm + (int) E[3 * em + k] - 1]; y3[2] = C[2 * cm + (int) E[3 * em + k] - 1]; - for (i = 0; i<3;++i) + for (i = 0; i < 3; ++i) ya[i] = y1[i] - y0[i]; - for (i = 0; i<3;++i) + for (i = 0; i < 3; ++i) yb[i] = y3[i] - y0[i]; yn[0] = (ya[1]) * (yb[2]) - (ya[2]) * (yb[1]); @@ -194,27 +193,27 @@ void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { //kleinste Ecke finden und fuer \delta verwenden - if(ya[rya]>0){ - if(yb[ryb]>0){ - for (i = 0; i<3;++i) + if (ya[rya] > 0) { + if (yb[ryb] > 0) { + for (i = 0; i < 3; ++i) d[i] = dt[i] + y0[i]; - }else{ - for (i = 0; i<3;++i) + } else { + for (i = 0; i < 3; ++i) d[i] = dt[i] + y3[i]; } - }else{ - if(yb[ryb]>0){ - for (i = 0; i<3;++i) + } else { + if (yb[ryb] > 0) { + for (i = 0; i < 3; ++i) d[i] = dt[i] + y1[i]; - }else{ - for (i = 0; i<3;++i) + } else { + for (i = 0; i < 3; ++i) d[i] = dt[i] + y2[i]; //printf("Error! Daten existieren nicht. Zugriff auf vierten punkt"); } } - // for (i = 0; i<3;++i) - // d[i] = y0[i]-x0[i]; + // for (i = 0; i<3;++i) + // d[i] = y0[i]-x0[i]; //printf("(%d,%d)",rx,ry); if (rx == ry) { @@ -226,22 +225,52 @@ void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { //printf("%d%d %.1f %.1f | %.1f %.1f || %.1f %.1f | %.1f %.1f || %.1f %.1f %.1f\n",j,k,x0[0], x1[0], x0[1], x3[1], y0[0], // y1[0], y0[1], y3[1], d[0], d[1], d[2]); //printf("%d%d %.1f %.1f %.1f\n",j,k,d[0],d[1],d[2]); - tmp = quad0Int(F_par, fabs(xa[rxa]), fabs(xb[rxb]), - fabs(ya[rxa]), fabs(yb[rxb]), d[rxa], d[rxb], d[rx]); + tmp + = quad0Int(F_par, fabs(xa[rxa]), fabs(xb[rxb]), + fabs(ya[rxa]), fabs(yb[rxb]), d[rxa], + d[rxb], d[rx]); // printf("%d%d|%.2f\n",j,k,tmp); - } else{ + } else { //printf("%d%d %.1f %.1f | %.1f %.1f || %.1f %.1f | %.1f %.1f || %.1f %.1f %.1f\n",j,k,x0[0], x1[0], x0[1], x3[1], y0[0], // y1[0], y0[1], y3[1], d[0], d[1], d[2]); //printf("%d%d %.1f %.1f %.1f\n",j,k,d[0],d[1],d[2]); - tmp = quad0Int(F_par, fabs(xa[rxa]), fabs(xb[rxb]), - fabs(yb[rxa]), fabs(ya[rxb]), d[rxa], d[rxb], d[rx]); + tmp + = quad0Int(F_par, fabs(xa[rxa]), fabs(xb[rxb]), + fabs(yb[rxa]), fabs(ya[rxb]), d[rxa], + d[rxb], d[rx]); // printf("%d%d|%.2f\n",j,k,tmp); } - A[(k * em) + j] = 1. / (4 * my_PI) * tmp; } else { - A[(k * em) + j] = NAN; + //printf("(%d,%d@%d,%d)", rxa, rxb, rya, ryb); + //printf("(%d,%d)", rx, ry); + //printf("\n"); + + if (rxa == rya) { + tmp + = quad0Int(F_ort, fabs(xb[rxb]), fabs(xa[rxa]), + fabs(ya[rya]), fabs(yb[ryb]), d[rxb], + d[rxa], d[rx]); + } else if (rxa == ryb) { + tmp + = quad0Int(F_ort, fabs(xb[rxb]), fabs(xa[rxa]), + fabs(yb[ryb]), fabs(ya[rya]), d[rxb], + d[rxa], d[rx]); + } else if (rxb == rya) { + tmp + = quad0Int(F_ort, fabs(xa[rxa]), fabs(xb[rxb]), + fabs(ya[rya]), fabs(yb[ryb]), d[rxa], + d[rxb], d[rx]); + } else { + tmp + = quad0Int(F_ort, fabs(xa[rxa]), fabs(xb[rxb]), + fabs(yb[ryb]), fabs(ya[rya]), d[rxa], + d[rxb], d[rx]); + } + A[(k * em) + j] = tmp; + } + A[(k * em) + j] = 1. / (4 * my_PI) * tmp; // Vorbereiten der DATEN // ej = coordinates(elements(j,:)',:); diff --git a/src/exmpl_3DFichCube.mat b/src/exmpl_3DFichCube.mat new file mode 100644 index 0000000000000000000000000000000000000000..3c5c502061df8d68352be66b8e2f9629e9783250 GIT binary patch literal 322 zcmeZu4DoSvQZUssQ1EpO(M`+DN!3vZ$Vn_o%P-2cQgHY2i*PhE(NS8$o zrH&1vr^FeP(iGBIlJXS%&YjoyI(f!h$5WSWHS@{PhRFYo4UFfSK1e(iP&&mit-Z71 zh{4qZUyKx1x{A4n@-r}Q)#C>loCr2px5t~WL4n6*;gqI7j(v|yZ>*G#t*G%nq@w>h z(nrXthR3k%=ae{G;}a*Y9=BXqxSzkk?wOvdhKp~?fp2^sr+&^T%H7TFn)$fKW9OE; YZC55F9A2?f>PFSf@<;3&F0#!804FPKH2?qr literal 0 HcmV?d00001 diff --git a/src/exportCOEL.m b/src/exportCOEL.m index 7dbe086..30fe941 100644 --- a/src/exportCOEL.m +++ b/src/exportCOEL.m @@ -29,18 +29,18 @@ if(size(ele,2) == 3) end end if(size(ele,2)==4) -% disp 'schreibe in Datei' -% dat = fopen(file,'w'); -% -% for i=1:size(coo,1); -% fprintf(dat,'v %.4f %.4f %.4f\n',coo(i,:)); -% end -% fprintf(dat,'\n'); -% for i=1:size(ele,1); -% fprintf(dat,'f %.0f %.0f %.0f %.0f\n',ele(i,:)); -% end -% -% fclose(dat); + disp 'schreibe in Datei' + dat = fopen(file,'w'); + + for i=1:size(coo,1); + fprintf(dat,'v %.4f %.4f %.4f\n',coo(i,:)); + end + fprintf(dat,'\n'); + for i=1:size(ele,1); + fprintf(dat,'f %.0f %.0f %.0f %.0f\n',ele(i,:)); + end + + fclose(dat); end end diff --git a/src/mex_Fort.cpp b/src/mex_Fort.cpp new file mode 100644 index 0000000..7d4f894 --- /dev/null +++ b/src/mex_Fort.cpp @@ -0,0 +1,44 @@ +#include +#include +#include +#include "mex.h" +#include + +#include "SLPrecangle.hpp" + +#define my_PI 3.141592653589793 +#define EPS 0.02 + +using namespace std; + + +void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { + //sicherheitsabfragen zu Datengroessen + if (nrhs != 7) + mexErrMsgTxt("expected (x1,x2,y2,y3,d1,d2,d3)"); + if (nlhs > 2) + mexErrMsgTxt("has maximal two output arguments"); + + + plhs[0] = mxCreateDoubleMatrix(1, 1, mxREAL); + plhs[1] = mxCreateDoubleMatrix(1, 1, mxREAL); + +// plhs[0] = mxCreateDoubleMatrix(1, 