mirror of
https://github.com/NGSolve/netgen.git
synced 2024-12-25 21:40:33 +05:00
3786 lines
89 KiB
C++
3786 lines
89 KiB
C++
#include <mystdlib.h>
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#include "meshing.hpp"
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#include "../general/autodiff.hpp"
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namespace netgen
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{
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// bool rational = true;
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static void ComputeGaussRule (int n, Array<double> & xi, Array<double> & wi)
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{
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xi.SetSize (n);
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wi.SetSize (n);
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int m = (n+1)/2;
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double p1, p2, p3;
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double pp, z, z1;
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for (int i = 1; i <= m; i++)
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{
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z = cos ( M_PI * (i - 0.25) / (n + 0.5));
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while(1)
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{
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p1 = 1; p2 = 0;
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for (int j = 1; j <= n; j++)
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{
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p3 = p2; p2 = p1;
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p1 = ((2 * j - 1) * z * p2 - (j - 1) * p3) / j;
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}
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// p1 is legendre polynomial
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pp = n * (z*p1-p2) / (z*z - 1);
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z1 = z;
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z = z1-p1/pp;
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if (fabs (z - z1) < 1e-14) break;
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}
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xi[i-1] = 0.5 * (1 - z);
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xi[n-i] = 0.5 * (1 + z);
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wi[i-1] = wi[n-i] = 1.0 / ( (1 - z * z) * pp * pp);
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}
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}
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// compute edge bubbles up to order n, x \in (-1, 1)
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static void CalcEdgeShape (int n, double x, double * shape)
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{
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double p1 = x, p2 = -1, p3 = 0;
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for (int j=2; j<=n; j++)
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{
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p3=p2; p2=p1;
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p1=( (2*j-3) * x * p2 - (j-3) * p3) / j;
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shape[j-2] = p1;
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}
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}
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static void CalcEdgeDx (int n, double x, double * dshape)
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{
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double p1 = x, p2 = -1, p3 = 0;
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double p1dx = 1, p2dx = 0, p3dx = 0;
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for (int j=2; j<=n; j++)
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{
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p3=p2; p2=p1;
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p3dx = p2dx; p2dx = p1dx;
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p1=( (2*j-3) * x * p2 - (j-3) * p3) / j;
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p1dx = ( (2*j-3) * (x * p2dx + p2) - (j-3) * p3dx) / j;
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dshape[j-2] = p1dx;
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}
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}
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static void CalcEdgeShapeDx (int n, double x, double * shape, double * dshape)
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{
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double p1 = x, p2 = -1, p3 = 0;
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double p1dx = 1, p2dx = 0, p3dx = 0;
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for (int j=2; j<=n; j++)
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{
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p3=p2; p2=p1;
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p3dx = p2dx; p2dx = p1dx;
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p1=( (2*j-3) * x * p2 - (j-3) * p3) / j;
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p1dx = ( (2*j-3) * (x * p2dx + p2) - (j-3) * p3dx) / j;
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shape[j-2] = p1;
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dshape[j-2] = p1dx;
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}
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}
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// compute L_i(x/t) * t^i
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static void CalcScaledEdgeShape (int n, double x, double t, double * shape)
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{
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static bool init = false;
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static double coefs[100][2];
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if (!init)
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{
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for (int j = 0; j < 100; j++)
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{
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coefs[j][0] = double(2*j+1)/(j+2);
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coefs[j][1] = -double(j-1)/(j+2);
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}
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init = true;
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}
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double p1 = x, p2 = -1, p3 = 0;
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double tt = t*t;
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for (int j=0; j<=n-2; j++)
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{
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p3=p2; p2=p1;
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p1= coefs[j][0] * x * p2 + coefs[j][1] * tt*p3;
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// p1=( (2*j+1) * x * p2 - t*t*(j-1) * p3) / (j+2);
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shape[j] = p1;
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}
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}
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template <int DIST>
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static void CalcScaledEdgeShapeDxDt (int n, double x, double t, double * dshape)
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{
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double p1 = x, p2 = -1, p3 = 0;
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double p1dx = 1, p1dt = 0;
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double p2dx = 0, p2dt = 0;
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double p3dx = 0, p3dt = 0;
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for (int j=0; j<=n-2; j++)
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{
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p3=p2; p3dx=p2dx; p3dt = p2dt;
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p2=p1; p2dx=p1dx; p2dt = p1dt;
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p1 = ( (2*j+1) * x * p2 - t*t*(j-1) * p3) / (j+2);
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p1dx = ( (2*j+1) * (x * p2dx + p2) - t*t*(j-1) * p3dx) / (j+2);
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p1dt = ( (2*j+1) * x * p2dt - (j-1)* (t*t*p3dt+2*t*p3)) / (j+2);
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// shape[j] = p1;
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dshape[DIST*j ] = p1dx;
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dshape[DIST*j+1] = p1dt;
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}
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}
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template <class Tx, class Tres>
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static void LegendrePolynomial (int n, Tx x, Tres * values)
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{
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switch (n)
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{
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case 0:
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values[0] = 1;
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break;
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case 1:
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values[0] = 1;
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values[1] = x;
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break;
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default:
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if (n < 0) return;
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Tx p1 = 1.0, p2 = 0.0, p3;
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values[0] = 1.0;
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for (int j=1; j<=n; j++)
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{
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p3 = p2; p2 = p1;
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p1 = ((2.0*j-1.0)*x*p2 - (j-1.0)*p3) / j;
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values[j] = p1;
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}
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}
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}
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template <class Tx, class Tt, class Tres>
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static void ScaledLegendrePolynomial (int n, Tx x, Tt t, Tres * values)
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{
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switch (n)
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{
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case 0:
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values[0] = 1.0;
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break;
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case 1:
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values[0] = 1.0;
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values[1] = x;
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break;
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default:
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if (n < 0) return;
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Tx p1 = 1.0, p2 = 0.0, p3;
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values[0] = 1.0;
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for (int j=1; j<=n; j++)
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{
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p3 = p2; p2 = p1;
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p1 = ((2.0*j-1.0)*x*p2 - t*t*(j-1.0)*p3) / j;
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values[j] = p1;
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}
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}
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}
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class RecPol
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{
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protected:
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int maxorder;
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double *a, *b, *c;
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public:
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RecPol (int amaxorder)
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{
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maxorder = amaxorder;
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// cout << "maxo = " << maxorder << endl;
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a = new double[maxorder+1];
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b = new double[maxorder+1];
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c = new double[maxorder+1];
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}
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~RecPol ()
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{
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delete a;
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delete b;
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delete c;
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}
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template <class S, class T>
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void Evaluate (int n, S x, T * values)
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{
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S p1 = 1.0, p2 = 0.0, p3;
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if (n >= 0)
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p2 = values[0] = 1.0;
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if (n >= 1)
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p1 = values[1] = a[0]+b[0]*x;
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for (int i = 1; i < n; i++)
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{
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p3 = p2; p2=p1;
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p1 = (a[i]+b[i]*x)*p2-c[i]*p3;
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values[i+1] = p1;
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}
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}
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};
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class JacobiRecPol : public RecPol
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{
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public:
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JacobiRecPol (int amo, double al, double be)
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: RecPol (amo)
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{
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for (int i = 0; i <= maxorder; i++)
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{
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double den = 2*(i+1)*(i+al+be+1)*(2*i+al+be);
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a[i] = (2*i+al+be+1)*(al*al-be*be) / den;
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b[i] = (2*i+al+be)*(2*i+al+be+1)*(2*i+al+be+2) / den;
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c[i] = 2*(i+al)*(i+be)*(2*i+al+be+2) / den;
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}
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}
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};
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template <class S, class T>
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inline void JacobiPolynomial (int n, S x, double alpha, double beta, T * values)
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{
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S p1 = 1.0, p2 = 0.0, p3;
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if (n >= 0)
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p2 = values[0] = 1.0;
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if (n >= 1)
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p1 = values[1] = 0.5 * (2*(alpha+1)+(alpha+beta+2)*(x-1));
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for (int i = 1; i < n; i++)
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{
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p3 = p2; p2=p1;
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p1 =
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1.0 / ( 2 * (i+1) * (i+alpha+beta+1) * (2*i+alpha+beta) ) *
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(
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( (2*i+alpha+beta+1)*(alpha*alpha-beta*beta) +
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(2*i+alpha+beta)*(2*i+alpha+beta+1)*(2*i+alpha+beta+2) * x)
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* p2
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- 2*(i+alpha)*(i+beta) * (2*i+alpha+beta+2) * p3
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);
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values[i+1] = p1;
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}
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}
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template <class S, class St, class T>
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inline void ScaledJacobiPolynomial (int n, S x, St t, double alpha, double beta, T * values)
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{
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/*
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S p1 = 1.0, p2 = 0.0, p3;
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if (n >= 0) values[0] = 1.0;
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*/
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S p1 = 1.0, p2 = 0.0, p3;
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if (n >= 0)
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p2 = values[0] = 1.0;
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if (n >= 1)
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p1 = values[1] = 0.5 * (2*(alpha+1)*t+(alpha+beta+2)*(x-t));
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for (int i=1; i < n; i++)
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{
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p3 = p2; p2=p1;
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p1 =
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1.0 / ( 2 * (i+1) * (i+alpha+beta+1) * (2*i+alpha+beta) ) *
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(
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( (2*i+alpha+beta+1)*(alpha*alpha-beta*beta) * t +
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(2*i+alpha+beta)*(2*i+alpha+beta+1)*(2*i+alpha+beta+2) * x)
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* p2
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- 2*(i+alpha)*(i+beta) * (2*i+alpha+beta+2) * t * t * p3
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);
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values[i+1] = p1;
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}
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}
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Array<RecPol*> jacpols2;
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// compute face bubbles up to order n, 0 < y, y-x < 1, x+y < 1
