static void GenerateMatrix (const AFEL & bfel, const MIP & sip, MAT & mat, LocalHeap & lh) { HeapReset hr(lh); const HDivDivFiniteElement<2> & fel = dynamic_cast<const HDivDivFiniteElement<2>&> (bfel); int nd = fel.GetNDof(); Mat<3,2> jac = sip.GetJacobian(); double det = fabs (sip.GetJacobiDet()); FlatMatrix<> shape(nd, 3, lh); fel.CalcShape (sip.IP(), shape); Mat<3,9> trans; for (int i = 0; i < 3; i++) { Mat<2> sigma_ref; sigma_ref = 0.0; switch (i) { case 0: sigma_ref(0,0) = 1.0; break; case 1: sigma_ref(1,1) = 1.0; break; case 2: sigma_ref(0,1) = sigma_ref(1,0) = 1.0; break; } auto hm = jac * sigma_ref; auto sigma = hm * Trans(jac); sigma *= (1.0 / sqr(det)); trans ( i, 0 ) = sigma(0,0); trans ( i, 1 ) = sigma(0,1); trans ( i, 2 ) = sigma(0,2); trans ( i, 3 ) = sigma(1,0); trans ( i, 4 ) = sigma(1,1); trans ( i, 5 ) = sigma(1,2); trans ( i, 6 ) = sigma(2,0); trans ( i, 7 ) = sigma(2,1); trans ( i, 8 ) = sigma(2,2); } mat = Trans(trans) * Trans (shape); }
static void GenerateMatrix (const AFEL & bfel, const MIP & sip, MAT & mat, LocalHeap & lh) { const HDivDivFiniteElement<2> & fel = dynamic_cast<const HDivDivFiniteElement<2>&> (bfel); int nd = fel.GetNDof(); FlatMatrix<> div_shape(nd, 2, lh); fel.CalcDivShape (sip.IP(), div_shape); FlatMatrix<> shape(nd, 3, lh); fel.CalcShape (sip.IP(), shape); Mat<3,2> jac = sip.GetJacobian(); double det = fabs (sip.GetJacobiDet()); Mat<3,2> sjac = (1.0/(det*det)) * jac; mat = (sjac) * Trans (div_shape); //for non-curved elements, divergence transformation is finished, otherwise derivatives of Jacobian have to be computed... if (!sip.GetTransformation().IsCurvedElement()) return; Mat<2,2> hesse[3]; sip.CalcHesse (hesse[0], hesse[1], hesse[2]); Mat<3,2,AutoDiff<2> > fad; for (int i = 0; i < 3; i++) { for (int j = 0; j < 2; j++) { fad(i,j).Value() = jac(i,j); for (int k = 0; k < 2; k++) fad(i,j).DValue(k) = hesse[i](j,k); } } Vec<3, AutoDiff<2>> n = Cross(Vec<3,AutoDiff<2>>(fad.Col(0)),Vec<3,AutoDiff<2>>(fad.Col(1))); AutoDiff<2> iad_det = 1.0/sqrt(n(0)*n(0)+n(1)*n(1)+n(2)*n(2)); fad *= iad_det; Vec<3> hv2; Mat<2> sigma_ref; for (int i = 0; i < nd; i++) { sigma_ref(0,0) = shape(i, 0); sigma_ref(1,1) = shape(i, 1); sigma_ref(0,1) = sigma_ref(1,0) = shape(i, 2); hv2 = 0.0; for (int j = 0; j < 2; j++) for (int k = 0; k < 3; k++) for (int l = 0; l < 2; l++) hv2(k) += fad(k,l).DValue(j) * sigma_ref(l,j); hv2 *= iad_det.Value(); /* //Mat<D> inv_jac = sip.GetJacobianInverse(); // this term is zero !!! Vec<3> hv2b = 0.0; for ( int j = 0; j < 2; j++ ) for ( int k = 0; k < 3; k++ ) for ( int l = 0; l < 2; l++ ) for ( int m = 0; m < 2; m++ ) for ( int n = 0; n < 3; n++ ) hv2b(n) += inv_jac(m,k) *fad(n,j).Value() * sigma_ref(j,l) * fad(k,l).DValue(m); */ for ( int j = 0; j < 3; j++) mat(j,i) += hv2(j); } }