2, mxREAL); + + + //printf("%f,%f,%f,%f",*mxGetPr(prhs[0]),*mxGetPr(prhs[1]),*mxGetPr(prhs[2]),*mxGetPr(prhs[3])); + + //sol = G00(p,y1,y2,x1,x2,l); + + *mxGetPr(plhs[0]) = F_ort(*mxGetPr(prhs[0]),*mxGetPr(prhs[1]),*mxGetPr(prhs[2]),*mxGetPr(prhs[3]),*mxGetPr(prhs[4]),*mxGetPr(prhs[5]),*mxGetPr(prhs[6])); + *mxGetPr(plhs[1]) = FLO_perp(*mxGetPr(prhs[0]),*mxGetPr(prhs[1]),*mxGetPr(prhs[2]),*mxGetPr(prhs[3]),*mxGetPr(prhs[4]),*mxGetPr(prhs[5]),*mxGetPr(prhs[6])); + +// printf("%f",FLO_plane(*mxGetPr(prhs[0]),*mxGetPr(prhs[1]),*mxGetPr(prhs[2]),*mxGetPr(prhs[3]),*mxGetPr(prhs[4]),*mxGetPr(prhs[5]),*mxGetPr(prhs[6]))); + +// *(mxGetPr(plhs[0])+1) = FLO_plane(*mxGetPr(prhs[0]),*mxGetPr(prhs[1]),*mxGetPr(prhs[2]),*mxGetPr(prhs[3]),*mxGetPr(prhs[4]),*mxGetPr(prhs[5]),*mxGetPr(prhs[6])); + + +} + + + diff --git a/src/mex_Fpar.cpp b/src/mex_Fpar.cpp index 9af5fac..ab8ae94 100644 --- a/src/mex_Fpar.cpp +++ b/src/mex_Fpar.cpp @@ -15,7 +15,7 @@ using namespace std; void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { //sicherheitsabfragen zu Datengroessen if (nrhs != 7) - mexErrMsgTxt("expected (1,x2,y1,y2,d1,d2,d3)"); + mexErrMsgTxt("expected (x1,x2,y1,y2,d1,d2,d3)"); if (nlhs > 2) mexErrMsgTxt("has maximal two output arguments"); diff --git a/src/mexit.m b/src/mexit.m index 4057572..f552eff 100644 --- a/src/mexit.m +++ b/src/mexit.m @@ -2,6 +2,7 @@ mex mex_g0.cpp SLPrecangle.cpp mex mex_G00.cpp SLPrecangle.cpp mex mex_Fpar.cpp SLPrecangle.cpp +mex mex_Fort.cpp SLPrecangle.cpp mex build_A.cpp SLPrecangle.cpp diff --git a/src/surfDoubleQuad.m b/src/surfDoubleQuad.m index a93accd..86ed43c 100644 --- a/src/surfDoubleQuad.m +++ b/src/surfDoubleQuad.m @@ -45,60 +45,60 @@ % end -% function in = surfDoubleQuad(f,a,b,c,d,r,t,u,v,w) -% -% [x1n x1w] = gauss(w,a,b); -% [x2n x2w] = gauss(w,c,d); -% [y1n y1w] = gauss(w,r,t); -% [y2n y2w] = gauss(w,u,v); -% -% in = 0; -% for i=1:length(y2n) -% for j=1:length(y1n) -% for k=1:length(x2n) -% for l = 1:length(x1n) -% -% in = in + y2w(i) * y1w(j) * x2w(k) * x1w(l) * f(x1n(l),x2n(k),y1n(j),y2n(i)); -% -% end -% end -% end -% end -% -% end - function in = surfDoubleQuad(f,a,b,c,d,r,t,u,v,w) [x1n x1w] = gauss(w,a,b); [x2n x2w] = gauss(w,c,d); - - - d1=r-a; - d2=u-c; -% sum(x1w)a - x1n=x1n-d1; x2n=x2n-d2; -% c -% d - - p = -0.5; + [y1n y1w] = gauss(w,r,t); + [y2n y2w] = gauss(w,u,v); in = 0; - + for i=1:length(y2n) + for j=1:length(y1n) for k=1:length(x2n) for l = 