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template <class Tx, class Ty, class Ts>
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static void CalcTrigShape (int n, Tx x, Ty y, Ts * shape)
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{
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// static int timer = NgProfiler::CreateTimer ("Curvedels - CalcTrigShape");
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// NgProfiler::RegionTimer reg (timer);
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if (n < 3) return;
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Tx hx[50], hy[50*50];
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ScaledJacobiPolynomial (n-3, x, 1-y, 2, 2, hx);
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// for (int ix = 0; ix <= n-3; ix++)
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// JacobiPolynomial (n-3, 2*y-1, 2*ix+5, 2, hy+50*ix);
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for (int ix = 0; ix <= n-3; ix++)
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jacpols2[2*ix+5] -> Evaluate (n-3, 2*y-1, hy+50*ix);
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int ii = 0;
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Tx bub = (1+x-y)*y*(1-x-y);
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for (int ix = 0; ix <= n-3; ix++)
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hx[ix] *= bub;
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for (int iy = 0; iy <= n-3; iy++)
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for (int ix = 0; ix <= n-3-iy; ix++)
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shape[ii++] = hx[ix]*hy[iy+50*ix];
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}
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static void CalcTrigShapeDxDy (int n, double x, double y, double * dshape)
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{
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if (n < 3) return;
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AutoDiff<2> adx(x, 0);
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AutoDiff<2> ady(y, 1);
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AutoDiff<2> res[2000];
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CalcTrigShape (n, adx, ady, &res[0]);
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int ndof = (n-1)*(n-2)/2;
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for (int i = 0; i < ndof; i++)
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{
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dshape[2*i] = res[i].DValue(0);
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dshape[2*i+1] = res[i].DValue(1);
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}
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/*
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if (n < 3) return;
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int ndof = (n-1)*(n-2)/2;
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double h1[1000], h2[1000];
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double eps = 1e-4;
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CalcTrigShape (n, x+eps, y, h1);
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CalcTrigShape (n, x-eps, y, h2);
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for (int i = 0; i < ndof; i++)
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dshape[2*i] = (h1[i]-h2[i])/(2*eps);
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CalcTrigShape (n, x, y+eps, h1);
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CalcTrigShape (n, x, y-eps, h2);
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for (int i = 0; i < ndof; i++)
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dshape[2*i+1] = (h1[i]-h2[i])/(2*eps);
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*/
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}
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// compute face bubbles up to order n, 0 < y, y-x < 1, x+y < 1
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template <class Tx, class Ty, class Tt, class Tr>
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static void CalcScaledTrigShape (int n, Tx x, Ty y, Tt t, Tr * shape)
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{
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if (n < 3) return;
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Tx hx[50], hy[50*50];
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// ScaledLegendrePolynomial (n-3, (2*x-1), t-y, hx);
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ScaledJacobiPolynomial (n-3, x, t-y, 2, 2, hx);
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// ScaledLegendrePolynomial (n-3, (2*y-1), t, hy);
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for (int ix = 0; ix <= n-3; ix++)
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ScaledJacobiPolynomial (n-3, 2*y-1, t, 2*ix+5, 2, hy+50*ix);
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int ii = 0;
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Tx bub = (t+x-y)*y*(t-x-y);
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for (int iy = 0; iy <= n-3; iy++)
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for (int ix = 0; ix <= n-3-iy; ix++)
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shape[ii++] = bub * hx[ix]*hy[iy+50*ix];
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}
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// compute face bubbles up to order n, 0 < y, y-x < 1, x+y < 1
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static void CalcScaledTrigShapeDxDyDt (int n, double x, double y, double t, double * dshape)
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{
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if (n < 3) return;
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AutoDiff<3> adx(x, 0);
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AutoDiff<3> ady(y, 1);
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AutoDiff<3> adt(t, 2);
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AutoDiff<3> res[2000];
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CalcScaledTrigShape (n, adx, ady, adt, &res[0]);
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int ndof = (n-1)*(n-2)/2;
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for (int i = 0; i < ndof; i++)
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{
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dshape[3*i] = res[i].DValue(0);
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dshape[3*i+1] = res[i].DValue(1);
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dshape[3*i+2] = res[i].DValue(2);
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}
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/*
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double dshape1[6000];
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if (n < 3) return;
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double hvl[1000], hvr[1000];
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int nd = (n-1)*(n-2)/2;
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double eps = 1e-6;
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CalcScaledTrigShape (n, x-eps, y, t, hvl);
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CalcScaledTrigShape (n, x+eps, y, t, hvr);
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for (int i = 0; i < nd; i++)
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dshape[3*i] = (hvr[i]-hvl[i])/(2*eps);
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CalcScaledTrigShape (n, x, y-eps, t, hvl);
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CalcScaledTrigShape (n, x, y+eps, t, hvr);
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for (int i = 0; i < nd; i++)
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dshape[3*i+1] = (hvr[i]-hvl[i])/(2*eps);
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CalcScaledTrigShape (n, x, y, t-eps, hvl);
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CalcScaledTrigShape (n, x, y, t+eps, hvr);
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for (int i = 0; i < nd; i++)
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dshape[3*i+2] = (hvr[i]-hvl[i])/(2*eps);
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*/
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/*
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for (int i = 0; i < 3*nd; i++)
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if (fabs (dshape[i]-dshape1[i]) > 1e-8 * fabs(dshape[i]) + 1e-6)
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{
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cerr
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cerr << "big difference: " << dshape1[i] << " != " << dshape[i] << endl;
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}
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*/
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}
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CurvedElements :: CurvedElements (const Mesh & amesh)
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: mesh (amesh)
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{
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order = 1;
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rational = 0;
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ishighorder = 0;
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}
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CurvedElements :: ~CurvedElements()
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{
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for (int i = 0; i < jacpols2.Size(); i++)
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delete jacpols2[i];
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}
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void CurvedElements :: BuildCurvedElements(const Refinement * ref, int aorder,
|
|
bool arational)
|
|
{
|
|
bool working = (ntasks == 1) || (id > 0);
|
|
|
|
ishighorder = 0;
|
|
order = 1;
|
|
|
|
|
|
#ifdef PARALLEL
|
|
enum { MPI_TAG_CURVE = MPI_TAG_MESH+20 };
|
|
|
|
const ParallelMeshTopology & partop = mesh.GetParallelTopology ();
|
|
MPI_Comm curve_comm;
|
|
MPI_Comm_dup (MPI_COMM_WORLD, &curve_comm);
|
|
Array<int> procs;
|
|
#endif
|
|
|
|
if (working)
|
|
order = aorder;
|
|
|
|
if (mesh.coarsemesh)
|
|
{
|
|
mesh.coarsemesh->GetCurvedElements().BuildCurvedElements (ref, aorder, arational);
|
|
order = aorder;
|
|
rational = arational;
|
|
ishighorder = (order > 1);
|
|
return;
|
|
}
|
|
|
|
|
|
PrintMessage (1, "Curve elements, order = ", aorder);
|
|
if (rational) PrintMessage (1, "curved elements with rational splines");
|
|
|
|
if (working)
|
|
const_cast<Mesh&> (mesh).UpdateTopology();
|
|
const MeshTopology & top = mesh.GetTopology();
|
|
|
|
rational = arational;
|
|
|
|
Array<int> edgenrs;
|
|
int nedges = top.GetNEdges();
|
|
int nfaces = top.GetNFaces();
|
|
|
|
edgeorder.SetSize (nedges);
|
|
faceorder.SetSize (nfaces);
|
|
|
|
edgeorder = 1;
|
|
faceorder = 1;
|
|
|
|
if (rational)
|
|
{
|
|
edgeweight.SetSize (nedges);
|
|
edgeweight = 1.0;
|
|
}
|
|
|
|
|
|
if (aorder <= 1)
|
|
{
|
|
for (ElementIndex ei = 0; ei < mesh.GetNE(); ei++)
|
|
if (mesh[ei].GetType() == TET10)
|
|
ishighorder = 1;
|
|
return;
|
|
}
|
|
|
|
|
|
if (rational) aorder = 2;
|
|
|
|
if (working)
|
|
{
|
|
if (mesh.GetDimension() == 3)
|
|
for (SurfaceElementIndex i = 0; i < mesh.GetNSE(); i++)
|
|
{
|
|
top.GetEdges (i, edgenrs);
|
|
for (int j = 0; j < edgenrs.Size(); j++)
|
|
edgeorder[edgenrs[j]] = aorder;
|
|
faceorder[top.GetFace (i)] = aorder;
|
|
}
|
|
for (SegmentIndex i = 0; i < mesh.GetNSeg(); i++)
|
|
edgeorder[top.GetEdge (i)] = aorder;
|
|
}
|
|
|
|
if (rational)
|
|
{
|
|
edgeorder = 2;
|
|
faceorder = 1;
|
|
}
|
|
|
|
|
|
#ifdef PARALLEL
|
|
TABLE<int> send_orders(ntasks), recv_orders(ntasks);
|
|
|
|
if (ntasks > 1 && working)
|
|
{
|
|
for (int e = 0; e < edgeorder.Size(); e++)
|
|
{
|
|
partop.GetDistantEdgeNums (e+1, procs);
|
|
for (int j = 0; j < procs.Size(); j++)
|
|
send_orders.Add (procs[j], edgeorder[e]);
|
|
}
|
|
for (int f = 0; f < faceorder.Size(); f++)
|
|
{
|
|
partop.GetDistantFaceNums (f+1, procs);
|
|
for (int j = 0; j < procs.Size(); j++)
|
|
send_orders.Add (procs[j], faceorder[f]);
|
|
}
|
|
}
|
|
|
|
|
|
MyMPI_ExchangeTable (send_orders, recv_orders, MPI_TAG_CURVE, curve_comm);
|
|
|
|
if (ntasks > 1 && working)
|
|
{
|
|
Array<int> cnt(ntasks);
|
|
cnt = 0;
|
|
for (int e = 0; e < edgeorder.Size(); e++)
|
|
{
|
|
partop.GetDistantEdgeNums (e+1, procs);
|
|
for (int j = 0; j < procs.Size(); j++)
|
|
edgeorder[e] = max(edgeorder[e], recv_orders[procs[j]][cnt[procs[j]]++]);
|
|
}
|
|
for (int f = 0; f < faceorder.Size(); f++)
|
|
{
|
|
partop.GetDistantFaceNums (f+1, procs);
|
|
for (int j = 0; j < procs.Size(); j++)
|
|
faceorder[f] = max(faceorder[f], recv_orders[procs[j]][cnt[procs[j]]++]);
|
|
}
|
|
}
|
|
#endif
|
|
|
|
|
|
edgecoeffsindex.SetSize (nedges+1);
|
|
int nd = 0;
|
|
for (int i = 0; i < nedges; i++)
|
|
{
|
|
edgecoeffsindex[i] = nd;
|
|
nd += max (0, edgeorder[i]-1);
|
|
}
|
|
edgecoeffsindex[nedges] = nd;
|
|
|
|
edgecoeffs.SetSize (nd);
|
|
edgecoeffs = Vec<3> (0,0,0);
|
|
|
|
|
|
facecoeffsindex.SetSize (nfaces+1);
|
|
nd = 0;
|
|
for (int i = 0; i < nfaces; i++)
|
|
{
|
|
facecoeffsindex[i] = nd;
|
|
if (top.GetFaceType(i+1) == TRIG)
|
|
nd += max (0, (faceorder[i]-1)*(faceorder[i]-2)/2);
|
|
else
|
|
nd += max (0, sqr(faceorder[i]-1));
|
|
}
|
|
facecoeffsindex[nfaces] = nd;
|
|
|
|
facecoeffs.SetSize (nd);
|
|
facecoeffs = Vec<3> (0,0,0);
|
|
|
|
|
|
if (!ref || aorder <= 1)
|
|
{
|
|
order = aorder;
|
|
return;
|
|
}
|
|
|
|
Array<double> xi, weight;
|
|
|
|
ComputeGaussRule (aorder+4, xi, weight); // on (0,1)
|
|
|
|
if (!jacpols2.Size())
|
|
{
|
|
jacpols2.SetSize (100);
|
|
for (int i = 0; i < 100; i++)
|
|
jacpols2[i] = new JacobiRecPol (100, i, 2);
|
|
}
|
|
|
|
PrintMessage (3, "Curving edges");
|
|
|
|
if (mesh.GetDimension() == 3 || rational)
|
|
{
|
|
Array<int> surfnr(nedges);
|
|
Array<PointGeomInfo> gi0(nedges);
|
|
Array<PointGeomInfo> gi1(nedges);
|
|
surfnr = -1;
|
|
|
|
if (working)
|
|
for (SurfaceElementIndex i = 0; i < mesh.GetNSE(); i++)
|
|
{
|
|
top.GetEdges (i, edgenrs);
|
|
const Element2d & el = mesh[i];
|
|
const ELEMENT_EDGE * edges = MeshTopology::GetEdges0 (el.GetType());
|
|
|
|
for (int i2 = 0; i2 < edgenrs.Size(); i2++)
|
|
{
|
|
PointIndex pi1 = el[edges[i2][0]];
|
|
PointIndex pi2 = el[edges[i2][1]];
|
|
|
|
bool swap = pi1 > pi2;
|
|
|
|
Point<3> p1 = mesh[pi1];
|
|
Point<3> p2 = mesh[pi2];
|
|
|
|
int order1 = edgeorder[edgenrs[i2]];
|
|
int ndof = max (0, order1-1);
|
|
|
|
surfnr[edgenrs[i2]] = mesh.GetFaceDescriptor(el.GetIndex()).SurfNr();
|
|
gi0[edgenrs[i2]] = el.GeomInfoPi(edges[i2][0]+1);
|
|
gi1[edgenrs[i2]] = el.GeomInfoPi(edges[i2][1]+1);
|
|
}
|
|
}
|
|
|
|
|
|
#ifdef PARALLEL
|
|
if (ntasks > 1)
|
|
{
|
|
// distribute it ...
|
|
TABLE<double> senddata(ntasks), recvdata(ntasks);
|
|
if (working)
|
|
for (int e = 0; e < nedges; e++)
|
|
{
|
|
partop.GetDistantEdgeNums (e+1, procs);
|
|
for (int j = 0; j < procs.Size(); j++)
|
|
{
|
|
senddata.Add (procs[j], surfnr[e]);
|
|
if (surfnr[e] != -1)
|
|
{
|
|
senddata.Add (procs[j], gi0[e].trignum);
|
|
senddata.Add (procs[j], gi0[e].u);
|
|
senddata.Add (procs[j], gi0[e].v);
|
|
senddata.Add (procs[j], gi1[e].trignum);
|
|
senddata.Add (procs[j], gi1[e].u);
|
|
senddata.Add (procs[j], gi1[e].v);
|
|
}
|
|
}
|
|
}
|
|
|
|
MyMPI_ExchangeTable (senddata, recvdata, MPI_TAG_CURVE, curve_comm);
|
|
|
|
|
|
Array<int> cnt(ntasks);
|
|
cnt = 0;
|
|
if (working)
|
|
for (int e = 0; e < nedges; e++)
|
|
{
|
|
partop.GetDistantEdgeNums (e+1, procs);
|
|
for (int j = 0; j < procs.Size(); j++)
|
|
{
|
|
int surfnr1 = recvdata[procs[j]][cnt[procs[j]]++];
|
|
if (surfnr1 != -1)
|
|
{
|
|
surfnr[e] = surfnr1;
|
|
gi0[e].trignum = int (recvdata[procs[j]][cnt[procs[j]]++]);
|
|
gi0[e].u = recvdata[procs[j]][cnt[procs[j]]++];
|
|
gi0[e].v = recvdata[procs[j]][cnt[procs[j]]++];
|
|
gi1[e].trignum = int (recvdata[procs[j]][cnt[procs[j]]++]);
|
|
gi1[e].u = recvdata[procs[j]][cnt[procs[j]]++];
|
|
gi1[e].v = recvdata[procs[j]][cnt[procs[j]]++];
|
|
}
|
|
}
|
|
}
|
|
|
|
}
|
|
#endif
|
|
|
|
|
|
if (working)
|
|
for (int e = 0; e < surfnr.Size(); e++)
|
|
{
|
|
if (surfnr[e] == -1) continue;
|
|
SetThreadPercent(double(e)/surfnr.Size()*100.);
|
|
|
|
PointIndex pi1, pi2;
|
|
top.GetEdgeVertices (e+1, pi1, pi2);
|
|
bool swap = (pi1 > pi2);
|
|
|
|
Point<3> p1 = mesh[pi1];
|
|
Point<3> p2 = mesh[pi2];
|
|
|
|
int order1 = edgeorder[e];
|
|
int ndof = max (0, order1-1);
|
|
|
|
if (rational && order1 >= 2)
|
|
{
|
|
Point<3> pm = Center (p1, p2);
|
|
|
|
Vec<3> n1 = ref -> GetNormal (p1, surfnr[e], gi0[e]);
|
|
Vec<3> n2 = ref -> GetNormal (p2, surfnr[e], gi1[e]);
|
|
|
|
// p3 = pm + alpha1 n1 + alpha2 n2
|
|
|
|
Mat<2> mat, inv;
|
|
Vec<2> rhs, sol;
|
|
|
|
mat(0,0) = n1*n1;
|
|
mat(0,1) = mat(1,0) = n1*n2;
|
|
mat(1,1) = n2*n2;
|
|
|
|
rhs(0) = n1 * (p1-pm);
|
|
rhs(1) = n2 * (p2-pm);
|
|
|
|
|
|
Point<3> p3;
|
|
|
|
if (fabs (Det (mat)) > 1e-10)
|
|
{
|
|
CalcInverse (mat, inv);
|
|
sol = inv * rhs;
|
|
|
|
p3 = pm + sol(0) * n1 + sol(1) * n2;
|
|
}
|
|
else
|
|
p3 = pm;
|
|
|
|
edgecoeffs[edgecoeffsindex[e]] = Vec<3> (p3);
|
|
|
|
|
|
double wold = 1, w = 1, dw = 0.1;
|
|
double dold = 1e99;
|
|
while (fabs (dw) > 1e-12)
|
|
{
|
|
Vec<3> v05 = 0.25 * Vec<3> (p1) + 0.5*w* Vec<3>(p3) + 0.25 * Vec<3> (p2);
|
|
v05 /= 1 + (w-1) * 0.5;
|
|
Point<3> p05 (v05), pp05(v05);
|
|
ref -> ProjectToSurface (pp05, surfnr[e], gi0[e]);
|
|
double d = Dist (pp05, p05);
|
|
|
|
if (d < dold)
|
|
{
|
|
dold = d;
|
|
wold = w;
|
|
w += dw;
|
|
}
|
|
else
|
|
{
|
|
dw *= -0.7;
|
|
w = wold + dw;
|
|
}
|
|
}
|
|
|
|
edgeweight[e] = w;
|
|
continue;
|
|
}
|
|
|
|
Vector shape(ndof);
|
|
DenseMatrix mat(ndof, ndof), inv(ndof, ndof),
|
|
rhs(ndof, 3), sol(ndof, 3);
|
|
|
|
rhs = 0.0;
|
|
mat = 0.0;
|
|
for (int j = 0; j < xi.Size(); j++)
|
|
{
|
|
Point<3> p;
|
|
Point<3> pp;
|
|
PointGeomInfo ppgi;
|
|
|
|
if (swap)
|
|
{
|
|
p = p1 + xi[j] * (p2-p1);
|
|
ref -> PointBetween (p1, p2, xi[j],
|
|
surfnr[e], gi0[e], gi1[e],
|
|
pp, ppgi);
|
|
}
|
|
else
|
|
{
|
|
p = p2 + xi[j] * (p1-p2);
|
|
ref -> PointBetween (p2, p1, xi[j],
|
|
surfnr[e], gi1[e], gi0[e],
|
|
pp, ppgi);
|
|
}
|
|
|
|
Vec<3> dist = pp - p;
|
|
|
|
CalcEdgeShape (order1, 2*xi[j]-1, &shape(0));
|
|
|
|
for (int k = 0; k < ndof; k++)
|
|
for (int l = 0; l < ndof; l++)
|
|
mat(k,l) += weight[j] * shape(k) * shape(l);
|
|
|
|
for (int k = 0; k < ndof; k++)
|
|
for (int l = 0; l < 3; l++)
|
|
rhs(k,l) += weight[j] * shape(k) * dist(l);
|
|
}
|
|
|
|
CalcInverse (mat, inv);
|
|
Mult (inv, rhs, sol);
|
|
|
|
int first = edgecoeffsindex[e];
|
|
for (int j = 0; j < ndof; j++)
|
|
for (int k = 0; k < 3; k++)
|
|
edgecoeffs[first+j](k) = sol(j,k);
|
|
}
|
|
}
|
|
|
|
|
|
Array<int> use_edge(nedges);
|
|
Array<int> edge_surfnr1(nedges);
|
|
Array<int> edge_surfnr2(nedges);
|
|
Array<int> swap_edge(nedges);
|
|
Array<EdgePointGeomInfo> edge_gi0(nedges);
|
|
Array<EdgePointGeomInfo> edge_gi1(nedges);
|
|
use_edge = 0;
|
|
|
|
if (working)
|
|
for (SegmentIndex i = 0; i < mesh.GetNSeg(); i++)
|
|
{
|
|
const Segment & seg = mesh[i];
|
|
int edgenr = top.GetEdge (i);
|
|
use_edge[edgenr] = 1;
|
|
edge_surfnr1[edgenr] = seg.surfnr1;
|
|
edge_surfnr2[edgenr] = seg.surfnr2;
|
|
edge_gi0[edgenr] = seg.epgeominfo[0];
|
|
edge_gi1[edgenr] = seg.epgeominfo[1];
|
|
swap_edge[edgenr] = int (seg[0] > seg[1]);
|
|
}
|
|
|
|
#ifdef PARALLEL
|
|
if (ntasks > 1)
|
|
{
|
|
// distribute it ...
