bool ASMs3DLag::integrate (Integrand& integrand, GlobalIntegral& glInt, const TimeDomain& time) { if (!svol) return true; // silently ignore empty patches // Get Gaussian quadrature points and weights const double* xg = GaussQuadrature::getCoord(nGauss); const double* wg = GaussQuadrature::getWeight(nGauss); if (!xg || !wg) return false; // Get the reduced integration quadrature points, if needed const double* xr = nullptr; const double* wr = nullptr; int nRed = integrand.getReducedIntegration(nGauss); if (nRed > 0) { xr = GaussQuadrature::getCoord(nRed); wr = GaussQuadrature::getWeight(nRed); if (!xr || !wr) return false; } else if (nRed < 0) nRed = nGauss; // The integrand needs to know nGauss // Get parametric coordinates of the elements RealArray upar, vpar, wpar; this->getGridParameters(upar,0,1); this->getGridParameters(vpar,1,1); this->getGridParameters(wpar,2,1); // Number of elements in each direction const int nel1 = upar.size() - 1; const int nel2 = vpar.size() - 1; // Order of basis in the three parametric directions (order = degree + 1) const int p1 = svol->order(0); const int p2 = svol->order(1); const int p3 = svol->order(2); // === Assembly loop over all elements in the patch ========================== bool ok = true; for (size_t g = 0; g < threadGroupsVol.size() && ok; g++) { #pragma omp parallel for schedule(static) for (size_t t = 0; t < threadGroupsVol[g].size(); t++) { FiniteElement fe(p1*p2*p3); Matrix dNdu, Xnod, Jac; Vec4 X; for (size_t l = 0; l < threadGroupsVol[g][t].size() && ok; l++) { int iel = threadGroupsVol[g][t][l]; int i1 = iel % nel1; int i2 = (iel / nel1) % nel2; int i3 = iel / (nel1*nel2); // Set up nodal point coordinates for current element if (!this->getElementCoordinates(Xnod,++iel)) { ok = false; break; } if (integrand.getIntegrandType() & Integrand::ELEMENT_CENTER) { // Compute the element "center" (average of element node coordinates) X = 0.0; for (size_t i = 1; i <= 3; i++) for (size_t j = 1; j <= Xnod.cols(); j++) X[i-1] += Xnod(i,j); X *= 1.0/(double)Xnod.cols(); } // Initialize element quantities fe.iel = MLGE[iel-1]; LocalIntegral* A = integrand.getLocalIntegral(fe.N.size(),fe.iel); if (!integrand.initElement(MNPC[iel-1],fe,X,nRed*nRed*nRed,*A)) { A->destruct(); ok = false; break; } if (xr) { // --- Selective reduced integration loop ---------------------------- for (int k = 0; k < nRed; k++) for (int j = 0; j < nRed; j++) for (int i = 0; i < nRed; i++) { // Local element coordinates of current integration point fe.xi = xr[i]; fe.eta = xr[j]; fe.zeta = xr[k]; // Parameter value of current integration point fe.u = 0.5*(upar[i1]*(1.0-xr[i]) + upar[i1+1]*(1.0+xr[i])); fe.v = 0.5*(vpar[i2]*(1.0-xr[j]) + vpar[i2+1]*(1.0+xr[j])); fe.w = 0.5*(wpar[i3]*(1.0-xr[k]) + wpar[i3+1]*(1.0+xr[k])); // Compute basis function derivatives at current point // using tensor product of one-dimensional Lagrange polynomials if (!Lagrange::computeBasis(fe.N,dNdu, p1,xr[i],p2,xr[j],p3,xr[k])) { ok = false; break; } // Compute Jacobian inverse and derivatives fe.detJxW = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu); // Cartesian coordinates of current integration point X = Xnod * fe.N; X.t = time.t; // Compute the reduced integration terms of the integrand fe.detJxW *= wr[i]*wr[j]*wr[k]; if (!integrand.reducedInt(*A,fe,X)) ok = false; } } // --- Integration loop over all Gauss points in each direction -------- int jp = ((i3*nel2 + i2)*nel1 + i1)*nGauss*nGauss*nGauss; fe.iGP = firstIp + jp; // Global integration point counter for (int k = 0; k < nGauss; k++) for (int j = 0; j < nGauss; j++) for (int i = 0; i < nGauss; i++, fe.iGP++) { // Local element coordinates of current integration point fe.xi = xg[i]; fe.eta = xg[j]; fe.zeta = xg[k]; // Parameter value of current integration point fe.u = 0.5*(upar[i1]*(1.0-xg[i]) + upar[i1+1]*(1.0+xg[i])); fe.v = 0.5*(vpar[i2]*(1.0-xg[j]) + vpar[i2+1]*(1.0+xg[j])); fe.w = 0.5*(wpar[i3]*(1.0-xg[k]) + wpar[i3+1]*(1.0+xg[k])); // Compute basis function derivatives at current integration point // using tensor product of one-dimensional