1:length(x1n) - [my(1) mk(1)] = mex_G00(p,r,u,x1n(l),x2n(k),0); - [my(2) mk(2)] = mex_G00(p,t,v,x1n(l),x2n(k),0); - [my(3) mk(3)] = mex_G00(p,t,u,x1n(l),x2n(k),0); - [my(4) mk(4)] = mex_G00(p,r,v,x1n(l),x2n(k),0); - - -% my_sol = my(1)+my(2)-my(3)-my(4); - - in = in + x2w(k) * x1w(l) * (my(1)+my(2)-my(3)-my(4)); + in = in + y2w(i) * y1w(j) * x2w(k) * x1w(l) * f(x1n(l),x2n(k),y1n(j),y2n(i)); end end -% in + end + end + +end -end \ No newline at end of file +% function in = surfDoubleQuad(f,a,b,c,d,r,t,u,v,w) +% +% [x1n x1w] = gauss(w,a,b); +% [x2n x2w] = gauss(w,c,d); +% +% +% d1=r-a; +% d2=u-c; +% % sum(x1w)a +% x1n=x1n-d1; x2n=x2n-d2; +% % c +% % d +% +% p = -0.5; +% +% in = 0; +% +% for k=1:length(x2n) +% for l = 1:length(x1n) +% +% [my(1) mk(1)] = mex_G00(p,r,u,x1n(l),x2n(k),0); +% [my(2) mk(2)] = mex_G00(p,t,v,x1n(l),x2n(k),0); +% [my(3) mk(3)] = mex_G00(p,t,u,x1n(l),x2n(k),0); +% [my(4) mk(4)] = mex_G00(p,r,v,x1n(l),x2n(k),0); +% +% +% % my_sol = my(1)+my(2)-my(3)-my(4); +% +% in = in + x2w(k) * x1w(l) * (my(1)+my(2)-my(3)-my(4)); +% +% end +% end +% % in +% +% end \ No newline at end of file diff --git a/src/test_Fort.m b/src/test_Fort.m new file mode 100644 index 0000000..ad326d2 --- /dev/null +++ b/src/test_Fort.m @@ -0,0 +1,19 @@ +function [ret] = test_Fort(a,b,c,d,r,t,u,v,l1,l2,l3) + + + quad_sol = surfDoubleQuad(@(x1,x2,y2,y3)1/sqrt((x1-l1).^2+(x2-y2-l2).^2+(y3+l3).^2)... + ,a,b,c,d,r,t,u,v,4); + + intF = @(f,a,b,c,d,r,t,u,v)... + f(b,d,t,v)-f(b,d,t,u)-f(b,d,r,v)+f(b,d,r,u)... + -f(b,c,t,v)+f(b,c,t,u)+f(b,c,r,v)-f(b,c,r,u)... + -f(a,d,t,v)+f(a,d,t,u)+f(a,d,r,v)-f(a,d,r,u)... + +f(a,c,t,v)-f(a,c,t,u)-f(a,c,r,v)+f(a,c,r,u); + + sol = intF(@(x1,x2,y1,y2)mex_Fort(x1,x2,y1,y2,l1,l2,l3),a,b,c,d,r,t,u,v); + + + + ret = [quad_sol sol]; +end + diff --git a/src/test_solveError.m b/src/test_solveError.m index 9730b85..ae4f5c3 100644 --- a/src/test_solveError.m +++ b/src/test_solveError.m @@ -1,6 +1,6 @@ %% Laden des Gitters -load exmpl_2DLShape %Energienorm sollte gegen 8.28466 konvergieren +load exmpl_3DFichCube %Energienorm sollte gegen 8.28466 konvergieren %% Rotationen einzelnen von Elementen (zum Testen) % coordinates = coordinates(:,[ 1 3 2]); @@ -16,7 +16,7 @@ end % [coordinates,elements]=refineQuad(coordinates,elements,ones(1,size(elements,1))); % [coordinates,elements]=refineQuad(coordinates,elements,ones(1,size(elements,1))); -for ref = 1:4 +for ref = 1:3 %% Testen mit Quadratur... und mex_G00 % A = build_A2(coordinates,elements); -- 2.47.3