|
|
TABLE<double> senddata(ntasks), recvdata(ntasks);
|
|
if (working)
|
|
for (int e = 0; e < nedges; e++)
|
|
{
|
|
partop.GetDistantEdgeNums (e+1, procs);
|
|
for (int j = 0; j < procs.Size(); j++)
|
|
{
|
|
senddata.Add (procs[j], use_edge[e]);
|
|
if (use_edge[e])
|
|
{
|
|
senddata.Add (procs[j], edge_surfnr1[e]);
|
|
senddata.Add (procs[j], edge_surfnr2[e]);
|
|
senddata.Add (procs[j], edge_gi0[e].edgenr);
|
|
senddata.Add (procs[j], edge_gi0[e].body);
|
|
senddata.Add (procs[j], edge_gi0[e].dist);
|
|
senddata.Add (procs[j], edge_gi0[e].u);
|
|
senddata.Add (procs[j], edge_gi0[e].v);
|
|
senddata.Add (procs[j], edge_gi1[e].edgenr);
|
|
senddata.Add (procs[j], edge_gi1[e].body);
|
|
senddata.Add (procs[j], edge_gi1[e].dist);
|
|
senddata.Add (procs[j], edge_gi1[e].u);
|
|
senddata.Add (procs[j], edge_gi1[e].v);
|
|
senddata.Add (procs[j], swap_edge[e]);
|
|
}
|
|
}
|
|
}
|
|
MyMPI_ExchangeTable (senddata, recvdata, MPI_TAG_CURVE, curve_comm);
|
|
Array<int> cnt(ntasks);
|
|
cnt = 0;
|
|
if (working)
|
|
for (int e = 0; e < edge_surfnr1.Size(); e++)
|
|
{
|
|
partop.GetDistantEdgeNums (e+1, procs);
|
|
for (int j = 0; j < procs.Size(); j++)
|
|
{
|
|
int get_edge = int(recvdata[procs[j]][cnt[procs[j]]++]);
|
|
if (get_edge)
|
|
{
|
|
use_edge[e] = 1;
|
|
edge_surfnr1[e] = int (recvdata[procs[j]][cnt[procs[j]]++]);
|
|
edge_surfnr2[e] = int (recvdata[procs[j]][cnt[procs[j]]++]);
|
|
edge_gi0[e].edgenr = int (recvdata[procs[j]][cnt[procs[j]]++]);
|
|
edge_gi0[e].body = int (recvdata[procs[j]][cnt[procs[j]]++]);
|
|
edge_gi0[e].dist = recvdata[procs[j]][cnt[procs[j]]++];
|
|
edge_gi0[e].u = recvdata[procs[j]][cnt[procs[j]]++];
|
|
edge_gi0[e].v = recvdata[procs[j]][cnt[procs[j]]++];
|
|
edge_gi1[e].edgenr = int (recvdata[procs[j]][cnt[procs[j]]++]);
|
|
edge_gi1[e].body = int (recvdata[procs[j]][cnt[procs[j]]++]);
|
|
edge_gi1[e].dist = recvdata[procs[j]][cnt[procs[j]]++];
|
|
edge_gi1[e].u = recvdata[procs[j]][cnt[procs[j]]++];
|
|
edge_gi1[e].v = recvdata[procs[j]][cnt[procs[j]]++];
|
|
swap_edge[e] = recvdata[procs[j]][cnt[procs[j]]++];
|
|
}
|
|
}
|
|
}
|
|
|
|
}
|
|
#endif
|
|
|
|
if (working)
|
|
for (int edgenr = 0; edgenr < use_edge.Size(); edgenr++)
|
|
{
|
|
int segnr = edgenr;
|
|
if (!use_edge[edgenr]) continue;
|
|
|
|
SetThreadPercent(double(edgenr)/edge_surfnr1.Size()*100.);
|
|
|
|
PointIndex pi1, pi2;
|
|
top.GetEdgeVertices (edgenr+1, pi1, pi2);
|
|
|
|
bool swap = swap_edge[edgenr]; // (pi1 > pi2);
|
|
if (swap) Swap (pi1, pi2);
|
|
|
|
Point<3> p1 = mesh[pi1];
|
|
Point<3> p2 = mesh[pi2];
|
|
|
|
int order1 = edgeorder[segnr];
|
|
int ndof = max (0, order1-1);
|
|
|
|
if (rational)
|
|
{
|
|
Vec<3> tau1 = ref -> GetTangent (p1, edge_surfnr2[edgenr], edge_surfnr1[edgenr],
|
|
edge_gi0[edgenr]);
|
|
Vec<3> tau2 = ref -> GetTangent (p2, edge_surfnr2[edgenr], edge_surfnr1[edgenr],
|
|
edge_gi1[edgenr]);
|
|
// p1 + alpha1 tau1 = p2 + alpha2 tau2;
|
|
|
|
Mat<3,2> mat;
|
|
Mat<2,3> inv;
|
|
Vec<3> rhs;
|
|
Vec<2> sol;
|
|
for (int j = 0; j < 3; j++)
|
|
{
|
|
mat(j,0) = tau1(j);
|
|
mat(j,1) = -tau2(j);
|
|
rhs(j) = p2(j)-p1(j);
|
|
}
|
|
CalcInverse (mat, inv);
|
|
sol = inv * rhs;
|
|
|
|
Point<3> p3 = p1+sol(0) * tau1;
|
|
edgecoeffs[edgecoeffsindex[segnr]] = Vec<3> (p3);
|
|
|
|
double wold = 1, w = 1, dw = 0.1;
|
|
double dold = 1e99;
|
|
while (fabs (dw) > 1e-12)
|
|
{
|
|
Vec<3> v05 = 0.25 * Vec<3> (p1) + 0.5*w* Vec<3>(p3) + 0.25 * Vec<3> (p2);
|
|
v05 /= 1 + (w-1) * 0.5;
|
|
Point<3> p05 (v05), pp05(v05);
|
|
ref -> ProjectToEdge (pp05, edge_surfnr1[edgenr], edge_surfnr2[edgenr],
|
|
edge_gi0[edgenr]);
|
|
double d = Dist (pp05, p05);
|
|
|
|
if (d < dold)
|
|
{
|
|
dold = d;
|
|
wold = w;
|
|
w += dw;
|
|
}
|
|
else
|
|
{
|
|
dw *= -0.7;
|
|
w = wold + dw;
|
|
}
|
|
// *testout << "w = " << w << ", dw = " << dw << endl;
|
|
}
|
|
|
|
// cout << "wopt = " << w << ", dopt = " << dold << endl;
|
|
edgeweight[segnr] = w;
|
|
|
|
// cout << "p1 = " << p1 << ", tau1 = " << tau1 << ", alpha1 = " << sol(0) << endl;
|
|
// cout << "p2 = " << p2 << ", tau2 = " << tau2 << ", alpha2 = " << -sol(1) << endl;
|
|
// cout << "p+alpha tau = " << p1 + sol(0) * tau1
|
|
// << " =?= " << p2 +sol(1) * tau2 << endl;
|
|
|
|
}
|
|
|
|
else
|
|
|
|
{
|
|
Vector shape(ndof);
|
|
DenseMatrix mat(ndof, ndof), inv(ndof, ndof),
|
|
rhs(ndof, 3), sol(ndof, 3);
|
|
|
|
rhs = 0.0;
|
|
mat = 0.0;
|
|
for (int j = 0; j < xi.Size(); j++)
|
|
{
|
|
Point<3> p, pp;
|
|
EdgePointGeomInfo ppgi;
|
|
|
|
if (swap)
|
|
{
|
|
p = p1 + xi[j] * (p2-p1);
|
|
ref -> PointBetween (p1, p2, xi[j],
|
|
edge_surfnr2[edgenr], edge_surfnr1[edgenr],
|
|
edge_gi0[edgenr], edge_gi1[edgenr],
|
|
pp, ppgi);
|
|
}
|
|
else
|
|
{
|
|
p = p2 + xi[j] * (p1-p2);
|
|
ref -> PointBetween (p2, p1, xi[j],
|
|
edge_surfnr2[edgenr], edge_surfnr1[edgenr],
|
|
edge_gi1[edgenr], edge_gi0[edgenr],
|
|
pp, ppgi);
|
|
}
|
|
|
|
Vec<3> dist = pp - p;
|
|
|
|
CalcEdgeShape (order1, 2*xi[j]-1, &shape(0));
|
|
|
|
for (int k = 0; k < ndof; k++)
|
|
for (int l = 0; l < ndof; l++)
|
|
mat(k,l) += weight[j] * shape(k) * shape(l);
|
|
|
|
for (int k = 0; k < ndof; k++)
|
|
for (int l = 0; l < 3; l++)
|
|
rhs(k,l) += weight[j] * shape(k) * dist(l);
|
|
}
|
|
|
|
|
|
CalcInverse (mat, inv);
|
|
Mult (inv, rhs, sol);
|
|
|
|
int first = edgecoeffsindex[segnr];
|
|
for (int j = 0; j < ndof; j++)
|
|
for (int k = 0; k < 3; k++)
|
|
edgecoeffs[first+j](k) = sol(j,k);
|
|
}
|
|
}
|
|
|
|
|
|
|
|
PrintMessage (3, "Curving faces");
|
|
|
|
Array<int> surfnr(nfaces);
|
|
surfnr = -1;
|
|
|
|
if (working)
|
|
for (SurfaceElementIndex i = 0; i < mesh.GetNSE(); i++)
|
|
surfnr[top.GetFace(i)] =
|
|
mesh.GetFaceDescriptor(mesh[i].GetIndex()).SurfNr();
|
|
|
|
#ifdef PARALLEL
|
|
TABLE<int> send_surfnr(ntasks), recv_surfnr(ntasks);
|
|
|
|
if (ntasks > 1 && working)
|
|
{
|
|
for (int f = 0; f < nfaces; f++)
|
|
{
|
|
partop.GetDistantFaceNums (f+1, procs);
|
|
for (int j = 0; j < procs.Size(); j++)
|
|
send_surfnr.Add (procs[j], surfnr[f]);
|
|
}
|
|
}
|
|
|
|
MyMPI_ExchangeTable (send_surfnr, recv_surfnr, MPI_TAG_CURVE, curve_comm);
|
|
|
|
if (ntasks > 1 && working)
|
|
{
|
|
Array<int> cnt(ntasks);
|
|
cnt = 0;
|
|
for (int f = 0; f < nfaces; f++)
|
|
{
|
|
partop.GetDistantFaceNums (f+1, procs);
|
|
for (int j = 0; j < procs.Size(); j++)
|
|
surfnr[f] = max(surfnr[f], recv_surfnr[procs[j]][cnt[procs[j]]++]);
|
|
}
|
|
}
|
|
#endif
|
|
|
|
if (mesh.GetDimension() == 3 && working)
|
|
{
|
|
for (int f = 0; f < nfaces; f++)
|
|
{
|
|
int facenr = f;
|
|
if (surfnr[f] == -1) continue;
|
|
// if (el.GetType() == TRIG && order >= 3)
|
|
if (top.GetFaceType(facenr+1) == TRIG && order >= 3)
|
|
{
|
|
ArrayMem<int, 3> verts(3);
|
|
top.GetFaceVertices (facenr+1, verts);
|
|
|
|
int fnums[] = { 0, 1, 2 };
|
|
/*
|
|
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
|
|
if (el[fnums[1]] > el[fnums[2]]) swap (fnums[1], fnums[2]);
|
|
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
|
|
*/
|
|
if (verts[fnums[0]] > verts[fnums[1]]) swap (fnums[0], fnums[1]);
|
|
if (verts[fnums[1]] > verts[fnums[2]]) swap (fnums[1], fnums[2]);
|
|
if (verts[fnums[0]] > verts[fnums[1]]) swap (fnums[0], fnums[1]);
|
|
|
|
int order1 = faceorder[facenr];
|
|
int ndof = max (0, (order1-1)*(order1-2)/2);
|
|
|
|
Vector shape(ndof), dmat(ndof);
|
|
MatrixFixWidth<3> rhs(ndof), sol(ndof);
|
|
|
|
rhs = 0.0;
|
|
dmat = 0.0;
|
|
|
|
int np = sqr(xi.Size());
|
|
Array<Point<2> > xia(np);
|
|
Array<Point<3> > xa(np);
|
|
|
|
for (int jx = 0, jj = 0; jx < xi.Size(); jx++)
|
|
for (int jy = 0; jy < xi.Size(); jy++, jj++)
|
|
xia[jj] = Point<2> ((1-xi[jy])*xi[jx], xi[jy]);
|
|
|
|
// CalcMultiPointSurfaceTransformation (&xia, i, &xa, NULL);
|
|
|
|
Array<int> edgenrs;
|
|
top.GetFaceEdges (facenr+1, edgenrs);
|
|
for (int k = 0; k < edgenrs.Size(); k++) edgenrs[k]--;
|
|
|
|
for (int jj = 0; jj < np; jj++)
|
|
{
|
|
Point<3> pp(0,0,0);
|
|
double lami[] = { xia[jj](0), xia[jj](1), 1-xia[jj](0)-xia[jj](1)};
|
|
|
|
for (int k = 0; k < verts.Size(); k++)
|
|
pp += lami[k] * Vec<3> (mesh.Point(verts[k]));
|
|
|
|
const ELEMENT_EDGE * edges = MeshTopology::GetEdges0 (TRIG);
|
|
for (int k = 0; k < edgenrs.Size(); k++)
|
|
{
|
|
int eorder = edgeorder[edgenrs[k]];
|
|
if (eorder < 2) continue;
|
|
|
|
int first = edgecoeffsindex[edgenrs[k]];
|
|
Vector eshape(eorder-1);
|
|
int vi1, vi2;
|
|
top.GetEdgeVertices (edgenrs[k]+1, vi1, vi2);
|
|
if (vi1 > vi2) swap (vi1, vi2);
|
|
int v1 = -1, v2 = -1;
|
|
for (int j = 0; j < 3; j++)
|
|
{
|
|
if (verts[j] == vi1) v1 = j;
|
|
if (verts[j] == vi2) v2 = j;
|
|
}
|
|
|
|
CalcScaledEdgeShape (eorder, lami[v1]-lami[v2], lami[v1]+lami[v2], &eshape(0));
|
|
for (int n = 0; n < eshape.Size(); n++)
|
|
pp += eshape(n) * edgecoeffs[first+n];
|
|
}
|
|
xa[jj] = pp;
|
|
}
|
|
|
|
for (int jx = 0, jj = 0; jx < xi.Size(); jx++)
|
|
for (int jy = 0; jy < xi.Size(); jy++, jj++)
|
|
{
|
|
double y = xi[jy];
|
|
double x = (1-y) * xi[jx];
|
|
double lami[] = { x, y, 1-x-y };
|
|
double wi = weight[jx]*weight[jy]*(1-y);
|
|
|
|
Point<3> pp = xa[jj];
|
|
// ref -> ProjectToSurface (pp, mesh.GetFaceDescriptor(el.GetIndex()).SurfNr());
|
|
ref -> ProjectToSurface (pp, surfnr[facenr]);
|
|
Vec<3> dist = pp-xa[jj];
|
|
|
|
CalcTrigShape (order1, lami[fnums[1]]-lami[fnums[0]],
|
|
1-lami[fnums[1]]-lami[fnums[0]], &shape(0));
|
|
|
|
for (int k = 0; k < ndof; k++)
|
|
dmat(k) += wi * shape(k) * shape(k);
|
|
|
|
dist *= wi;
|
|
for (int k = 0; k < ndof; k++)
|
|
for (int l = 0; l < 3; l++)
|
|
rhs(k,l) += shape(k) * dist(l);
|
|
}
|
|
|
|
for (int i = 0; i < ndof; i++)
|
|
for (int j = 0; j < 3; j++)
|
|
sol(i,j) = rhs(i,j) / dmat(i); // Orthogonal basis !
|
|
|
|
int first = facecoeffsindex[facenr];
|
|
for (int j = 0; j < ndof; j++)
|
|
for (int k = 0; k < 3; k++)
|
|
facecoeffs[first+j](k) = sol(j,k);
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
// compress edge and face tables
|
|
int newbase = 0;
|
|
for (int i = 0; i < edgeorder.Size(); i++)
|
|
{
|
|
bool curved = 0;
|
|
int oldbase = edgecoeffsindex[i];
|
|
int nd = edgecoeffsindex[i+1] - edgecoeffsindex[i];
|
|
|
|
for (int j = 0; j < nd; j++)
|
|
if (edgecoeffs[oldbase+j].Length() > 1e-12)
|
|
curved = 1;
|
|
if (rational) curved = 1;
|
|
|
|
if (curved && newbase != oldbase)
|
|
for (int j = 0; j < nd; j++)
|
|
edgecoeffs[newbase+j] = edgecoeffs[oldbase+j];
|
|
|
|
edgecoeffsindex[i] = newbase;
|
|
if (!curved) edgeorder[i] = 1;
|
|
if (curved) newbase += nd;
|
|
}
|
|
edgecoeffsindex.Last() = newbase;
|
|
|
|
|
|
newbase = 0;
|
|
for (int i = 0; i < faceorder.Size(); i++)
|
|
{
|
|
bool curved = 0;
|
|
int oldbase = facecoeffsindex[i];
|
|
int nd = facecoeffsindex[i+1] - facecoeffsindex[i];
|
|
|
|
for (int j = 0; j < nd; j++)
|
|
if (facecoeffs[oldbase+j].Length() > 1e-12)
|
|
curved = 1;
|
|
|
|
if (curved && newbase != oldbase)
|
|
for (int j = 0; j < nd; j++)
|
|
facecoeffs[newbase+j] = facecoeffs[oldbase+j];
|
|
|
|
facecoeffsindex[i] = newbase;
|
|
if (!curved) faceorder[i] = 1;
|
|
if (curved) newbase += nd;
|
|
}
|
|
facecoeffsindex.Last() = newbase;
|
|
|
|
if (working)
|
|
ishighorder = (order > 1);
|
|
// (*testout) << "edgecoeffs = " << endl << edgecoeffs << endl;
|
|
// (*testout) << "facecoeffs = " << endl << facecoeffs << endl;
|
|
|
|
|
|
#ifdef PARALLEL
|
|
MPI_Barrier (curve_comm);
|
|
MPI_Comm_free (&curve_comm);
|
|
#endif
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
// *********************** Transform edges *****************************
|
|
|
|
|
|
bool CurvedElements :: IsSegmentCurved (SegmentIndex elnr) const
|
|
{
|
|
if (mesh.coarsemesh)
|
|
{
|
|
const HPRefElement & hpref_el =
|
|
(*mesh.hpelements) [mesh[elnr].hp_elnr];
|
|
|
|
return mesh.coarsemesh->GetCurvedElements().IsSegmentCurved (hpref_el.coarse_elnr);
|
|
}
|
|
|
|
SegmentInfo info;
|
|
info.elnr = elnr;
|
|
info.order = order;
|
|
info.ndof = info.nv = 2;
|
|
if (info.order > 1)
|
|
{
|
|
const MeshTopology & top = mesh.GetTopology();
|
|
info.edgenr = top.GetSegmentEdge (elnr+1)-1;
|
|
info.ndof += edgeorder[info.edgenr]-1;
|
|
}
|
|
|
|
return (info.ndof > info.nv);
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
void CurvedElements ::
|
|
CalcSegmentTransformation (double xi, SegmentIndex elnr,
|
|
Point<3> * x, Vec<3> * dxdxi, bool * curved)
|
|
{
|
|
if (mesh.coarsemesh)
|
|
{
|
|
const HPRefElement & hpref_el =
|
|
(*mesh.hpelements) [mesh[elnr].hp_elnr];
|
|
|
|
// xi umrechnen
|
|
double lami[2] = { xi, 1-xi };
|
|
double dlami[2] = { 1, -1 };
|
|
|
|
double coarse_xi = 0;
|
|
double trans = 0;
|
|
for (int i = 0; i < 2; i++)
|
|
{
|
|
coarse_xi += hpref_el.param[i][0] * lami[i];
|
|
trans += hpref_el.param[i][0] * dlami[i];
|
|
}
|
|
|
|
mesh.coarsemesh->GetCurvedElements().CalcSegmentTransformation (coarse_xi, hpref_el.coarse_elnr, x, dxdxi, curved);
|
|
if (dxdxi) *dxdxi *= trans;
|
|
|
|
return;
|
|
}
|
|
|
|
|
|
Vector shapes, dshapes;
|
|
Array<Vec<3> > coefs;
|
|
|
|
SegmentInfo info;
|
|
info.elnr = elnr;
|
|
info.order = order;
|
|
info.ndof = info.nv = 2;
|
|
|
|
if (info.order > 1)
|
|
{
|
|
const MeshTopology & top = mesh.GetTopology();
|
|
info.edgenr = top.GetSegmentEdge (elnr+1)-1;
|
|
info.ndof += edgeorder[info.edgenr]-1;
|
|
}
|
|
|
|
CalcElementShapes (info, xi, shapes);
|
|
GetCoefficients (info, coefs);
|
|
|
|
*x = 0;
|
|
for (int i = 0; i < shapes.Size(); i++)
|
|
*x += shapes(i) * coefs[i];
|
|
|
|
|
|
if (dxdxi)
|
|
{
|
|
CalcElementDShapes (info, xi, dshapes);
|
|
|
|
*dxdxi = 0;
|
|
for (int i = 0; i < shapes.Size(); i++)
|
|
for (int j = 0; j < 3; j++)
|
|
(*dxdxi)(j) += dshapes(i) * coefs[i](j);
|
|
}
|
|
|
|
if (curved)
|
|
*curved = (info.order > 1);
|
|
|
|
// cout << "Segment, |x| = " << Abs2(Vec<3> (*x) ) << endl;
|
|
}
|
|
|
|
|
|
|
|
|
|
void CurvedElements ::
|
|
CalcElementShapes (SegmentInfo & info, double xi, Vector & shapes) const
|
|
{
|
|
if (rational && info.order == 2)
|
|
{
|
|
shapes.SetSize(3);
|
|
double w = edgeweight[info.edgenr];
|
|
shapes(0) = xi*xi;
|
|
shapes(1) = (1-xi)*(1-xi);
|
|
shapes(2) = 2*w*xi*(1-xi);
|
|
shapes *= 1.0 / (1 + (w-1) *2*xi*(1-xi));
|
|
return;
|
|
}
|
|
|
|
|
|
shapes.SetSize(info.ndof);
|
|
shapes(0) = xi;
|
|
shapes(1) = 1-xi;
|
|
|
|
if (info.order >= 2)
|
|
{
|
|
if (mesh[info.elnr][0] > mesh[info.elnr][1])
|
|
xi = 1-xi;
|
|
CalcEdgeShape (edgeorder[info.edgenr], 2*xi-1, &shapes(2));
|
|
}
|
|
}
|
|
|
|
void CurvedElements ::
|
|
CalcElementDShapes (SegmentInfo & info, double xi, Vector & dshapes) const
|
|
{
|
|
if (rational && info.order == 2)
|
|
{
|
|
dshapes.SetSize(3);
|
|
double wi = edgeweight[info.edgenr];
|
|
double shapes[3];
|
|
shapes[0] = xi*xi;
|
|
shapes[1] = (1-xi)*(1-xi);
|
|
shapes[2] = 2*wi*xi*(1-xi);
|
|
double w = 1 + (wi-1) *2*xi*(1-xi);
|
|
double dw = (wi-1) * (2 - 4*xi);
|
|
|
|
dshapes(0) = 2*xi;
|
|
dshapes(1) = 2*(xi-1);
|
|
dshapes(2) = 2*wi*(1-2*xi);
|
|
|
|
for (int j = 0;j < 3; j++)
|
|
dshapes(j) = dshapes(j) / w - shapes[j] * dw / (w*w);
|
|
return;
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
dshapes.SetSize(info.ndof);
|
|
dshapes = 0;
|
|
dshapes(0) = 1;
|
|
dshapes(1) = -1;
|
|
|
|
// int order = edgeorder[info.edgenr];
|
|
|
|
if (info.order >= 2)
|
|
{
|
|
double fac = 2;
|
|
if (mesh[info.elnr][0] > mesh[info.elnr][1])
|
|
{
|
|
xi = 1-xi;
|
|
fac *= -1;
|
|
}
|
|
CalcEdgeDx (edgeorder[info.edgenr], 2*xi-1, &dshapes(2));
|
|
for (int i = 2; i < dshapes.Size(); i++)
|
|
dshapes(i) *= fac;
|
|
}
|
|
|
|
// ??? not implemented ????
