mirror of
https://github.com/NGSolve/netgen.git
synced 2024-12-25 21:40:33 +05:00
evaluate curved element mapping without storing shape functions
This commit is contained in:
Joachim Schöberl
parent
d0abcd4778
commit
ffb5a8c8da
@ -348,8 +348,8 @@ namespace netgen
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template <int D>
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inline ostream & operator<< (ostream & ost, const Vec<D> & a)
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template <int D, typename T>
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inline ostream & operator<< (ostream & ost, const Vec<D,T> & a)
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{
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ost << "(";
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for (int i = 0; i < D-1; i++)
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@ -358,8 +358,8 @@ namespace netgen
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return ost;
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}
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template <int D>
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inline ostream & operator<< (ostream & ost, const Point<D> & a)
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template <int D, typename T>
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inline ostream & operator<< (ostream & ost, const Point<D,T> & a)
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{
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ost << "(";
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for (int i = 0; i < D-1; i++)
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@ -375,8 +375,8 @@ namespace netgen
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return ost;
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}
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template <int H, int W>
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inline ostream & operator<< (ostream & ost, const Mat<H,W> & m)
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template <int H, int W, typename T>
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inline ostream & operator<< (ostream & ost, const Mat<H,W,T> & m)
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{
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ost << "(";
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for (int i = 0; i < H; i++)
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@ -650,7 +650,6 @@ namespace netgen
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reinterpret_cast<const SIMD<double>*> (xi), sxi,
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reinterpret_cast<SIMD<double>*> (x), sx,
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reinterpret_cast<SIMD<double>*> (dxdxi), sdxdxi);
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/*
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for (int i = 0; i < npts; i++)
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{
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@ -59,7 +59,19 @@ namespace netgen
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shape[j-2] = p1;
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}
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}
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template <typename T, typename FUNC>
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static void CalcEdgeShapeLambda (int n, T x, FUNC func)
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{
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T p1(x), p2(-1.0), p3(0.0);
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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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func(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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@ -122,7 +134,35 @@ namespace netgen
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shape[j] = p1;
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}
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}
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template <typename T, typename FUNC>
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static void CalcScaledEdgeShapeLambda (int n, T x, T t, FUNC func)
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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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T p1(x), p2(-1.0), p3(0.0);
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T 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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func(j, p1);
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}
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}
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template <int DIST, typename T>
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static void CalcScaledEdgeShapeDxDt (int n, T x, T t, T * dshape)
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{
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@ -346,26 +386,12 @@ namespace netgen
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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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{
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// cout << "calc trig shape" << endl;
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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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/*
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cout << "scaled jacobi, old: " << endl;
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for (int i = 0; i <= n-3; i++)
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cout << i << ": " << hx[i] << endl;
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*/
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jacpols2[2] -> EvaluateScaled (n-3, x, 1-y, hx);
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/*
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cout << "scaled jacobi, new: " << endl;
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for (int i = 0; i <= n-3; i++)
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cout << i << ": " << hx[i] << endl;
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*/
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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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@ -376,9 +402,15 @@ namespace netgen
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for (int ix = 0; ix <= n-3; ix++)
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hx[ix] *= bub;
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/*
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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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// change loops:
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for (int ix = 0; ix <= n-3; ix++)
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for (int iy = 0; iy <= n-3-ix; iy++)
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shape[ii++] = hx[ix]*hy[iy+50*ix];
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}
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template <typename T>
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@ -405,28 +437,43 @@ namespace netgen