Lagrange polynomials if (!Lagrange::computeBasis(fe.N,dNdu,p1,xg[i],p2,xg[j],p3,xg[k])) ok = false; // Compute Jacobian inverse of coordinate mapping and derivatives fe.detJxW = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu); if (fe.detJxW == 0.0) continue; // skip singular points // Cartesian coordinates of current integration point X = Xnod * fe.N; X.t = time.t; // Evaluate the integrand and accumulate element contributions fe.detJxW *= wg[i]*wg[j]*wg[k]; if (!integrand.evalInt(*A,fe,time,X)) ok = false; } // Finalize the element quantities if (ok && !integrand.finalizeElement(*A,time,firstIp+jp)) ok = false; // Assembly of global system integral if (ok && !glInt.assemble(A->ref(),fe.iel)) ok = false; A->destruct(); } } } return ok; }
bool ASMs1D::integrate (Integrand& integrand, GlobalIntegral& glInt, const TimeDomain& time) { if (!curv) return true; // silently ignore empty patches // Get Gaussian quadrature points and weights const double* xg = GaussQuadrature::getCoord(nGauss); const double* wg = GaussQuadrature::getWeight(nGauss); if (!xg || !wg) return false; // Get the reduced integration quadrature points, if needed const double* xr = nullptr; const double* wr = nullptr; int nRed = integrand.getReducedIntegration(nGauss); if (nRed > 0) { xr = GaussQuadrature::getCoord(nRed); wr = GaussQuadrature::getWeight(nRed); if (!xr || !wr) return false; } else if (nRed < 0) nRed = nGauss; // The integrand needs to know nGauss if (integrand.getIntegrandType() & Integrand::SECOND_DERIVATIVES) if (curv->rational()) { std::cerr <<" *** ASMs1D::integrate: Second-derivatives of NURBS " <<" is not implemented yet, sorry..."<< std::endl; return false; } // Compute parameter values of the Gauss points over the whole patch Matrix gpar, redpar; this->getGaussPointParameters(gpar,nGauss,xg); if (xr) this->getGaussPointParameters(redpar,nRed,xr); const int p1 = curv->order(); FiniteElement fe(p1); Matrix dNdu, Jac; Matrix3D d2Ndu2, Hess; Vec4 X; if (nsd > 1 && (integrand.getIntegrandType() & Integrand::SECOND_DERIVATIVES)) fe.G.resize(nsd,2); // For storing d{X}/du and d2{X}/du2 // === Assembly loop over all elements in the patch ========================== for (size_t iel = 0; iel < nel; iel++) { fe.iel = MLGE[iel]; if (fe.iel < 1) continue; // zero-length element // Check that the current element has nonzero length double dL = this->getParametricLength(1+iel); if (dL < 0.0) return false; // topology error (probably logic error) // Set up control point coordinates for current element if (!this->getElementCoordinates(fe.Xn,1+iel)) return false; if (integrand.getIntegrandType() & Integrand::ELEMENT_CORNERS) this->getElementEnds(p1+iel,fe.XC); if (integrand.getIntegrandType() & Integrand::NODAL_ROTATIONS) { this->getElementNodalRotations(fe.Tn,iel); if (!elmCS.empty()) fe.Te = elmCS[iel]; } // Initialize element matrices LocalIntegral* A = integrand.getLocalIntegral(fe.N.size(),fe.iel); bool ok = integrand.initElement(MNPC[iel],fe,X,nRed,*A); if (xr) { // --- Selective reduced integration loop -------------------------------- for (int i = 0; i < nRed && ok; i++) { // Local element coordinates of current integration point fe.xi = xr[i]; // Parameter values of current integration point fe.u = redpar(1+i,1+iel); if (integrand.getIntegrandType() & Integrand::NO_DERIVATIVES) this->extractBasis(fe.u,fe.N); else { // Fetch basis function derivatives at current point this->extractBasis(fe.u,fe.N,dNdu); // Compute Jacobian inverse and derivatives dNdu.multiply(0.5*dL); // Derivatives w.r.t. xi=[-1,1] fe.detJxW = utl::Jacobian(Jac,fe.dNdX,fe.Xn,dNdu)*wr[i]; } // Cartesian coordinates of current integration point X = fe.Xn * fe.N; X.t = time.t; // Compute the reduced integration terms of the integrand ok = integrand.reducedInt(*A,fe,X); } } // --- Integration loop over all Gauss points in current element ----------- int jp = iel*nGauss; fe.iGP = firstIp + jp; // Global integration point counter for (int i = 0; i < nGauss && ok; i++, fe.iGP++) { // Local element coordinate of current integration point fe.xi = xg[i]; // Parameter