|
|
}
|
|
|
|
void CurvedElements ::
|
|
GetCoefficients (SegmentInfo & info, Array<Vec<3> > & coefs) const
|
|
{
|
|
const Segment & el = mesh[info.elnr];
|
|
|
|
coefs.SetSize(info.ndof);
|
|
|
|
coefs[0] = Vec<3> (mesh[el[0]]);
|
|
coefs[1] = Vec<3> (mesh[el[1]]);
|
|
|
|
if (info.order >= 2)
|
|
{
|
|
int first = edgecoeffsindex[info.edgenr];
|
|
int next = edgecoeffsindex[info.edgenr+1];
|
|
for (int i = 0; i < next-first; i++)
|
|
coefs[i+2] = edgecoeffs[first+i];
|
|
}
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
// ********************** Transform surface elements *******************
|
|
|
|
|
|
bool CurvedElements :: IsSurfaceElementCurved (SurfaceElementIndex elnr) const
|
|
{
|
|
if (!IsHighOrder()) return false;
|
|
|
|
if (mesh.coarsemesh)
|
|
{
|
|
const HPRefElement & hpref_el =
|
|
(*mesh.hpelements) [mesh[elnr].hp_elnr];
|
|
|
|
return mesh.coarsemesh->GetCurvedElements().IsSurfaceElementCurved (hpref_el.coarse_elnr);
|
|
}
|
|
|
|
const Element2d & el = mesh[elnr];
|
|
ELEMENT_TYPE type = el.GetType();
|
|
|
|
SurfaceElementInfo info;
|
|
info.elnr = elnr;
|
|
info.order = order;
|
|
|
|
switch (type)
|
|
{
|
|
case TRIG : info.nv = 3; break;
|
|
case QUAD : info.nv = 4; break;
|
|
case TRIG6: return true;
|
|
default:
|
|
cerr << "undef element in CalcSurfaceTrafo" << endl;
|
|
}
|
|
info.ndof = info.nv;
|
|
|
|
// info.ndof = info.nv = ( (type == TRIG) || (type == TRIG6) ) ? 3 : 4;
|
|
if (info.order > 1)
|
|
{
|
|
const MeshTopology & top = mesh.GetTopology();
|
|
|
|
top.GetSurfaceElementEdges (elnr+1, info.edgenrs);
|
|
for (int i = 0; i < info.edgenrs.Size(); i++)
|
|
info.edgenrs[i]--;
|
|
info.facenr = top.GetSurfaceElementFace (elnr+1)-1;
|
|
|
|
for (int i = 0; i < info.edgenrs.Size(); i++)
|
|
info.ndof += edgecoeffsindex[info.edgenrs[i]+1] - edgecoeffsindex[info.edgenrs[i]];
|
|
info.ndof += facecoeffsindex[info.facenr+1] - facecoeffsindex[info.facenr];
|
|
}
|
|
|
|
return (info.ndof > info.nv);
|
|
}
|
|
|
|
void CurvedElements ::
|
|
CalcSurfaceTransformation (Point<2> xi, SurfaceElementIndex elnr,
|
|
Point<3> * x, Mat<3,2> * dxdxi, bool * curved)
|
|
{
|
|
if (mesh.coarsemesh)
|
|
{
|
|
const HPRefElement & hpref_el =
|
|
(*mesh.hpelements) [mesh[elnr].hp_elnr];
|
|
|
|
// xi umrechnen
|
|
double lami[4];
|
|
FlatVector vlami(4, lami);
|
|
vlami = 0;
|
|
mesh[elnr].GetShapeNew (xi, vlami);
|
|
|
|
Mat<2,2> trans;
|
|
Mat<3,2> dxdxic;
|
|
if (dxdxi)
|
|
{
|
|
MatrixFixWidth<2> dlami(4);
|
|
dlami = 0;
|
|
mesh[elnr].GetDShapeNew (xi, dlami);
|
|
|
|
trans = 0;
|
|
for (int k = 0; k < 2; k++)
|
|
for (int l = 0; l < 2; l++)
|
|
for (int i = 0; i < hpref_el.np; i++)
|
|
trans(l,k) += hpref_el.param[i][l] * dlami(i, k);
|
|
}
|
|
|
|
Point<2> coarse_xi(0,0);
|
|
for (int i = 0; i < hpref_el.np; i++)
|
|
for (int j = 0; j < 2; j++)
|
|
coarse_xi(j) += hpref_el.param[i][j] * lami[i];
|
|
|
|
mesh.coarsemesh->GetCurvedElements().CalcSurfaceTransformation (coarse_xi, hpref_el.coarse_elnr, x, &dxdxic, curved);
|
|
|
|
if (dxdxi)
|
|
*dxdxi = dxdxic * trans;
|
|
|
|
return;
|
|
}
|
|
|
|
|
|
|
|
Vector shapes;
|
|
MatrixFixWidth<2> dshapes;
|
|
Array<Vec<3> > coefs;
|
|
|
|
const Element2d & el = mesh[elnr];
|
|
ELEMENT_TYPE type = el.GetType();
|
|
|
|
SurfaceElementInfo info;
|
|
info.elnr = elnr;
|
|
info.order = order;
|
|
|
|
switch (type)
|
|
{
|
|
case TRIG : info.nv = 3; break;
|
|
case QUAD : info.nv = 4; break;
|
|
case TRIG6: info.nv = 6; break;
|
|
default:
|
|
cerr << "undef element in CalcSurfaceTrafo" << endl;
|
|
}
|
|
info.ndof = info.nv;
|
|
|
|
if (info.order > 1)
|
|
{
|
|
const MeshTopology & top = mesh.GetTopology();
|
|
|
|
top.GetSurfaceElementEdges (elnr+1, info.edgenrs);
|
|
for (int i = 0; i < info.edgenrs.Size(); i++)
|
|
info.edgenrs[i]--;
|
|
info.facenr = top.GetSurfaceElementFace (elnr+1)-1;
|
|
|
|
|
|
bool firsttry = true;
|
|
bool problem = false;
|
|
|
|
while(firsttry || problem)
|
|
{
|
|
problem = false;
|
|
|
|
for (int i = 0; !problem && i < info.edgenrs.Size(); i++)
|
|
{
|
|
if(info.edgenrs[i]+1 >= edgecoeffsindex.Size())
|
|
problem = true;
|
|
else
|
|
info.ndof += edgecoeffsindex[info.edgenrs[i]+1] - edgecoeffsindex[info.edgenrs[i]];
|
|
}
|
|
if(info.facenr+1 >= facecoeffsindex.Size())
|
|
problem = true;
|
|
else
|
|
info.ndof += facecoeffsindex[info.facenr+1] - facecoeffsindex[info.facenr];
|
|
|
|
if(problem && !firsttry)
|
|
throw NgException("something wrong with curved elements");
|
|
|
|
if(problem)
|
|
BuildCurvedElements(NULL,order,rational);
|
|
|
|
firsttry = false;
|
|
}
|
|
}
|
|
|
|
CalcElementShapes (info, xi, shapes);
|
|
GetCoefficients (info, coefs);
|
|
|
|
*x = 0;
|
|
for (int i = 0; i < coefs.Size(); i++)
|
|
*x += shapes(i) * coefs[i];
|
|
|
|
if (dxdxi)
|
|
{
|
|
CalcElementDShapes (info, xi, dshapes);
|
|
|
|
*dxdxi = 0;
|
|
for (int i = 0; i < coefs.Size(); i++)
|
|
for (int j = 0; j < 3; j++)
|
|
for (int k = 0; k < 2; k++)
|
|
(*dxdxi)(j,k) += dshapes(i,k) * coefs[i](j);
|
|
}
|
|
|
|
if (curved)
|
|
*curved = (info.ndof > info.nv);
|
|
}
|
|
|
|
|
|
|
|
|
|
void CurvedElements ::
|
|
CalcElementShapes (SurfaceElementInfo & info, const Point<2> & xi, Vector & shapes) const
|
|
{
|
|
const Element2d & el = mesh[info.elnr];
|
|
shapes.SetSize(info.ndof);
|
|
|
|
if (rational && info.order >= 2)
|
|
{
|
|
shapes.SetSize(6);
|
|
double w = 1;
|
|
double lami[3] = { xi(0), xi(1), 1-xi(0)-xi(1) };
|
|
for (int j = 0; j < 3; j++)
|
|
shapes(j) = lami[j] * lami[j];
|
|
|
|
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (TRIG);
|
|
for (int j = 0; j < 3; j++)
|
|
{
|
|
double wi = edgeweight[info.edgenrs[j]];
|
|
shapes(j+3) = 2 * wi * lami[edges[j][0]-1] * lami[edges[j][1]-1];
|
|
w += (wi-1) * 2 * lami[edges[j][0]-1] * lami[edges[j][1]-1];
|
|
}
|
|
|
|
shapes *= 1.0 / w;
|
|
return;
|
|
}
|
|
|
|
switch (el.GetType())
|
|
{
|
|
case TRIG:
|
|
{
|
|
shapes(0) = xi(0);
|
|
shapes(1) = xi(1);
|
|
shapes(2) = 1-xi(0)-xi(1);
|
|
|
|
if (info.order == 1) return;
|
|
|
|
int ii = 3;
|
|
const ELEMENT_EDGE * edges = MeshTopology::GetEdges0 (TRIG);
|
|
|
|
for (int i = 0; i < 3; i++)
|
|
{
|
|
int eorder = edgeorder[info.edgenrs[i]];
|
|
if (eorder >= 2)
|
|
{
|
|
int vi1 = edges[i][0], vi2 = edges[i][1];
|
|
if (el[vi1] > el[vi2]) swap (vi1, vi2);
|
|
|
|
CalcScaledEdgeShape (eorder, shapes(vi1)-shapes(vi2), shapes(vi1)+shapes(vi2), &shapes(ii));
|
|
ii += eorder-1;
|
|
}
|
|
}
|
|
|
|
int forder = faceorder[info.facenr];
|
|
if (forder >= 3)
|
|
{
|
|
int fnums[] = { 0, 1, 2 };
|
|
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
|
|
if (el[fnums[1]] > el[fnums[2]]) swap (fnums[1], fnums[2]);
|
|
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
|
|
|
|
CalcTrigShape (forder,
|
|
shapes(fnums[1])-shapes(fnums[0]),
|
|
1-shapes(fnums[1])-shapes(fnums[0]), &shapes(ii));
|
|
}
|
|
break;
|
|
}
|
|
|
|
case TRIG6:
|
|
{
|
|
if (shapes.Size() == 3)
|
|
{
|
|
shapes(0) = xi(0);
|
|
shapes(1) = xi(1);
|
|
shapes(2) = 1-xi(0)-xi(1);
|
|
}
|
|
else
|
|
{
|
|
double x = xi(0);
|
|
double y = xi(1);
|
|
double lam3 = 1-x-y;
|
|
|
|
shapes(0) = x * (2*x-1);
|
|
shapes(1) = y * (2*y-1);
|
|
shapes(2) = lam3 * (2*lam3-1);
|
|
shapes(3) = 4 * y * lam3;
|
|
shapes(4) = 4 * x * lam3;
|
|
shapes(5) = 4 * x * y;
|
|
}
|
|
break;
|
|
}
|
|
|
|
case QUAD:
|
|
{
|
|
shapes(0) = (1-xi(0))*(1-xi(1));
|
|
shapes(1) = xi(0) *(1-xi(1));
|
|
shapes(2) = xi(0) * xi(1) ;
|
|
shapes(3) = (1-xi(0))* xi(1) ;
|
|
|
|
if (info.order == 1) return;
|
|
|
|
double mu[4] = {
|
|
1 - xi(0) + 1 - xi(1),
|
|
xi(0) + 1 - xi(1),
|
|
xi(0) + xi(1),
|
|
1 - xi(0) + xi(1),
|
|
};
|
|
|
|
int ii = 4;
|
|
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (QUAD);
|
|
|
|
for (int i = 0; i < 4; i++)
|
|
{
|
|
int eorder = edgeorder[info.edgenrs[i]];
|
|
if (eorder >= 2)
|
|
{
|
|
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
|
|
if (el[vi1] > el[vi2]) swap (vi1, vi2);
|
|
|
|
CalcEdgeShape (eorder, mu[vi1]-mu[vi2], &shapes(ii));
|
|
double lame = shapes(vi1)+shapes(vi2);
|
|
for (int j = 0; j < order-1; j++)
|
|
shapes(ii+j) *= lame;
|
|
ii += eorder-1;
|
|
}
|
|
}
|
|
|
|
for (int i = ii; i < info.ndof; i++)
|
|
shapes(i) = 0;
|
|
|
|
break;
|
|
}
|
|
|
|
default:
|
|
throw NgException("CurvedElements::CalcShape 2d, element type not handled");
|
|
};
|
|
}
|
|
|
|
|
|
void CurvedElements ::
|
|
CalcElementDShapes (SurfaceElementInfo & info, const Point<2> & xi, MatrixFixWidth<2> & dshapes) const
|
|
{
|
|
const Element2d & el = mesh[info.elnr];
|
|
ELEMENT_TYPE type = el.GetType();
|
|
|
|
double lami[4];
|
|
|
|
dshapes.SetSize(info.ndof);
|
|
// dshapes = 0;
|
|
|
|
// *testout << "calcelementdshapes, info.ndof = " << info.ndof << endl;
|
|
|
|
if (rational && info.order >= 2)
|
|
{
|
|
double w = 1;
|
|
double dw[2] = { 0, 0 };
|
|
|
|
|
|
lami[0] = xi(0); lami[1] = xi(1); lami[2] = 1-xi(0)-xi(1);
|
|
double dlami[3][2] = { { 1, 0 }, { 0, 1 }, { -1, -1 }};
|
|
double shapes[6];
|
|
|
|
for (int j = 0; j < 3; j++)
|
|
{
|
|
shapes[j] = lami[j] * lami[j];
|
|
dshapes(j,0) = 2 * lami[j] * dlami[j][0];
|
|
dshapes(j,1) = 2 * lami[j] * dlami[j][1];
|
|
}
|
|
|
|
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (TRIG);
|
|
for (int j = 0; j < 3; j++)
|
|
{
|
|
double wi = edgeweight[info.edgenrs[j]];
|
|
|
|
shapes[j+3] = 2 * wi * lami[edges[j][0]-1] * lami[edges[j][1]-1];
|
|
for (int k = 0; k < 2; k++)
|
|
dshapes(j+3,k) = 2*wi* (lami[edges[j][0]-1] * dlami[edges[j][1]-1][k] +
|
|
lami[edges[j][1]-1] * dlami[edges[j][0]-1][k]);
|
|
|
|
w += (wi-1) * 2 * lami[edges[j][0]-1] * lami[edges[j][1]-1];
|
|
for (int k = 0; k < 2; k++)
|
|
dw[k] += 2*(wi-1) * (lami[edges[j][0]-1] * dlami[edges[j][1]-1][k] +
|
|
lami[edges[j][1]-1] * dlami[edges[j][0]-1][k]);
|
|
}
|
|
// shapes *= 1.0 / w;
|
|
dshapes *= 1.0 / w;
|
|
for (int i = 0; i < 6; i++)
|
|
for (int j = 0; j < 2; j++)
|
|
dshapes(i,j) -= shapes[i] * dw[j] / (w*w);
|
|
return;
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
switch (type)
|
|
{
|
|
case TRIG:
|
|
{
|
|
dshapes(0,0) = 1;
|
|
dshapes(0,1) = 0.0;
|
|
dshapes(1,0) = 0.0;
|