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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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Tx hx[50], hy[50];
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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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jacpols2[2*ix+5] -> EvaluateScaled (n-3, 2*y-1, t, hy+50*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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for (int ix = 0; ix <= n-3; ix++)
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{
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jacpols2[2*ix+5] -> EvaluateScaled (n-3, 2*y-1, t, hy);
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for (int iy = 0; iy <= n-3-ix; iy++)
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shape[ii++] = bub * hx[ix]*hy[iy];
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}
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}
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template <class Tx, class Ty, class Tt, typename FUNC>
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static void CalcScaledTrigShapeLambda (int n, Tx x, Ty y, Tt t, FUNC func)
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{
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if (n < 3) return;
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Tx hx[50], hy[50];
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ScaledJacobiPolynomial (n-3, x, t-y, 2, 2, hx);
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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 ix = 0; ix <= n-3; ix++)
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{
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jacpols2[2*ix+5] -> EvaluateScaled (n-3, 2*y-1, t, hy);
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for (int iy = 0; iy <= n-3-ix; iy++)
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func(ii++, bub * hx[ix]*hy[iy]);
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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 <typename T>
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static void CalcScaledTrigShapeDxDyDt (int n, T x, T y, T t, T * dshape)
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{
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/*
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if (n < 3) return;
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AutoDiff<3,T> adx(x, 0);
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AutoDiff<3,T> ady(y, 1);
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@ -440,6 +487,18 @@ namespace netgen
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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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if (n < 3) return;
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AutoDiff<3,T> adx(x, 0);
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AutoDiff<3,T> ady(y, 1);
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AutoDiff<3,T> adt(t, 2);
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CalcScaledTrigShapeLambda (n, adx, ady, adt,
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[&] (int i, AutoDiff<3,T> shape)
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{
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dshape[3*i] = shape.DValue(0);
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dshape[3*i+1] = shape.DValue(1);
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dshape[3*i+2] = shape.DValue(2);
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});
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}
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@ -2701,10 +2760,20 @@ namespace netgen
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return;
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}
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/*
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if (typeid(T) == typeid(SIMD<double>))
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{
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if (el.GetType() == HEX)
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dshapes = T(0.0);
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return;
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}
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*/
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switch (el.GetType())
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{
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case TET:
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{
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// if (typeid(T) == typeid(SIMD<double>)) return;
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dshapes = T(0.0);
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dshapes(0,0) = 1;
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@ -2793,6 +2862,8 @@ namespace netgen
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case TET10:
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{
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// if (typeid(T) == typeid(SIMD<double>)) return;
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if (dshapes.Height() == 4)
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{
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dshapes = T(0.0);
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@ -2862,7 +2933,7 @@ namespace netgen
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if (info.order == 1) return;
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const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (PRISM);
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for (int i = 0; i < 6; i++) // horizontal edges
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{
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@ -2909,6 +2980,9 @@ namespace netgen
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}
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}
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if (typeid(T) == typeid(SIMD<double>)) return;
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for (int i = 6; i < 9; i++) // vertical edges
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{
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int eorder = edgeorder[info.edgenrs[i]];
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@ -2954,8 +3028,8 @@ namespace netgen
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if(el[fav[1]] > el[fav[2]]) swap(fav[1],fav[2]);
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if(el[fav[0]] > el[fav[1]]) swap(fav[0],fav[1]);
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ArrayMem<T,2*100> dshapei_mem(ndf);
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ArrayMem<T,100> shapei_mem(ndf);
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ArrayMem<T,2*20> dshapei_mem(ndf);
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ArrayMem<T,20> shapei_mem(ndf);
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MatrixFixWidth<2,T> dshapei(ndf, &dshapei_mem[0]);
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TFlatVector<T> shapei(ndf, &shapei_mem[0]);
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@ -2997,6 +3071,8 @@ namespace netgen
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case PYRAMID:
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{
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if (typeid(T) == typeid(SIMD<double>)) return;
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dshapes = T(0.0);
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T x = xi(0);
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T y = xi(1);
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@ -3092,6 +3168,8 @@ namespace netgen
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case HEX:
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{
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// if (typeid(T) == typeid(SIMD<double>)) return;
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// NgProfiler::StartTimer(timer);
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T x = xi(0);
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T y = xi(1);
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@ -3261,7 +3339,165 @@ namespace netgen
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}
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template <typename T>
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bool CurvedElements ::
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EvaluateMapping (ElementInfo & info, Point<3,T> xi, Point<3,T> & mx, Mat<3,3,T> & jac) const
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{
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const Element & el = mesh[info.elnr];
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if (rational && info.order >= 2) return false; // not supported
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AutoDiff<3,T> x(xi(0), 0);
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AutoDiff<3,T> y(xi(1), 1);
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AutoDiff<3,T> z(xi(2), 2);
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AutoDiff<3,T> mapped_x[3] = { T(0.0), T(0.0), T(0.0) } ;
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switch (el.GetType())
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{
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case TET:
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{
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// if (info.order >= 2) return false; // not yet supported
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AutoDiff<3,T> lami[4] = { x, y, z, 1-x-y-z };
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for (int j = 0; j < 4; j++)
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{
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Point<3> p = mesh[el[j]];
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for (int k = 0; k < 3; k++)
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mapped_x[k] += p(k) * lami[j];
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}
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const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (TET);
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for (int i = 0; i < 6; i++)
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{
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int eorder = edgeorder[info.edgenrs[i]];
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if (eorder >= 2)
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{
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int first = edgecoeffsindex[info.edgenrs[i]];
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int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
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if (el[vi1] > el[vi2]) swap (vi1, vi2);
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CalcScaledEdgeShapeLambda (eorder, lami[vi1]-lami[vi2], lami[vi1]+lami[vi2],
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[&](int i, AutoDiff<3,T> shape)
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{
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Vec<3> coef = edgecoeffs[first+i];
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for (int k = 0; k < 3; k++)
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mapped_x[k] += coef(k) * shape;
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});
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}
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}
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const ELEMENT_FACE * faces = MeshTopology::GetFaces1 (TET);
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for (int i = 0; i < 4; i++)
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{
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int forder = faceorder[info.facenrs[i]];
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if (forder >= 3)
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{
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int first = facecoeffsindex[info.facenrs[i]];
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int fnums[] = { faces[i][0]-1, faces[i][1]-1, faces[i][2]-1 };
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if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
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if (el[fnums[1]] > el[fnums[2]]) swap (fnums[1], fnums[2]);
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if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
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CalcScaledTrigShapeLambda (forder,
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lami[fnums[1]]-lami[fnums[0]], lami[fnums[2]],
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lami[fnums[0]]+lami[fnums[1]]+lami[fnums[2]],
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[&](int i, AutoDiff<3,T> shape)
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{
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Vec<3> coef = facecoeffs[first+i];
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for (int k = 0; k < 3; k++)
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mapped_x[k] += coef(k) * shape;
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});
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}
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}
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break;
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}
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case HEX:
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{
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if (info.order >= 2) return false; // not yet supported
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AutoDiff<3,T> lami[8] =
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{ (1-x)*(1-y)*(1-z),
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( x)*(1-y)*(1-z),
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( x)* y *(1-z),
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(1-x)* y *(1-z),
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(1-x)*(1-y)*(z),
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( x)*(1-y)*(z),
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( x)* y *(z),
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(1-x)* y *(z) };
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for (int j = 0; j < 8; j++)
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{
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Point<3> p = mesh[el[j]];
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for (int k = 0; k < 3; k++)