|
dshapes(1,1) = 1;
|
|
dshapes(2,0) = -1;
|
|
dshapes(2,1) = -1;
|
|
|
|
if (info.order == 1) return;
|
|
|
|
// *testout << "info.order = " << info.order << endl;
|
|
|
|
|
|
lami[0] = xi(0);
|
|
lami[1] = xi(1);
|
|
lami[2] = 1-xi(0)-xi(1);
|
|
|
|
int ii = 3;
|
|
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (TRIG);
|
|
|
|
for (int i = 0; i < 3; i++)
|
|
{
|
|
int eorder = edgeorder[info.edgenrs[i]];
|
|
if (eorder >= 2)
|
|
{
|
|
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
|
|
if (el[vi1] > el[vi2]) swap (vi1, vi2);
|
|
|
|
CalcScaledEdgeShapeDxDt<2> (eorder, lami[vi1]-lami[vi2], lami[vi1]+lami[vi2], &dshapes(ii,0));
|
|
|
|
Mat<2,2> trans;
|
|
for (int j = 0; j < 2; j++)
|
|
{
|
|
trans(0,j) = dshapes(vi1,j)-dshapes(vi2,j);
|
|
trans(1,j) = dshapes(vi1,j)+dshapes(vi2,j);
|
|
}
|
|
|
|
for (int j = 0; j < eorder-1; j++)
|
|
{
|
|
double ddx = dshapes(ii+j,0);
|
|
double ddt = dshapes(ii+j,1);
|
|
dshapes(ii+j,0) = ddx * trans(0,0) + ddt * trans(1,0);
|
|
dshapes(ii+j,1) = ddx * trans(0,1) + ddt * trans(1,1);
|
|
}
|
|
|
|
ii += eorder-1;
|
|
}
|
|
}
|
|
|
|
int forder = faceorder[info.facenr];
|
|
// *testout << "forder = " << forder << endl;
|
|
if (forder >= 3)
|
|
{
|
|
int fnums[] = { 0, 1, 2 };
|
|
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
|
|
if (el[fnums[1]] > el[fnums[2]]) swap (fnums[1], fnums[2]);
|
|
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
|
|
|
|
CalcTrigShapeDxDy (forder,
|
|
lami[fnums[1]]-lami[fnums[0]],
|
|
1-lami[fnums[1]]-lami[fnums[0]], &dshapes(ii,0));
|
|
|
|
int nd = (forder-1)*(forder-2)/2;
|
|
Mat<2,2> trans;
|
|
for (int j = 0; j < 2; j++)
|
|
{
|
|
trans(0,j) = dshapes(fnums[1],j)-dshapes(fnums[0],j);
|
|
trans(1,j) = -dshapes(fnums[1],j)-dshapes(fnums[0],j);
|
|
}
|
|
|
|
for (int j = 0; j < nd; j++)
|
|
{
|
|
double ddx = dshapes(ii+j,0);
|
|
double ddt = dshapes(ii+j,1);
|
|
dshapes(ii+j,0) = ddx * trans(0,0) + ddt * trans(1,0);
|
|
dshapes(ii+j,1) = ddx * trans(0,1) + ddt * trans(1,1);
|
|
}
|
|
}
|
|
|
|
break;
|
|
}
|
|
|
|
case TRIG6:
|
|
{
|
|
if (dshapes.Height() == 3)
|
|
{
|
|
dshapes = 0.0;
|
|
dshapes(0,0) = 1;
|
|
dshapes(1,1) = 1;
|
|
dshapes(2,0) = -1;
|
|
dshapes(2,1) = -1;
|
|
}
|
|
else
|
|
{
|
|
AutoDiff<2> x(xi(0), 0);
|
|
AutoDiff<2> y(xi(1), 1);
|
|
AutoDiff<2> lam3 = 1-x-y;
|
|
AutoDiff<2> shapes[6];
|
|
shapes[0] = x * (2*x-1);
|
|
shapes[1] = y * (2*y-1);
|
|
shapes[2] = lam3 * (2*lam3-1);
|
|
shapes[3] = 4 * y * lam3;
|
|
shapes[4] = 4 * x * lam3;
|
|
shapes[5] = 4 * x * y;
|
|
|
|
for (int i = 0; i < 6; i++)
|
|
{
|
|
dshapes(i,0) = shapes[i].DValue(0);
|
|
dshapes(i,1) = shapes[i].DValue(1);
|
|
}
|
|
|
|
}
|
|
break;
|
|
}
|
|
|
|
case QUAD:
|
|
{
|
|
dshapes(0,0) = -(1-xi(1));
|
|
dshapes(0,1) = -(1-xi(0));
|
|
dshapes(1,0) = (1-xi(1));
|
|
dshapes(1,1) = -xi(0);
|
|
dshapes(2,0) = xi(1);
|
|
dshapes(2,1) = xi(0);
|
|
dshapes(3,0) = -xi(1);
|
|
dshapes(3,1) = (1-xi(0));
|
|
|
|
if (info.order == 1) return;
|
|
|
|
double shapes[4] = {
|
|
(1-xi(0))*(1-xi(1)),
|
|
xi(0) *(1-xi(1)),
|
|
xi(0) * xi(1) ,
|
|
(1-xi(0))* xi(1)
|
|
};
|
|
|
|
double mu[4] = {
|
|
1 - xi(0) + 1 - xi(1),
|
|
xi(0) + 1 - xi(1),
|
|
xi(0) + xi(1),
|
|
1 - xi(0) + xi(1),
|
|
};
|
|
|
|
double dmu[4][2] = {
|
|
{ -1, -1 },
|
|
{ 1, -1 },
|
|
{ 1, 1 },
|
|
{ -1, 1 } };
|
|
|
|
// double hshapes[20], hdshapes[20];
|
|
ArrayMem<double, 20> hshapes(order+1), hdshapes(order+1);
|
|
|
|
int ii = 4;
|
|
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (QUAD);
|
|
|
|
for (int i = 0; i < 4; i++)
|
|
{
|
|
int eorder = edgeorder[info.edgenrs[i]];
|
|
if (eorder >= 2)
|
|
{
|
|
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
|
|
if (el[vi1] > el[vi2]) swap (vi1, vi2);
|
|
|
|
CalcEdgeShapeDx (eorder, mu[vi1]-mu[vi2], &hshapes[0], &hdshapes[0]);
|
|
|
|
double lame = shapes[vi1]+shapes[vi2];
|
|
double dlame[2] = {
|
|
dshapes(vi1, 0) + dshapes(vi2, 0),
|
|
dshapes(vi1, 1) + dshapes(vi2, 1) };
|
|
|
|
for (int j = 0; j < eorder-1; j++)
|
|
for (int k = 0; k < 2; k++)
|
|
dshapes(ii+j, k) =
|
|
lame * hdshapes[j] * (dmu[vi1][k]-dmu[vi2][k])
|
|
+ dlame[k] * hshapes[j];
|
|
|
|
ii += eorder-1;
|
|
}
|
|
}
|
|
|
|
/*
|
|
*testout << "quad, dshape = " << endl << dshapes << endl;
|
|
for (int i = 0; i < 2; i++)
|
|
{
|
|
Point<2> xil = xi, xir = xi;
|
|
Vector shapesl(dshapes.Height()), shapesr(dshapes.Height());
|
|
xil(i) -= 1e-6;
|
|
xir(i) += 1e-6;
|
|
CalcElementShapes (info, xil, shapesl);
|
|
CalcElementShapes (info, xir, shapesr);
|
|
|
|
for (int j = 0; j < dshapes.Height(); j++)
|
|
dshapes(j,i) = 1.0 / 2e-6 * (shapesr(j)-shapesl(j));
|
|
}
|
|
|
|
*testout << "quad, num dshape = " << endl << dshapes << endl;
|
|
*/
|
|
break;
|
|
}
|
|
default:
|
|
throw NgException("CurvedElements::CalcDShape 2d, element type not handled");
|
|
|
|
};
|
|
}
|
|
|
|
|
|
template <int DIM_SPACE>
|
|
void CurvedElements ::
|
|
GetCoefficients (SurfaceElementInfo & info, Array<Vec<DIM_SPACE> > & coefs) const
|
|
{
|
|
const Element2d & el = mesh[info.elnr];
|
|
coefs.SetSize (info.ndof);
|
|
|
|
for (int i = 0; i < info.nv; i++)
|
|
{
|
|
Point<3> hv = mesh[el[i]];
|
|
for (int j = 0; j < DIM_SPACE; j++)
|
|
coefs[i](j) = hv(j);
|
|
}
|
|
|
|
if (info.order == 1) return;
|
|
|
|
int ii = info.nv;
|
|
|
|
for (int i = 0; i < info.edgenrs.Size(); i++)
|
|
{
|
|
int first = edgecoeffsindex[info.edgenrs[i]];
|
|
int next = edgecoeffsindex[info.edgenrs[i]+1];
|
|
for (int j = first; j < next; j++, ii++)
|
|
for (int k = 0; k < DIM_SPACE; k++)
|
|
coefs[ii](k) = edgecoeffs[j](k);
|
|
}
|
|
|
|
int first = facecoeffsindex[info.facenr];
|
|
int next = facecoeffsindex[info.facenr+1];
|
|
for (int j = first; j < next; j++, ii++)
|
|
for (int k = 0; k < DIM_SPACE; k++)
|
|
coefs[ii](k) = facecoeffs[j](k);
|
|
}
|
|
|
|
|
|
template void CurvedElements ::
|
|
GetCoefficients<2> (SurfaceElementInfo & info, Array<Vec<2> > & coefs) const;
|
|
|
|
template void CurvedElements ::
|
|
GetCoefficients<3> (SurfaceElementInfo & info, Array<Vec<3> > & coefs) const;
|
|
|
|
|
|
|
|
|
|
|
|
// ********************** Transform volume elements *******************
|
|
|
|
|
|
bool CurvedElements :: IsElementCurved (ElementIndex elnr) const
|
|
{
|
|
if (mesh.coarsemesh)
|
|
{
|
|
const HPRefElement & hpref_el =
|
|
(*mesh.hpelements) [mesh[elnr].hp_elnr];
|
|
|
|
return mesh.coarsemesh->GetCurvedElements().IsElementCurved (hpref_el.coarse_elnr);
|
|
}
|
|
|
|
const Element & el = mesh[elnr];
|
|
ELEMENT_TYPE type = el.GetType();
|
|
|
|
int nfaces = MeshTopology::GetNFaces (type);
|
|
if (nfaces > 4)
|
|
{ // not a tet
|
|
const ELEMENT_FACE * faces = MeshTopology::GetFaces0 (type);
|
|
for (int j = 0; j < nfaces; j++)
|
|
{
|
|
if (faces[j][3] != -1)
|
|
{ // a quad face
|
|
Point<3> pts[4];
|
|
for (int k = 0; k < 4; k++)
|
|
pts[k] = mesh.Point(el[faces[j][k]]);
|
|
Vec<3> twist = (pts[1] - pts[0]) - (pts[2]-pts[3]);
|
|
if (twist.Length() > 1e-8 * (pts[1]-pts[0]).Length())
|
|
return true;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
|
|
ElementInfo info;
|
|
info.elnr = elnr;
|
|
info.order = order;
|
|
info.ndof = info.nv = MeshTopology::GetNPoints (type);
|
|
if (info.order > 1)
|
|
{
|
|
const MeshTopology & top = mesh.GetTopology();
|
|
|
|
info.nedges = top.GetElementEdges (elnr+1, info.edgenrs, 0);
|
|
for (int i = 0; i < info.nedges; i++)
|
|
info.edgenrs[i]--;
|
|
|
|
info.nfaces = top.GetElementFaces (elnr+1, info.facenrs, 0);
|
|
for (int i = 0; i < info.nfaces; i++)
|
|
info.facenrs[i]--;
|
|
|
|
for (int i = 0; i < info.nedges; i++)
|
|
info.ndof += edgecoeffsindex[info.edgenrs[i]+1] - edgecoeffsindex[info.edgenrs[i]];
|
|
for (int i = 0; i < info.nfaces; i++)
|
|
info.ndof += facecoeffsindex[info.facenrs[i]+1] - facecoeffsindex[info.facenrs[i]];
|
|
}
|
|
|
|
return (info.ndof > info.nv);
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
void CurvedElements ::
|
|
CalcElementTransformation (Point<3> xi, ElementIndex elnr,
|
|
Point<3> * x, Mat<3,3> * dxdxi, // bool * curved,
|
|
void * buffer, bool valid)
|
|
{
|
|
if (mesh.coarsemesh)
|
|
{
|
|
const HPRefElement & hpref_el =
|
|
(*mesh.hpelements) [mesh[elnr].hp_elnr];
|
|
|
|
// xi umrechnen
|
|
double lami[8];
|
|
FlatVector vlami(8, lami);
|
|
vlami = 0;
|
|
mesh[elnr].GetShapeNew (xi, vlami);
|
|
|
|
Mat<3,3> trans, dxdxic;
|
|
if (dxdxi)
|
|
{
|
|
MatrixFixWidth<3> dlami(8);
|
|
dlami = 0;
|
|
mesh[elnr].GetDShapeNew (xi, dlami);
|
|
|
|
trans = 0;
|
|
for (int k = 0; k < 3; k++)
|
|
for (int l = 0; l < 3; l++)
|
|
for (int i = 0; i < hpref_el.np; i++)
|
|
trans(l,k) += hpref_el.param[i][l] * dlami(i, k);
|
|
}
|
|
|
|
Point<3> coarse_xi(0,0,0);
|
|
for (int i = 0; i < hpref_el.np; i++)
|
|
for (int j = 0; j < 3; j++)
|
|
coarse_xi(j) += hpref_el.param[i][j] * lami[i];
|
|
|
|
mesh.coarsemesh->GetCurvedElements().CalcElementTransformation (coarse_xi, hpref_el.coarse_elnr, x, &dxdxic /* , curved */);
|
|
|
|
if (dxdxi)
|
|
*dxdxi = dxdxic * trans;
|
|
|
|
return;
|
|
}
|
|
|
|
|
|
Vector shapes;
|
|
MatrixFixWidth<3> dshapes;
|
|
|
|
const Element & el = mesh[elnr];
|
|
ELEMENT_TYPE type = el.GetType();
|
|
|
|
ElementInfo hinfo;
|
|
ElementInfo & info = (buffer) ? *static_cast<ElementInfo*> (buffer) : hinfo;
|
|
|
|
|
|
if (!valid)
|
|
{
|
|
info.elnr = elnr;
|
|
info.order = order;
|
|
info.ndof = info.nv = MeshTopology::GetNPoints (type);
|
|
if (info.order > 1)
|
|
{
|
|
const MeshTopology & top = mesh.GetTopology();
|
|
|
|
info.nedges = top.GetElementEdges (elnr+1, info.edgenrs, 0);
|
|
for (int i = 0; i < info.nedges; i++)
|
|
info.edgenrs[i]--;
|
|
|
|
info.nfaces = top.GetElementFaces (elnr+1, info.facenrs, 0);
|
|
for (int i = 0; i < info.nfaces; i++)
|
|
info.facenrs[i]--;
|
|
|
|
for (int i = 0; i < info.nedges; i++)
|
|
info.ndof += edgecoeffsindex[info.edgenrs[i]+1] - edgecoeffsindex[info.edgenrs[i]];
|
|
for (int i = 0; i < info.nfaces; i++)
|
|
info.ndof += facecoeffsindex[info.facenrs[i]+1] - facecoeffsindex[info.facenrs[i]];
|
|
}
|
|
}
|
|
|
|
CalcElementShapes (info, xi, shapes);
|
|
|
|
Vec<3> * coefs = (info.ndof <= 10) ?
|
|
&info.hcoefs[0] : new Vec<3> [info.ndof];
|
|
|
|
if (info.ndof > 10 || !valid)
|
|
GetCoefficients (info, coefs);
|
|
|
|
if (x)
|
|
{
|
|
*x = 0;
|
|
for (int i = 0; i < shapes.Size(); i++)
|
|
*x += shapes(i) * coefs[i];
|
|
}
|
|
|
|
if (dxdxi)
|
|
{
|
|
if (valid && info.order == 1 && info.nv == 4) // a linear tet
|
|
{
|
|
*dxdxi = info.hdxdxi;
|
|
}
|
|
else
|
|
{
|
|
CalcElementDShapes (info, xi, dshapes);
|
|
|
|
*dxdxi = 0;
|
|
for (int i = 0; i < shapes.Size(); i++)
|
|
for (int j = 0; j < 3; j++)
|
|
for (int k = 0; k < 3; k++)
|
|
(*dxdxi)(j,k) += dshapes(i,k) * coefs[i](j);
|
|
|
|
info.hdxdxi = *dxdxi;
|
|
}
|
|
}
|
|
|
|
// *testout << "curved_elements, dshapes = " << endl << dshapes << endl;
|
|
|
|
// if (curved) *curved = (info.ndof > info.nv);
|
|
|
|
if (info.ndof > 10) delete [] coefs;
|
|
}
|
|
|
|
|
|
|
|
|
|
void CurvedElements :: CalcElementShapes (ElementInfo & info, const Point<3> & xi, Vector & shapes) const
|
|
{
|
|
const Element & el = mesh[info.elnr];
|
|
|
|
if (rational && info.order >= 2)
|
|
{
|
|
shapes.SetSize(10);
|
|
double w = 1;
|
|
double lami[4] = { xi(0), xi(1), xi(2), 1-xi(0)-xi(1)-xi(2) };
|
|
for (int j = 0; j < 4; j++)
|
|
shapes(j) = lami[j] * lami[j];
|
|
|
|
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (TET);
|
|
for (int j = 0; j < 6; j++)
|
|
{
|
|
double wi = edgeweight[info.edgenrs[j]];
|
|
shapes(j+4) = 2 * wi * lami[edges[j][0]-1] * lami[edges[j][1]-1];
|
|
w += (wi-1) * 2 * lami[edges[j][0]-1] * lami[edges[j][1]-1];
|
|
}
|
|
|
|
shapes *= 1.0 / w;
|
|
return;
|
|
}
|
|
|
|
shapes.SetSize(info.ndof);
|
|
|
|
switch (el.GetType())
|
|
{
|
|
case TET:
|
|
{
|
|
shapes(0) = xi(0);
|
|
shapes(1) = xi(1);
|
|
shapes(2) = xi(2);
|
|
shapes(3) = 1-xi(0)-xi(1)-xi(2);
|
|
|
|
if (info.order == 1) return;
|
|
|
|
int ii = 4;
|
|
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (TET);
|
|
for (int i = 0; i < 6; i++)
|
|
{
|
|
int eorder = edgeorder[info.edgenrs[i]];
|
|
if (eorder >= 2)
|
|
{
|
|
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
|
|
if (el[vi1] > el[vi2]) swap (vi1, vi2);
|
|
|
|
CalcScaledEdgeShape (eorder, shapes(vi1)-shapes(vi2), shapes(vi1)+shapes(vi2), &shapes(ii));
|
|
ii += eorder-1;
|
|
}
|
|
}
|
|
const ELEMENT_FACE * faces = MeshTopology::GetFaces1 (TET);
|
|
for (int i = 0; i < 4; i++)
|
|
{
|
|
int forder = faceorder[info.facenrs[i]];
|
|
if (forder >= 3)
|
|
{
|
|
int fnums[] = { faces[i][0]-1, faces[i][1]-1, faces[i][2]-1 };
|
|
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
|
|
if (el[fnums[1]] > el[fnums[2]]) swap (fnums[1], fnums[2]);
|
|
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
|
|
|
|
CalcScaledTrigShape (forder,
|
|
shapes(fnums[1])-shapes(fnums[0]), shapes(fnums[2]),
|
|
shapes(fnums[0])+shapes(fnums[1])+shapes(fnums[2]), &shapes(ii));
|
|
ii += (forder-1)*(forder-2)/2;
|
|
}
|
|
}
|
|
|
|
break;
|
|
}
|
|
|
|
case TET10:
|
|
{
|
|
double x = xi(0);
|
|
double y = xi(1);
|
|
double z = xi(2);
|
|
double lam4 = 1 - x - y - z;
|
|
/*
|
|
shapes(0) = xi(0);
|
|
shapes(1) = xi(1);
|
|
shapes(2) = xi(2);
|
|
shapes(3) = 1-xi(0)-xi(1)-xi(2);
|
|
*/
|
|
|
|
shapes(0) = 2 * x * x - x;
|
|
shapes(1) = 2 * y * y - y;
|
|
shapes(2) = 2 * z * z - z;
|
|
shapes(3) = 2 * lam4 * lam4 - lam4;
|
|
|
|
shapes(4) = 4 * x * y;
|
|
shapes(5) = 4 * x * z;
|
|
shapes(6) = 4 * x * lam4;
|
|
shapes(7) = 4 * y * z;
|
|
shapes(8) = 4 * y * lam4;
|
|
shapes(9) = 4 * z * lam4;
|
|
|
|
break;
|
|
}
|
|
|
|
case PRISM:
|
|
{
|
|
double lami[6] = { xi(0), xi(1), 1-xi(0)-xi(1), xi(0), xi(1), 1-xi(0)-xi(1) };
|
|
double lamiz[6] = { 1-xi(2), 1-xi(2), 1-xi(2), xi(2), xi(2), xi(2) };
|
|
for (int i = 0; i < 6; i++)
|
|
shapes(i) = lami[i] * lamiz[i];
|
|
for (int i = 6; i < info.ndof; i++)
|
|
shapes(i) = 0;
|
|
|
|
if (info.order == 1) return;
|
|
|
|
|
|
int ii = 6;
|
|
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (PRISM);
|
|
for (int i = 0; i < 6; i++) // horizontal edges
|
|
{
|
|
int eorder = edgeorder[info.edgenrs[i]];
|
|
if (eorder >= 2)
|
|
{
|
|
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
|
|
if (el[vi1] > el[vi2]) swap (vi1, vi2);
|
|
|
|
CalcScaledEdgeShape (eorder, lami[vi1]-lami[vi2], lami[vi1]+lami[vi2], &shapes(ii));
|
|
double facz = (i < 3) ? (1-xi(2)) : xi(2);
|
|
for (int j = 0; j < eorder-1; j++)
|
|
shapes(ii+j) *= facz;
|
|
|
|
ii += eorder-1;
|
|
}
|
|
}
|
|
|
|
for (int i = 6; i < 9; i++) // vertical edges
|
|
{
|
|
int eorder = edgeorder[info.edgenrs[i]];
|
|
if (eorder >= 2)
|
|
{
|
|
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
|
|
if (el[vi1] > el[vi2]) swap (vi1, vi2);
|
|
|
|
double bubz = lamiz[vi1]*lamiz[vi2];
|
|
double polyz = lamiz[vi1] - lamiz[vi2];
|
|
double bubxy = lami[vi1];
|
|
|
|
for (int j = 0; j < eorder-1; j++)
|
|
{
|
|
shapes(ii+j) = bubxy * bubz;
|
|
bubz *= polyz;
|
|
}
|
|
ii += eorder-1;
|
|
}
|
|
}
|
|
|
|
// FACE SHAPES
|
|
const ELEMENT_FACE * faces = MeshTopology::GetFaces1 (PRISM);
|
|
for (int i = 0; i < 2; i++)
|
|
{
|
|
int forder = faceorder[info.facenrs[i]];
|
|
if ( forder < 3 ) continue;
|
|
int fav[3] = { faces[i][0]-1, faces[i][1]-1, faces[i][2]-1 };
|
|
if(el[fav[0]] > el[fav[1]]) swap(fav[0],fav[1]);
|
|
if(el[fav[1]] > el[fav[2]]) swap(fav[1],fav[2]);
|
|
if(el[fav[0]] > el[fav[1]]) swap(fav[0],fav[1]);
|
|
|
|
CalcTrigShape (forder,
|
|
lami[fav[2]]-lami[fav[1]], lami[fav[0]],
|
|
&shapes(ii));
|
|
|
|
int ndf = (forder+1)*(forder+2)/2 - 3 - 3*(forder-1);
|
|
for ( int j = 0; j < ndf; j++ )
|
|
shapes(ii+j) *= lamiz[fav[1]];
|
|
ii += ndf;
|
|
}
|
|
break;
|
|
}
|
|
|
|
case PYRAMID:
|
|
{
|
|
shapes = 0.0;
|
|
double x = xi(0);
|
|
double y = xi(1);
|
|
double z = xi(2);
|
|
|
|
if (z == 1.) z = 1-1e-10;
|
|
shapes[0] = (1-z-x)*(1-z-y) / (1-z);
|
|
shapes[1] = x*(1-z-y) / (1-z);
|
|
shapes[2] = x*y / (1-z);
|
|
shapes[3] = (1-z-x)*y / (1-z);
|
|
shapes[4] = z;
|
|
|
|
if (info.order == 1) return;
|
|
|
|
int ii = 5;
|
|
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (PYRAMID);
|
|
for (int i = 0; i < 4; i++) // horizontal edges
|
|
{
|
|
int eorder = edgeorder[info.edgenrs[i]];
|
|
if (eorder >= 2)
|
|
{
|
|
int vi1 = (edges[i][0]-1), vi2 = (edges[i][1]-1);
|
|
if (el[vi1] > el[vi2]) swap (vi1, vi2);
|
|
|
|
CalcScaledEdgeShape (eorder, shapes[vi1]-shapes[vi2], shapes[vi1]+shapes[vi2], &shapes(ii));
|
|
double fac = (shapes[vi1]+shapes[vi2]) / (1-z);
|
|
for (int j = 0; j < eorder-1; j++)
|
|
shapes(ii+j) *= fac;
|
|
|
|
ii += eorder-1;
|
|
}
|
|
}
|
|
|
|
|
|
|
|
break;
|
|
}
|
|
|
|
case HEX:
|
|
{
|
|
shapes = 0.0;
|
|
double x = xi(0);
|
|
double y = xi(1);
|
|
double z = xi(2);
|
|
|
|
shapes[0] = (1-x)*(1-y)*(1-z);
|
|
shapes[1] = x *(1-y)*(1-z);
|
|
shapes[2] = x * y *(1-z);
|
|
shapes[3] = (1-x)* y *(1-z);
|
|
shapes[4] = (1-x)*(1-y)*(z);
|
|
shapes[5] = x *(1-y)*(z);
|
|
shapes[6] = x * y *(z);
|
|
shapes[7] = (1-x)* y *(z);
|
|
break;
|
|
}
|
|
|
|
default:
|
|
throw NgException("CurvedElements::CalcShape 3d, element type not handled");
|
|
|
|
};
|
|
}
|
|
|
|
|
|
void CurvedElements ::
|
|
CalcElementDShapes (ElementInfo & info, const Point<3> & xi, MatrixFixWidth<3> & dshapes) const
|
|
{
|
|
const Element & el = mesh[info.elnr];
|
|
|
|
dshapes.SetSize(info.ndof);
|
|
dshapes = 0.0;
|
|
|
|
|
|
|
|
if (rational && info.order >= 2)
|
|
{
|
|
double w = 1;
|
|
double dw[3] = { 0, 0, 0 };
|
|
|
|
double lami[4] = { xi(0), xi(1), xi(2), 1-xi(0)-xi(1)-xi(2) };
|
|
double dlami[4][3] = { { 1, 0, 0 }, { 0, 1, 0 }, { 0, 0, 1 }, { -1, -1, -1 }};
|
|
double shapes[10];
|
|
|
|
for (int j = 0; j < 4; j++)
|
|
{
|
|
shapes[j] = lami[j] * lami[j];
|
|
dshapes(j,0) = 2 * lami[j] * dlami[j][0];
|
|
dshapes(j,1) = 2 * lami[j] * dlami[j][1];
|
|
dshapes(j,2) = 2 * lami[j] * dlami[j][2];
|
|
}
|
|
|
|
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (TET);
|
|
for (int j = 0; j < 6; j++)
|
|
{
|
|
double wi = edgeweight[info.edgenrs[j]];
|
|
|
|
shapes[j+4] = 2 * wi * lami[edges[j][0]-1] * lami[edges[j][1]-1];
|
|
for (int k = 0; k < 3; k++)
|
|
dshapes(j+4,k) = 2*wi* (lami[edges[j][0]-1] * dlami[edges[j][1]-1][k] +
|
|
lami[edges[j][1]-1] * dlami[edges[j][0]-1][k]);
|
|
|
|
w += (wi-1) * 2 * lami[edges[j][0]-1] * lami[edges[j][1]-1];
|
|
for (int k = 0; k < 3; k++)
|
|
dw[k] += 2*(wi-1) * (lami[edges[j][0]-1] * dlami[edges[j][1]-1][k] +
|
|
lami[edges[j][1]-1] * dlami[edges[j][0]-1][k]);
|
|
}
|
|
// shapes *= 1.0 / w;
|
|
dshapes *= 1.0 / w;
|
|
for (int i = 0; i < 10; i++)
|
|
for (int j = 0; j < 3; j++)
|
|
dshapes(i,j) -= shapes[i] * dw[j] / (w*w);
|
|
return;
|
|
}
|
|
|
|
switch (el.GetType())
|
|
{
|
|
case TET:
|
|
{
|
|
dshapes(0,0) = 1;
|
|
dshapes(1,1) = 1;
|
|
dshapes(2,2) = 1;
|
|
dshapes(3,0) = -1;
|
|
dshapes(3,1) = -1;
|
|
dshapes(3,2) = -1;
|
|
|
|
if (info.order == 1) return;
|
|
|
|
double lami[] = { xi(0), xi(1), xi(2), 1-xi(0)-xi(1)-xi(2) };
|
|
int ii = 4;
|
|
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (TET);
|
|
for (int i = 0; i < 6; i++)
|
|
{
|
|
int eorder = edgeorder[info.edgenrs[i]];
|
|
if (eorder >= 2)
|
|
{
|
|
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
|
|
if (el[vi1] > el[vi2]) swap (vi1, vi2);
|
|
|
|
CalcScaledEdgeShapeDxDt<3> (eorder, lami[vi1]-lami[vi2], lami[vi1]+lami[vi2], &dshapes(ii,0));
|
|
|
|
Mat<2,3> trans;
|
|
for (int j = 0; j < 3; j++)
|
|
{
|
|
trans(0,j) = dshapes(vi1,j)-dshapes(vi2,j);
|
|
trans(1,j) = dshapes(vi1,j)+dshapes(vi2,j);
|
|
}
|
|
|
|
for (int j = 0; j < order-1; j++)
|
|
{
|
|
double ddx = dshapes(ii+j,0);
|
|
double ddt = dshapes(ii+j,1);
|
|
dshapes(ii+j,0) = ddx * trans(0,0) + ddt * trans(1,0);
|
|
dshapes(ii+j,1) = ddx * trans(0,1) + ddt * trans(1,1);
|
|
dshapes(ii+j,2) = ddx * trans(0,2) + ddt * trans(1,2);
|
|
}
|
|
|
|
ii += eorder-1;
|
|
}
|
|
}
|
|
|
|
const ELEMENT_FACE * faces = MeshTopology::GetFaces1 (TET);
|
|
for (int i = 0; i < 4; i++)
|
|
{
|
|
int forder = faceorder[info.facenrs[i]];
|
|
if (forder >= 3)
|
|
{
|
|
int fnums[] = { faces[i][0]-1, faces[i][1]-1, faces[i][2]-1 };
|
|
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
|
|
if (el[fnums[1]] > el[fnums[2]]) swap (fnums[1], fnums[2]);
|
|
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
|
|
|
|
CalcScaledTrigShapeDxDyDt (forder,
|
|
lami[fnums[1]]-lami[fnums[0]],
|
|
lami[fnums[2]], lami[fnums[0]]+lami[fnums[1]]+lami[fnums[2]],
|
|
&dshapes(ii,0));
|
|
|
|
Mat<3,3> trans;
|
|
for (int j = 0; j < 3; j++)
|
|
{
|
|
trans(0,j) = dshapes(fnums[1],j)-dshapes(fnums[0],j);
|
|
trans(1,j) = dshapes(fnums[2],j);
|
|
trans(2,j) = dshapes(fnums[0],j)+dshapes(fnums[1],j)+dshapes(fnums[2],j);
|
|
}
|
|
|
|
int nfd = (forder-1)*(forder-2)/2;
|
|
for (int j = 0; j < nfd; j++)
|
|
{
|
|
double ddx = dshapes(ii+j,0);
|
|
double ddy = dshapes(ii+j,1);
|
|
double ddt = dshapes(ii+j,2);
|
|
dshapes(ii+j,0) = ddx * trans(0,0) + ddy * trans(1,0) + ddt * trans(2,0);
|
|
dshapes(ii+j,1) = ddx * trans(0,1) + ddy * trans(1,1) + ddt * trans(2,1);
|
|
dshapes(ii+j,2) = ddx * trans(0,2) + ddy * trans(1,2) + ddt * trans(2,2);
|
|
}
|
|
|
|
ii += nfd;
|
|
}
|
|
}
|
|
|
|
break;
|
|
}
|
|
|
|
case TET10:
|
|
{
|
|
if (dshapes.Height() == 4)
|
|
{
|
|
dshapes = 0.0;
|
|
|
|
dshapes(0,0) = 1;
|
|
dshapes(1,1) = 1;
|
|
dshapes(2,2) = 1;
|
|
dshapes(3,0) = -1;
|
|