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mapped_x[k] += p(k) * lami[j];
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}
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if (info.order == 1) break;
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AutoDiff<3,T> mu[8] = {
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(1-x)+(1-y)+(1-z),
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x +(1-y)+(1-z),
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x + y +(1-z),
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(1-x)+ y +(1-z),
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(1-x)+(1-y)+(z),
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x +(1-y)+(z),
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x + y +(z),
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(1-x)+ y +(z),
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};
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int ii = 8;
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const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (HEX);
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for (int i = 0; i < 8; i++)
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{
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int eorder = edgeorder[info.edgenrs[i]];
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if (eorder >= 2)
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{
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int first = edgecoeffsindex[info.edgenrs[i]];
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int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
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if (el[vi1] > el[vi2]) swap (vi1, vi2);
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/*
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CalcEdgeShape (eorder, mu[vi1]-mu[vi2], &shapes(ii));
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T lame = shapes(vi1)+shapes(vi2);
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for (int j = 0; j < order-1; j++)
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shapes(ii+j) *= lame;
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*/
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AutoDiff<3,T> lame = lami[vi1]+lami[vi2];
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CalcEdgeShapeLambda (eorder, mu[vi1]-mu[vi2],
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[&](int i, AutoDiff<3,T> shape)
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{
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Vec<3> coef = edgecoeffs[first+i];
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for (int k = 0; k < 3; k++)
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mapped_x[k] += coef(k) * (lame*shape);
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});
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}
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}
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break;
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}
|
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default:
|
||||
return false;
|
||||
}
|
||||
|
||||
// for (int i = 0; i < 3; i++)
|
||||
// cout << mapped_x[i] << endl;
|
||||
for (int i = 0; i < 3; i++)
|
||||
{
|
||||
mx(i) = mapped_x[i].Value();
|
||||
for (int j = 0; j < 3; j++)
|
||||
jac(i,j) = mapped_x[i].DValue(j);
|
||||
}
|
||||
return true;
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
void CurvedElements ::
|
||||
GetCoefficients (ElementInfo & info, Vec<3> * coefs) const
|
||||
{
|
||||
@ -3809,6 +4045,7 @@ namespace netgen
|
||||
static int timer3 = NgProfiler::CreateTimer ("calcmultipointelementtrafo 3");
|
||||
static int timer4 = NgProfiler::CreateTimer ("calcmultipointelementtrafo 4");
|
||||
static int timer5 = NgProfiler::CreateTimer ("calcmultipointelementtrafo 5");
|
||||
NgProfiler::RegionTimer reg(timer);
|
||||
// NgProfiler::StartTimer (timer);
|
||||
// NgProfiler::StartTimer (timer1);
|
||||
if (mesh.coarsemesh)
|
||||
@ -3885,8 +4122,6 @@ namespace netgen
|
||||
return;
|
||||
}
|
||||
|
||||
|
||||
|
||||
// NgProfiler::StopTimer (timer1);
|
||||
// NgProfiler::StartTimer (timer2);
|
||||
|
||||
@ -3920,14 +4155,34 @@ namespace netgen
|
||||
|
||||
// NgProfiler::StopTimer (timer2);
|
||||
// NgProfiler::StartTimer (timer3);
|
||||
|
||||
|
||||
/*
|
||||
bool ok = true;
|
||||
for (int i = 0; i < n; i++)
|
||||
{
|
||||
Point<3,T> _xi(xi[i*sxi], xi[i*sxi+1], xi[i*sxi+2]);
|
||||
Point<3,T> _x;
|
||||
Mat<3,3,T> _dxdxi;
|
||||
if (!EvaluateMapping (info, _xi, _x, _dxdxi))
|
||||
{ ok = false; break; }
|
||||
// cout << "x = " << _x << ", dxdxi = " << _dxdxi << endl;
|
||||
if (x)
|
||||
for (int j = 0; j < 3; j++)
|
||||
x[i*sx+j] = _x[j];
|
||||
if (dxdxi)
|
||||
for (int j = 0; j < 3; j++)
|
||||
for (int k = 0; k < 3; k++)
|
||||
dxdxi[i*sdxdxi+3*j+k] = _dxdxi(j,k);
|
||||
}
|
||||
if (ok) return;
|
||||
*/
|
||||
|
||||
ArrayMem<Vec<3>,100> coefs(info.ndof);
|
||||
ArrayMem<T,2000> shapes_mem(info.ndof);
|
||||
ArrayMem<T,500> shapes_mem(info.ndof);
|
||||
|
||||
TFlatVector<T> shapes(info.ndof, &shapes_mem[0]);
|
||||
|
||||
ArrayMem<T,6000> dshapes_mem(3*info.ndof);
|
||||
ArrayMem<T,1500> dshapes_mem(3*info.ndof);
|
||||
MatrixFixWidth<3,T> dshapes(info.ndof, &dshapes_mem[0]);
|
||||
|
||||
// NgProfiler::StopTimer (timer3);
|
||||
@ -3947,11 +4202,14 @@ namespace netgen
|
||||
for (int k = 0; k < 3; k++)
|
||||
xj(k) += shapes(i) * coefs[i](k);
|
||||
|
||||
// cout << "old, xj = " << xj << endl;
|
||||
|
||||
for (int k = 0; k < 3; k++)
|
||||
x[j*sx+k] = xj(k);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// NgProfiler::StopTimer (timer4);
|
||||
// NgProfiler::StartTimer (timer5);
|
||||
|
||||
@ -3990,26 +4248,23 @@ namespace netgen
|
||||
for (int k = 0; k < 3; k++)
|
||||
xij(k) = xi[ip*sxi+k];
|
||||
|
||||
// just for testing ...
|
||||
dshapes = T(0.0);
|
||||
const Element & el = mesh[info.elnr];
|
||||
if (el.GetType() != HEX)
|
||||
throw NgException ("not a hex");
|
||||
CalcElementDShapes (info, xij, dshapes);
|
||||
CalcElementDShapes (info, xij, dshapes);
|
||||
|
||||
|
||||
/*
|
||||
Mat<3,3,T> dxdxij;
|
||||
dxdxij = 0.0;
|
||||
for (int i = 0; i < coefs.Size(); i++)
|
||||
for (int j = 0; j < 3; j++)
|
||||
for (int k = 0; k < 3; k++)
|
||||
dxdxij(j,k) += dshapes(i,k) * coefs[i](j);
|
||||
|
||||
// cout << "old, jac = " << dxdxij << endl;
|
||||
|
||||
for (int j = 0; j < 3; j++)
|
||||
for (int k = 0; k < 3; k++)
|
||||
dxdxi[ip*sdxdxi+3*j+k] = dxdxij(j,k);
|
||||
*/
|
||||
|
||||
|
||||
/*
|
||||
T dxdxi00 = T(0.0);
|
||||
T dxdxi01 = T(0.0);
|
||||
T dxdxi02 = T(0.0);
|
||||
@ -4051,10 +4306,10 @@ namespace netgen
|
||||
dxdxi[ip*sdxdxi+3*2+0] = dxdxi20;
|
||||
dxdxi[ip*sdxdxi+3*2+1] = dxdxi21;
|
||||
dxdxi[ip*sdxdxi+3*2+2] = dxdxi22;
|
||||
*/
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// NgProfiler::StopTimer (timer5);
|
||||
// NgProfiler::StopTimer (timer);
|
||||
}
|
||||
|
||||
@ -203,6 +203,8 @@ private:
|
||||
template <typename T>
|
||||
void CalcElementDShapes (ElementInfo & info, const Point<3,T> xi, MatrixFixWidth<3,T> dshapes) const;
|
||||
|
||||
template <typename T>
|
||||
bool EvaluateMapping (ElementInfo & info, const Point<3,T> xi, Point<3,T> & x, Mat<3,3,T> & jac) const;
|
||||
|
||||
class SurfaceElementInfo
|
||||
{
|
||||
|
||||
Loading…
Reference in New Issue
Block a user