dshapes(3,1) = -1;
|
|
dshapes(3,2) = -1;
|
|
}
|
|
else
|
|
{
|
|
AutoDiff<3> x(xi(0), 0);
|
|
AutoDiff<3> y(xi(1), 1);
|
|
AutoDiff<3> z(xi(2), 2);
|
|
AutoDiff<3> lam4 = 1-x-y-z;
|
|
AutoDiff<3> shapes[10];
|
|
|
|
shapes[0] = 2 * x * x - x;
|
|
shapes[1] = 2 * y * y - y;
|
|
shapes[2] = 2 * z * z - z;
|
|
shapes[3] = 2 * lam4 * lam4 - lam4;
|
|
|
|
shapes[4] = 4 * x * y;
|
|
shapes[5] = 4 * x * z;
|
|
shapes[6] = 4 * x * lam4;
|
|
shapes[7] = 4 * y * z;
|
|
shapes[8] = 4 * y * lam4;
|
|
shapes[9] = 4 * z * lam4;
|
|
|
|
for (int i = 0; i < 10; i++)
|
|
{
|
|
dshapes(i,0) = shapes[i].DValue(0);
|
|
dshapes(i,1) = shapes[i].DValue(1);
|
|
dshapes(i,2) = shapes[i].DValue(2);
|
|
}
|
|
|
|
}
|
|
break;
|
|
|
|
break;
|
|
}
|
|
|
|
|
|
case PRISM:
|
|
{
|
|
double lami[6] = { xi(0), xi(1), 1-xi(0)-xi(1), xi(0), xi(1), 1-xi(0)-xi(1) };
|
|
double lamiz[6] = { 1-xi(2), 1-xi(2), 1-xi(2), xi(2), xi(2), xi(2) };
|
|
double dlamiz[6] = { -1, -1, -1, 1, 1, 1 };
|
|
double dlami[6][2] =
|
|
{ { 1, 0, },
|
|
{ 0, 1, },
|
|
{ -1, -1 },
|
|
{ 1, 0, },
|
|
{ 0, 1, },
|
|
{ -1, -1 } };
|
|
for (int i = 0; i < 6; i++)
|
|
{
|
|
// shapes(i) = lami[i%3] * ( (i < 3) ? (1-xi(2)) : xi(2) );
|
|
dshapes(i,0) = dlami[i%3][0] * ( (i < 3) ? (1-xi(2)) : xi(2) );
|
|
dshapes(i,1) = dlami[i%3][1] * ( (i < 3) ? (1-xi(2)) : xi(2) );
|
|
dshapes(i,2) = lami[i%3] * ( (i < 3) ? -1 : 1 );
|
|
}
|
|
|
|
int ii = 6;
|
|
|
|
if (info.order == 1) return;
|
|
|
|
|
|
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (PRISM);
|
|
for (int i = 0; i < 6; i++) // horizontal edges
|
|
{
|
|
int order = edgeorder[info.edgenrs[i]];
|
|
if (order >= 2)
|
|
{
|
|
int vi1 = (edges[i][0]-1), vi2 = (edges[i][1]-1);
|
|
if (el[vi1] > el[vi2]) swap (vi1, vi2);
|
|
vi1 = vi1 % 3;
|
|
vi2 = vi2 % 3;
|
|
|
|
Vector shapei(order+1);
|
|
CalcScaledEdgeShapeDxDt<3> (order, lami[vi1]-lami[vi2], lami[vi1]+lami[vi2], &dshapes(ii,0) );
|
|
CalcScaledEdgeShape(order, lami[vi1]-lami[vi2], lami[vi1]+lami[vi2], &shapei(0) );
|
|
|
|
Mat<2,2> trans;
|
|
for (int j = 0; j < 2; j++)
|
|
{
|
|
trans(0,j) = dlami[vi1][j]-dlami[vi2][j];
|
|
trans(1,j) = dlami[vi1][j]+dlami[vi2][j];
|
|
}
|
|
|
|
for (int j = 0; j < order-1; j++)
|
|
{
|
|
double ddx = dshapes(ii+j,0);
|
|
double ddt = dshapes(ii+j,1);
|
|
dshapes(ii+j,0) = ddx * trans(0,0) + ddt * trans(1,0);
|
|
dshapes(ii+j,1) = ddx * trans(0,1) + ddt * trans(1,1);
|
|
}
|
|
|
|
|
|
|
|
double facz = (i < 3) ? (1-xi(2)) : xi(2);
|
|
double dfacz = (i < 3) ? (-1) : 1;
|
|
for (int j = 0; j < order-1; j++)
|
|
{
|
|
dshapes(ii+j,0) *= facz;
|
|
dshapes(ii+j,1) *= facz;
|
|
dshapes(ii+j,2) = shapei(j) * dfacz;
|
|
}
|
|
|
|
ii += order-1;
|
|
}
|
|
}
|
|
|
|
for (int i = 6; i < 9; i++) // vertical edges
|
|
{
|
|
int eorder = edgeorder[info.edgenrs[i]];
|
|
if (eorder >= 2)
|
|
{
|
|
int vi1 = (edges[i][0]-1), vi2 = (edges[i][1]-1);
|
|
if (el[vi1] > el[vi2]) swap (vi1, vi2);
|
|
|
|
double bubz = lamiz[vi1] * lamiz[vi2];
|
|
double dbubz = dlamiz[vi1]*lamiz[vi2] + lamiz[vi1]*dlamiz[vi2];
|
|
double polyz = lamiz[vi1] - lamiz[vi2];
|
|
double dpolyz = dlamiz[vi1] - dlamiz[vi2];
|
|
double bubxy = lami[(vi1)%3];
|
|
double dbubxydx = dlami[(vi1)%3][0];
|
|
double dbubxydy = dlami[(vi1)%3][1];
|
|
|
|
for (int j = 0; j < eorder-1; j++)
|
|
{
|
|
dshapes(ii+j,0) = dbubxydx * bubz;
|
|
dshapes(ii+j,1) = dbubxydy * bubz;
|
|
dshapes(ii+j,2) = bubxy * dbubz;
|
|
|
|
dbubz = bubz * dpolyz + dbubz * polyz;
|
|
bubz *= polyz;
|
|
}
|
|
ii += eorder-1;
|
|
}
|
|
}
|
|
|
|
|
|
if (info.order == 2) return;
|
|
// FACE SHAPES
|
|
const ELEMENT_FACE * faces = MeshTopology::GetFaces1 (PRISM);
|
|
for (int i = 0; i < 2; i++)
|
|
{
|
|
int forder = faceorder[info.facenrs[i]];
|
|
|
|
if ( forder < 3 ) continue;
|
|
int ndf = (forder+1)*(forder+2)/2 - 3 - 3*(forder-1);
|
|
|
|
int fav[3] = { faces[i][0]-1, faces[i][1]-1, faces[i][2]-1 };
|
|
if(el[fav[0]] > el[fav[1]]) swap(fav[0],fav[1]);
|
|
if(el[fav[1]] > el[fav[2]]) swap(fav[1],fav[2]);
|
|
if(el[fav[0]] > el[fav[1]]) swap(fav[0],fav[1]);
|
|
|
|
MatrixFixWidth<2> dshapei(ndf);
|
|
Vector shapei(ndf);
|
|
|
|
CalcTrigShapeDxDy (forder,
|
|
lami[fav[2]]-lami[fav[1]], lami[fav[0]],
|
|
&dshapei(0,0));
|
|
CalcTrigShape (forder, lami[fav[2]]-lami[fav[1]], lami[fav[0]],
|
|
&shapei(0));
|
|
|
|
Mat<2,2> trans;
|
|
for (int j = 0; j < 2; j++)
|
|
{
|
|
trans(0,j) = dlami[fav[2]][j]-dlami[fav[1]][j];
|
|
trans(1,j) = dlami[fav[0]][j];
|
|
}
|
|
|
|
for (int j = 0; j < ndf; j++)
|
|
{
|
|
// double ddx = dshapes(ii+j,0);
|
|
// double ddt = dshapes(ii+j,1);
|
|
double ddx = dshapei(j,0);
|
|
double ddt = dshapei(j,1);
|
|
dshapes(ii+j,0) = ddx * trans(0,0) + ddt * trans(1,0);
|
|
dshapes(ii+j,1) = ddx * trans(0,1) + ddt * trans(1,1);
|
|
}
|
|
|
|
for ( int j = 0; j < ndf; j++ )
|
|
{
|
|
dshapes(ii+j,0) *= lamiz[fav[1]];
|
|
dshapes(ii+j,1) *= lamiz[fav[1]];
|
|
dshapes(ii+j,2) = shapei(j) * dlamiz[fav[1]];
|
|
}
|
|
ii += ndf;
|
|
}
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
case PYRAMID:
|
|
{
|
|
dshapes = 0.0;
|
|
double x = xi(0);
|
|
double y = xi(1);
|
|
double z = xi(2);
|
|
|
|
if (z == 1.) z = 1-1e-10;
|
|
double z1 = 1-z;
|
|
double z2 = z1*z1;
|
|
|
|
dshapes(0,0) = -(z1-y)/z1;
|
|
dshapes(0,1) = -(z1-x)/z1;
|
|
dshapes(0,2) = ((x+y+2*z-2)*z1+(z1-y)*(z1-x))/z2;
|
|
|
|
dshapes(1,0) = (z1-y)/z1;
|
|
dshapes(1,1) = -x/z1;
|
|
dshapes(1,2) = (-x*z1+x*(z1-y))/z2;
|
|
|
|
dshapes(2,0) = y/z1;
|
|
dshapes(2,1) = x/z1;
|
|
dshapes(2,2) = x*y/z2;
|
|
|
|
dshapes(3,0) = -y/z1;
|
|
dshapes(3,1) = (z1-x)/z1;
|
|
dshapes(3,2) = (-y*z1+y*(z1-x))/z2;
|
|
|
|
dshapes(4,0) = 0;
|
|
dshapes(4,1) = 0;
|
|
dshapes(4,2) = 1;
|
|
/* old:
|
|
vdshape[0] = Vec<3>( -(z1-y)/z1, -(z1-x)/z1, ((x+y+2*z-2)*z1+(z1-y)*(z1-x))/z2 );
|
|
vdshape[1] = Vec<3>( (z1-y)/z1, -x/z1, (-x*z1+x*(z1-y))/z2 );
|
|
vdshape[2] = Vec<3>( y/z1, x/z1, x*y/z2 );
|
|
vdshape[3] = Vec<3>( -y/z1, (z1-x)/z1, (-y*z1+y*(z1-x))/z2 );
|
|
vdshape[4] = Vec<3>( 0, 0, 1 );
|
|
*/
|
|
break;
|
|
}
|
|
|
|
case HEX:
|
|
{
|
|
dshapes = 0.0;
|
|
|
|
double x = xi(0);
|
|
double y = xi(1);
|
|
double z = xi(2);
|
|
|
|
// shapes[0] = (1-x)*(1-y)*(1-z);
|
|
dshapes(0,0) = - (1-y)*(1-z);
|
|
dshapes(0,1) = (1-x) * (-1) * (1-z);
|
|
dshapes(0,2) = (1-x) * (1-y) * (-1);
|
|
|
|
// shapes[1] = x *(1-y)*(1-z);
|
|
dshapes(1,0) = (1-y)*(1-z);
|
|
dshapes(1,1) = -x * (1-z);
|
|
dshapes(1,2) = -x * (1-y);
|
|
|
|
// shapes[2] = x * y *(1-z);
|
|
dshapes(2,0) = y * (1-z);
|
|
dshapes(2,1) = x * (1-z);
|
|
dshapes(2,2) = -x * y;
|
|
|
|
// shapes[3] = (1-x)* y *(1-z);
|
|
dshapes(3,0) = -y * (1-z);
|
|
dshapes(3,1) = (1-x) * (1-z);
|
|
dshapes(3,2) = -(1-x) * y;
|
|
|
|
// shapes[4] = (1-x)*(1-y)*z;
|
|
dshapes(4,0) = - (1-y)*z;
|
|
dshapes(4,1) = (1-x) * (-1) * z;
|
|
dshapes(4,2) = (1-x) * (1-y) * 1;
|
|
|
|
// shapes[5] = x *(1-y)*z;
|
|
dshapes(5,0) = (1-y)*z;
|
|
dshapes(5,1) = -x * z;
|
|
dshapes(5,2) = x * (1-y);
|
|
|
|
// shapes[6] = x * y *z;
|
|
dshapes(6,0) = y * z;
|
|
dshapes(6,1) = x * z;
|
|
dshapes(6,2) = x * y;
|
|
|
|
// shapes[7] = (1-x)* y *z;
|
|
dshapes(7,0) = -y * z;
|
|
dshapes(7,1) = (1-x) * z;
|
|
dshapes(7,2) = (1-x) * y;
|
|
|
|
break;
|
|
}
|
|
|
|
default:
|
|
throw NgException("CurvedElements::CalcDShape 3d, element type not handled");
|
|
}
|
|
|
|
/*
|
|
DenseMatrix dshapes2 (info.ndof, 3);
|
|
Vector shapesl(info.ndof);
|
|
Vector shapesr(info.ndof);
|
|
|
|
double eps = 1e-6;
|
|
for (int i = 0; i < 3; i++)
|
|
{
|
|
Point<3> xl = xi;
|
|
Point<3> xr = xi;
|
|
|
|
xl(i) -= eps;
|
|
xr(i) += eps;
|
|
CalcElementShapes (info, xl, shapesl);
|
|
CalcElementShapes (info, xr, shapesr);
|
|
|
|
for (int j = 0; j < info.ndof; j++)
|
|
dshapes2(j,i) = (shapesr(j)-shapesl(j)) / (2*eps);
|
|
}
|
|
(*testout) << "dshapes = " << endl << dshapes << endl;
|
|
(*testout) << "dshapes2 = " << endl << dshapes2 << endl;
|
|
dshapes2 -= dshapes;
|
|
(*testout) << "diff = " << endl << dshapes2 << endl;
|
|
*/
|
|
}
|
|
|
|
|
|
|
|
void CurvedElements ::
|
|
GetCoefficients (ElementInfo & info, Vec<3> * coefs) const
|
|
{
|
|
const Element & el = mesh[info.elnr];
|
|
|
|
for (int i = 0; i < info.nv; i++)
|
|
coefs[i] = Vec<3> (mesh[el[i]]);
|
|
|
|
if (info.order == 1) return;
|
|
|
|
int ii = info.nv;
|
|
|
|
for (int i = 0; i < info.nedges; i++)
|
|
{
|
|
int first = edgecoeffsindex[info.edgenrs[i]];
|
|
int next = edgecoeffsindex[info.edgenrs[i]+1];
|
|
for (int j = first; j < next; j++, ii++)
|
|
coefs[ii] = edgecoeffs[j];
|
|
}
|
|
for (int i = 0; i < info.nfaces; i++)
|
|
{
|
|
int first = facecoeffsindex[info.facenrs[i]];
|
|
int next = facecoeffsindex[info.facenrs[i]+1];
|
|
for (int j = first; j < next; j++, ii++)
|
|
coefs[ii] = facecoeffs[j];
|
|
}
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
void CurvedElements ::
|
|
CalcMultiPointSegmentTransformation (Array<double> * xi, SegmentIndex segnr,
|
|
Array<Point<3> > * x,
|
|
Array<Vec<3> > * dxdxi)
|
|
{
|
|
;
|
|
}
|
|
|
|
|
|
template <int DIM_SPACE>
|
|
void CurvedElements ::
|
|
CalcMultiPointSegmentTransformation (SegmentIndex elnr, int n,
|
|
const double * xi, size_t sxi,
|
|
double * x, size_t sx,
|
|
double * dxdxi, size_t sdxdxi)
|
|
{
|
|
for (int ip = 0; ip < n; ip++)
|
|
{
|
|
Point<3> xg;
|
|
Vec<3> dx;
|
|
|
|
// mesh->GetCurvedElements().
|
|
CalcSegmentTransformation (xi[ip*sxi], elnr, xg, dx);
|
|
|
|
if (x)
|
|
for (int i = 0; i < DIM_SPACE; i++)
|
|
x[ip*sx+i] = xg(i);
|
|
|
|
if (dxdxi)
|
|
for (int i=0; i<DIM_SPACE; i++)
|
|
dxdxi[ip*sdxdxi+i] = dx(i);
|
|
}
|
|
}
|
|
|
|
template void CurvedElements ::
|
|
CalcMultiPointSegmentTransformation<2> (SegmentIndex elnr, int npts,
|
|
const double * xi, size_t sxi,
|
|
double * x, size_t sx,
|
|
double * dxdxi, size_t sdxdxi);
|
|
|
|
template void CurvedElements ::
|
|
CalcMultiPointSegmentTransformation<3> (SegmentIndex elnr, int npts,
|
|
const double * xi, size_t sxi,
|
|
double * x, size_t sx,
|
|
double * dxdxi, size_t sdxdxi);
|
|
|
|
|
|
|
|
void CurvedElements ::
|
|
CalcMultiPointSurfaceTransformation (Array< Point<2> > * xi, SurfaceElementIndex elnr,
|
|
Array< Point<3> > * x,
|
|
Array< Mat<3,2> > * dxdxi)
|
|
{
|
|
double * px = (x) ? &(*x)[0](0) : NULL;
|
|
double * pdxdxi = (dxdxi) ? &(*dxdxi)[0](0) : NULL;
|
|
|
|
CalcMultiPointSurfaceTransformation <3> (elnr, xi->Size(),
|
|
&(*xi)[0](0), 2,
|
|
px, 3,
|
|
pdxdxi, 6);
|
|
}
|
|
|
|
|
|
|
|
|
|
template <int DIM_SPACE>
|
|
void CurvedElements ::
|
|
CalcMultiPointSurfaceTransformation (SurfaceElementIndex elnr, int npts,
|
|
const double * xi, size_t sxi,
|
|
double * x, size_t sx,
|
|
double * dxdxi, size_t sdxdxi)
|
|
{
|
|
if (mesh.coarsemesh)
|
|
{
|
|
const HPRefElement & hpref_el =
|
|
(*mesh.hpelements) [mesh[elnr].hp_elnr];
|
|
|
|
// xi umrechnen
|
|
double lami[4];
|
|
FlatVector vlami(4, lami);
|
|
|
|
ArrayMem<Point<2>, 50> coarse_xi (npts);
|
|
|
|
for (int pi = 0; pi < npts; pi++)
|
|
{
|
|
vlami = 0;
|
|
Point<2> hxi(xi[pi*sxi], xi[pi*sxi+1]);
|
|
mesh[elnr].GetShapeNew ( hxi, vlami);
|
|
|
|
Point<2> cxi(0,0);
|
|
for (int i = 0; i < hpref_el.np; i++)
|
|
for (int j = 0; j < 2; j++)
|
|
cxi(j) += hpref_el.param[i][j] * lami[i];
|
|
|
|
coarse_xi[pi] = cxi;
|
|
}
|
|
|
|
mesh.coarsemesh->GetCurvedElements().
|
|
CalcMultiPointSurfaceTransformation<DIM_SPACE> (hpref_el.coarse_elnr, npts,
|
|
&coarse_xi[0](0), &coarse_xi[1](0)-&coarse_xi[0](0),
|
|
x, sx, dxdxi, sdxdxi);
|
|
|
|
// Mat<3,2> dxdxic;
|
|
if (dxdxi)
|
|
{
|
|
MatrixFixWidth<2> dlami(4);
|
|
dlami = 0;
|
|
|
|
for (int pi = 0; pi < npts; pi++)
|
|
{
|
|
Point<2> hxi(xi[pi*sxi], xi[pi*sxi+1]);
|
|
mesh[elnr].GetDShapeNew ( hxi, dlami);
|
|
|
|
Mat<2,2> trans;
|
|
trans = 0;
|
|
for (int k = 0; k < 2; k++)
|
|
for (int l = 0; l < 2; l++)
|
|
for (int i = 0; i < hpref_el.np; i++)
|
|
trans(l,k) += hpref_el.param[i][l] * dlami(i, k);
|
|
|
|
Mat<DIM_SPACE,2> hdxdxic, hdxdxi;
|
|
for (int k = 0; k < 2*DIM_SPACE; k++)
|
|
hdxdxic(k) = dxdxi[pi*sdxdxi+k];
|
|
|
|
hdxdxi = hdxdxic * trans;
|
|
|
|
for (int k = 0; k < 2*DIM_SPACE; k++)
|
|
dxdxi[pi*sdxdxi+k] = hdxdxi(k);
|
|
|
|
// dxdxic = (*dxdxi)[pi];
|
|
// (*dxdxi)[pi] = dxdxic * trans;
|
|
}
|
|
}
|
|
|
|
return;
|
|
}
|
|
|
|
Vector shapes;
|
|
MatrixFixWidth<2> dshapes;
|
|
Array<Vec<DIM_SPACE> > coefs;
|
|
|
|
|
|
const Element2d & el = mesh[elnr];
|
|
ELEMENT_TYPE type = el.GetType();
|
|
|
|
SurfaceElementInfo info;
|
|
info.elnr = elnr;
|
|
info.order = order;
|
|
switch (type)
|
|
{
|
|
case TRIG : info.nv = 3; break;
|
|
case QUAD : info.nv = 4; break;
|
|
case TRIG6: info.nv = 6; break;
|
|
default:
|
|
cerr << "undef element in CalcMultPointSurfaceTrao" << endl;
|
|
}
|
|
info.ndof = info.nv;
|
|
|
|
// if (info.order > 1)
|
|
// {
|
|
// const MeshTopology & top = mesh.GetTopology();
|
|
|
|
// top.GetSurfaceElementEdges (elnr+1, info.edgenrs);
|
|
// for (int i = 0; i < info.edgenrs.Size(); i++)
|
|
// info.edgenrs[i]--;
|
|
// info.facenr = top.GetSurfaceElementFace (elnr+1)-1;
|
|
|
|
// for (int i = 0; i < info.edgenrs.Size(); i++)
|
|
// info.ndof += edgecoeffsindex[info.edgenrs[i]+1] - edgecoeffsindex[info.edgenrs[i]];
|
|
// info.ndof += facecoeffsindex[info.facenr+1] - facecoeffsindex[info.facenr];
|
|
// }
|
|
|
|
// Michael Woopen: THESE FOLLOWING LINES ARE COPIED FROM CurvedElements::CalcSurfaceTransformation
|
|
|
|
if (info.order > 1)
|
|
{
|
|
const MeshTopology & top = mesh.GetTopology();
|
|
|
|
top.GetSurfaceElementEdges (elnr+1, info.edgenrs);
|
|
for (int i = 0; i < info.edgenrs.Size(); i++)
|
|
info.edgenrs[i]--;
|
|
info.facenr = top.GetSurfaceElementFace (elnr+1)-1;
|
|
|
|
|
|
bool firsttry = true;
|
|
bool problem = false;
|
|
|
|
while(firsttry || problem)
|
|
{
|
|
problem = false;
|
|
|
|
for (int i = 0; !problem && i < info.edgenrs.Size(); i++)
|
|
{
|
|
if(info.edgenrs[i]+1 >= edgecoeffsindex.Size())
|
|
problem = true;
|
|
else
|
|
info.ndof += edgecoeffsindex[info.edgenrs[i]+1] - edgecoeffsindex[info.edgenrs[i]];
|
|
}
|
|
if(info.facenr+1 >= facecoeffsindex.Size())
|
|
problem = true;
|
|
else
|
|
info.ndof += facecoeffsindex[info.facenr+1] - facecoeffsindex[info.facenr];
|
|
|
|
if(problem && !firsttry)
|
|
throw NgException("something wrong with curved elements");
|
|
|
|
if(problem)
|
|
BuildCurvedElements(NULL,order,rational);
|
|
|
|
firsttry = false;
|
|
}
|
|
}
|
|
|
|
// THESE LAST LINES ARE COPIED FROM CurvedElements::CalcSurfaceTransformation
|
|
|
|
GetCoefficients (info, coefs);
|
|
|
|
if (x)
|
|
{
|
|
if (info.order == 1 && type == TRIG)
|
|
{
|
|
for (int j = 0; j < npts; j++)
|
|
{
|
|
Point<2> vxi(xi[j*sxi], xi[j*sxi+1]);
|
|
|
|
Point<DIM_SPACE> val (coefs[2]);
|
|
val += vxi(0) * (coefs[0]-coefs[2]);
|
|
val += vxi(1) * (coefs[1]-coefs[2]);
|
|
|
|
for (int k = 0; k < DIM_SPACE; k++)
|
|
x[j*sx+k] = val(k);
|
|
}
|
|
}
|
|
else
|
|
for (int j = 0; j < npts; j++)
|
|
{
|
|
Point<2> vxi(xi[j*sxi], xi[j*sxi+1]);
|
|
CalcElementShapes (info, vxi, shapes);
|
|
|
|
Point<DIM_SPACE> val = 0.0;
|
|
for (int i = 0; i < coefs.Size(); i++)
|
|
val += shapes(i) * coefs[i];
|
|
|
|
for (int k = 0; k < DIM_SPACE; k++)
|
|
x[j*sx+k] = val(k);
|
|
}
|
|
}
|
|
|
|
if (dxdxi)
|
|
{
|
|
if (info.order == 1 && type == TRIG)
|
|
{
|
|
Point<2> xij(xi[0], xi[1]);
|
|
CalcElementDShapes (info, xij, dshapes);
|
|
|
|
Mat<3,2> dxdxij;
|
|
dxdxij = 0.0;
|
|
for (int i = 0; i < coefs.Size(); i++)
|
|
for (int j = 0; j < DIM_SPACE; j++)
|
|
for (int k = 0; k < 2; k++)
|
|
dxdxij(j,k) += dshapes(i,k) * coefs[i](j);
|
|
|
|
|
|
for (int ip = 0; ip < npts; ip++)
|
|
for (int j = 0; j < DIM_SPACE; j++)
|
|
for (int k = 0; k < 2; k++)
|
|
dxdxi[ip*sdxdxi+2*j+k] = dxdxij(j,k);
|
|
}
|
|
else
|
|
{
|
|
for (int j = 0; j < npts; j++)
|
|
{
|
|
Point<2> vxi(xi[j*sxi], xi[j*sxi+1]);
|
|
CalcElementDShapes (info, vxi, dshapes);
|
|
|
|
Mat<DIM_SPACE,2> ds;
|
|
ds = 0.0;
|
|
for (int i = 0; i < coefs.Size(); i++)
|
|
for (int j = 0; j < DIM_SPACE; j++)
|
|
for (int k = 0; k < 2; k++)
|
|
ds(j,k) += dshapes(i,k) * coefs[i](j);
|
|
// (*dxdxi)[ip] = ds;
|
|
|
|
for (int k = 0; k < 2*DIM_SPACE; k++)
|
|
dxdxi[j*sdxdxi+k] = ds(k);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
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template void CurvedElements ::
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CalcMultiPointSurfaceTransformation<2> (SurfaceElementIndex elnr, int npts,
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const double * xi, size_t sxi,
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double * x, size_t sx,
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double * dxdxi, size_t sdxdxi);
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template void CurvedElements ::
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CalcMultiPointSurfaceTransformation<3> (SurfaceElementIndex elnr, int npts,
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const double * xi, size_t sxi,
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double * x, size_t sx,
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double * dxdxi, size_t sdxdxi);
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void CurvedElements ::
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CalcMultiPointElementTransformation (Array< Point<3> > * xi, ElementIndex elnr,
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Array< Point<3> > * x,
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Array< Mat<3,3> > * dxdxi)
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{
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double * px = (x) ? &(*x)[0](0) : NULL;
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double * pdxdxi = (dxdxi) ? &(*dxdxi)[0](0) : NULL;
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CalcMultiPointElementTransformation (elnr, xi->Size(),
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&(*xi)[0](0), 3,
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px, 3,
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pdxdxi, 9);
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return;
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#ifdef OLD
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if (mesh.coarsemesh)
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{
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const HPRefElement & hpref_el =
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(*mesh.hpelements) [mesh[elnr].hp_elnr];
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// xi umrechnen
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double lami[8];
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FlatVector vlami(8, lami);
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ArrayMem<Point<3>, 50> coarse_xi (xi->Size());
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for (int pi = 0; pi < xi->Size(); pi++)
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{
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vlami = 0;
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mesh[elnr].GetShapeNew ( (*xi)[pi], vlami);
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Point<3> cxi(0,0,0);
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for (int i = 0; i < hpref_el.np; i++)
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for (int j = 0; j < 3; j++)
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cxi(j) += hpref_el.param[i][j] * lami[i];
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coarse_xi[pi] = cxi;
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}
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mesh.coarsemesh->GetCurvedElements().
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CalcMultiPointElementTransformation (&coarse_xi, hpref_el.coarse_elnr, x, dxdxi);
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Mat<3,3> trans, dxdxic;
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if (dxdxi)
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{
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MatrixFixWidth<3> dlami(8);
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dlami = 0;
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for (int pi = 0; pi < xi->Size(); pi++)
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{
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mesh[elnr].GetDShapeNew ( (*xi)[pi], dlami);
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trans = 0;
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for (int k = 0; k < 3; k++)
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for (int l = 0; l < 3; l++)
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for (int i = 0; i < hpref_el.np; i++)
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trans(l,k) += hpref_el.param[i][l] * dlami(i, k);
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dxdxic = (*dxdxi)[pi];
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(*dxdxi)[pi] = dxdxic * trans;
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}
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}
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return;
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}
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Vector shapes;
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MatrixFixWidth<3> dshapes;
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const Element & el = mesh[elnr];
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ELEMENT_TYPE type = el.GetType();
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ElementInfo info;
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info.elnr = elnr;
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info.order = order;
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info.ndof = info.nv = MeshTopology::GetNPoints (type);
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if (info.order > 1)
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{
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const MeshTopology & top = mesh.GetTopology();
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info.nedges = top.GetElementEdges (elnr+1, info.edgenrs, 0);
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for (int i = 0; i < info.nedges; i++)
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info.edgenrs[i]--;
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info.nfaces = top.GetElementFaces (elnr+1, info.facenrs, 0);
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for (int i = 0; i < info.nfaces; i++)
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info.facenrs[i]--;
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for (int i = 0; i < info.nedges; i++)
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info.ndof += edgecoeffsindex[info.edgenrs[i]+1] - edgecoeffsindex[info.edgenrs[i]];
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for (int i = 0; i < info.nfaces; i++)
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info.ndof += facecoeffsindex[info.facenrs[i]+1] - facecoeffsindex[info.facenrs[i]];
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// info.ndof += facecoeffsindex[info.facenr+1] - facecoeffsindex[info.facenr];
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}
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Array<Vec<3> > coefs(info.ndof);
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GetCoefficients (info, &coefs[0]);
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if (x)
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{
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for (int j = 0; j < xi->Size(); j++)
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{
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CalcElementShapes (info, (*xi)[j], shapes);
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(*x)[j] = 0;
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for (int i = 0; i < coefs.Size(); i++)
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(*x)[j] += shapes(i) * coefs[i];
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}
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}
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if (dxdxi)
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{
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if (info.order == 1 && type == TET)
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{
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if (xi->Size() > 0)
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{
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CalcElementDShapes (info, (*xi)[0], dshapes);
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Mat<3,3> ds;
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ds = 0;
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for (int i = 0; i < coefs.Size(); i++)
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for (int j = 0; j < 3; j++)
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for (int k = 0; k < 3; k++)
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ds(j,k) += dshapes(i,k) * coefs[i](j);
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for (int ip = 0; ip < xi->Size(); ip++)
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(*dxdxi)[ip] = ds;
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}
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}
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else
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for (int ip = 0; ip < xi->Size(); ip++)
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{
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CalcElementDShapes (info, (*xi)[ip], dshapes);
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Mat<3,3> ds;
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ds = 0;
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for (int i = 0; i < coefs.Size(); i++)
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for (int j = 0; j < 3; j++)
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for (int k = 0; k < 3; k++)
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ds(j,k) += dshapes(i,k) * coefs[i](j);
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(*dxdxi)[ip] = ds;
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}
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}
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#endif
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}
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void CurvedElements ::
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CalcMultiPointElementTransformation (ElementIndex elnr, int n,
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const double * xi, size_t sxi,
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double * x, size_t sx,
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double * dxdxi, size_t sdxdxi)
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{
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if (mesh.coarsemesh)
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{
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const HPRefElement & hpref_el =
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(*mesh.hpelements) [mesh[elnr].hp_elnr];
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// xi umrechnen
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double lami[8];
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FlatVector vlami(8, lami);
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ArrayMem<double, 100> coarse_xi (3*n);
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for (int pi = 0; pi < n; pi++)
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{
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vlami = 0;
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Point<3> pxi;
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for (int j = 0; j < 3; j++)
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pxi(j) = xi[pi*sxi+j];
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mesh[elnr].GetShapeNew ( pxi, vlami);
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Point<3> cxi(0,0,0);
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for (int i = 0; i < hpref_el.np; i++)
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for (int j = 0; j < 3; j++)
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cxi(j) += hpref_el.param[i][j] * lami[i];
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for (int j = 0; j < 3; j++)
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coarse_xi[3*pi+j] = cxi(j);
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}
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mesh.coarsemesh->GetCurvedElements().
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CalcMultiPointElementTransformation (hpref_el.coarse_elnr, n,
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&coarse_xi[0], 3,
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x, sx,
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dxdxi, sdxdxi);
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Mat<3,3> trans, dxdxic;
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if (dxdxi)
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{
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MatrixFixWidth<3> dlami(8);
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dlami = 0;
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for (int pi = 0; pi < n; pi++)
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{
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Point<3> pxi;
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for (int j = 0; j < 3; j++)
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pxi(j) = xi[pi*sxi+j];
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mesh[elnr].GetDShapeNew (pxi, dlami);
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trans = 0;
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for (int k = 0; k < 3; k++)
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for (int l = 0; l < 3; l++)
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for (int i = 0; i < hpref_el.np; i++)
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trans(l,k) += hpref_el.param[i][l] * dlami(i, k);
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Mat<3> mat_dxdxic, mat_dxdxi;
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for (int j = 0; j < 3; j++)
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for (int k = 0; k < 3; k++)
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mat_dxdxic(j,k) = dxdxi[pi*sdxdxi+3*j+k];
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mat_dxdxi = mat_dxdxic * trans;
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for (int j = 0; j < 3; j++)
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for (int k = 0; k < 3; k++)
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dxdxi[pi*sdxdxi+3*j+k] = mat_dxdxi(j,k);
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// dxdxic = (*dxdxi)[pi];
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// (*dxdxi)[pi] = dxdxic * trans;
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}
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}
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return;
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}
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Vector shapes;
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MatrixFixWidth<3> dshapes;
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const Element & el = mesh[elnr];
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ELEMENT_TYPE type = el.GetType();
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ElementInfo info;
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info.elnr = elnr;
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info.order = order;
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info.ndof = info.nv = MeshTopology::GetNPoints (type);
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if (info.order > 1)
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{
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const MeshTopology & top = mesh.GetTopology();
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info.nedges = top.GetElementEdges (elnr+1, info.edgenrs, 0);
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for (int i = 0; i < info.nedges; i++)
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info.edgenrs[i]--;
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info.nfaces = top.GetElementFaces (elnr+1, info.facenrs, 0);
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for (int i = 0; i < info.nfaces; i++)
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info.facenrs[i]--;
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for (int i = 0; i < info.nedges; i++)
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info.ndof += edgecoeffsindex[info.edgenrs[i]+1] - edgecoeffsindex[info.edgenrs[i]];
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for (int i = 0; i < info.nfaces; i++)
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info.ndof += facecoeffsindex[info.facenrs[i]+1] - facecoeffsindex[info.facenrs[i]];
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// info.ndof += facecoeffsindex[info.facenr+1] - facecoeffsindex[info.facenr];
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}
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Array<Vec<3> > coefs(info.ndof);
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GetCoefficients (info, &coefs[0]);
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if (x)
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{
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for (int j = 0; j < n; j++)
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{
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Point<3> xij, xj;
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for (int k = 0; k < 3; k++)
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xij(k) = xi[j*sxi+k];
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CalcElementShapes (info, xij, shapes);
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xj = 0;
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for (int i = 0; i < coefs.Size(); i++)
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xj += shapes(i) * coefs[i];
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for (int k = 0; k < 3; k++)
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x[j*sx+k] = xj(k);
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}
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}
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if (dxdxi)
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{
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if (info.order == 1 && type == TET)
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{
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if (n > 0)
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{
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Point<3> xij;
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for (int k = 0; k < 3; k++)
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xij(k) = xi[k];
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CalcElementDShapes (info, xij, dshapes);
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Mat<3> dxdxij;
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dxdxij = 0.0;
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for (int i = 0; i < coefs.Size(); i++)
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for (int j = 0; j < 3; j++)
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for (int k = 0; k < 3; k++)
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dxdxij(j,k) += dshapes(i,k) * coefs[i](j);
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for (int ip = 0; ip < n; ip++)
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for (int j = 0; j < 3; j++)
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for (int k = 0; k < 3; k++)
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dxdxi[ip*sdxdxi+3*j+k] = dxdxij(j,k);
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}
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}
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else
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{
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for (int ip = 0; ip < n; ip++)
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{
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Point<3> xij;
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for (int k = 0; k < 3; k++)
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xij(k) = xi[ip*sxi+k];
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CalcElementDShapes (info, xij, dshapes);
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Mat<3> dxdxij;
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dxdxij = 0.0;
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for (int i = 0; i < coefs.Size(); i++)
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for (int j = 0; j < 3; j++)
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for (int k = 0; k < 3; k++)
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dxdxij(j,k) += dshapes(i,k) * coefs[i](j);
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for (int j = 0; j < 3; j++)
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for (int k = 0; k < 3; k++)
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dxdxi[ip*sdxdxi+3*j+k] = dxdxij(j,k);
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}
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}
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}
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}
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};
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