value of current integration point fe.u = gpar(1+i,1+iel); // Compute basis functions and derivatives if (integrand.getIntegrandType() & Integrand::NO_DERIVATIVES) this->extractBasis(fe.u,fe.N); else if (integrand.getIntegrandType() & Integrand::SECOND_DERIVATIVES) this->extractBasis(fe.u,fe.N,dNdu,d2Ndu2); else this->extractBasis(fe.u,fe.N,dNdu); if (!dNdu.empty()) { // Compute derivatives in terms of physical coordinates dNdu.multiply(0.5*dL); // Derivatives w.r.t. xi=[-1,1] fe.detJxW = utl::Jacobian(Jac,fe.dNdX,fe.Xn,dNdu)*wg[i]; if (fe.detJxW == 0.0) continue; // skip singular points // Compute Hessian of coordinate mapping and 2nd order derivatives if (integrand.getIntegrandType() & Integrand::SECOND_DERIVATIVES) { d2Ndu2.multiply(0.25*dL*dL); // 2nd derivatives w.r.t. xi=[-1,1] if (!utl::Hessian(Hess,fe.d2NdX2,Jac,fe.Xn,d2Ndu2,fe.dNdX)) ok = false; else if (fe.G.cols() == 2) { // Store the first and second derivatives of {X} w.r.t. // the parametric coordinate (xi), in the G-matrix fe.G.fillColumn(1,Jac.ptr()); fe.G.fillColumn(2,Hess.ptr()); } } } // Cartesian coordinates of current integration point X = fe.Xn * fe.N; X.t = time.t; // Evaluate the integrand and accumulate element contributions if (ok && !integrand.evalInt(*A,fe,time,X)) ok = false; } // Finalize the element quantities if (ok && !integrand.finalizeElement(*A,fe,time,firstIp+jp)) ok = false; // Assembly of global system integral if (ok && !glInt.assemble(A->ref(),fe.iel)) ok = false; A->destruct(); if (!ok) return false; } return true; }
bool ASMs2DLag::integrate (Integrand& integrand, GlobalIntegral& glInt, const TimeDomain& time) { if (this->empty()) return true; // silently ignore empty patches // Get Gaussian quadrature points and weights std::array<int,2> ng; std::array<const double*,2> xg, wg; for (int d = 0; d < 2; d++) { ng[d] = this->getNoGaussPt(d == 0 ? p1 : p2); xg[d] = GaussQuadrature::getCoord(ng[d]); wg[d] = GaussQuadrature::getWeight(ng[d]); if (!xg[d] || !wg[d]) return false; } // Get the reduced integration quadrature points, if needed const double* xr = nullptr; const double* wr = nullptr; int nRed = integrand.getReducedIntegration(ng[0]); if (nRed > 0) { xr = GaussQuadrature::getCoord(nRed); wr = GaussQuadrature::getWeight(nRed); if (!xr || !wr) return false; } else if (nRed < 0) nRed = ng[0]; // The integrand needs to know nGauss // Get parametric coordinates of the elements RealArray upar, vpar; this->getGridParameters(upar,0,1); this->getGridParameters(vpar,1,1); // Number of elements in each direction const int nelx = upar.empty() ? 0 : upar.size() - 1; // === Assembly loop over all elements in the patch ========================== bool ok = true; for (size_t g = 0; g < threadGroups.size() && ok; g++) { #pragma omp parallel for schedule(static) for (size_t t = 0; t < threadGroups[g].size(); t++) { FiniteElement fe(p1*p2); Matrix dNdu, Xnod, Jac; Vec4 X; for (size_t i = 0; i < threadGroups[g][t].size() && ok; i++) { int iel = threadGroups[g][t][i]; int i1 = nelx > 0 ? iel % nelx : 0; int i2 = nelx > 0 ? iel / nelx : 0; // Set up nodal point coordinates for current element if (!this->getElementCoordinates(Xnod,1+iel)) { ok = false; break; } if (integrand.getIntegrandType() & Integrand::ELEMENT_CENTER) { // Compute the element "center" (average of element node coordinates) X = 0.0; for (size_t i = 1; i <= nsd; i++) for (size_t j = 1; j <= Xnod.cols(); j++) X[i-1] += Xnod(i,j); X *= 1.0/(double)Xnod.cols(); } // Initialize element quantities fe.iel = MLGE[iel]; LocalIntegral* A = integrand.getLocalIntegral(fe.N.size(),fe.iel); if (!integrand.initElement(MNPC[iel],fe,X,nRed*nRed,*A)) { A->destruct(); ok = false; break; } if (xr) { // --- Selective reduced integration loop ---------------------------- for (int j = 0; j < nRed; j++) for (int i = 0; i < nRed; i++) { // Local element coordinates of current integration point fe.xi = xr[i]; fe.eta = xr[j]; // Parameter value of current integration point if (!upar.empty()) fe.u = 0.5*(upar[i1]*(1.0-xr[i]) + upar[i1+1]*(1.0+xr[i])); if (!vpar.empty()) fe.v = 0.5*(vpar[i2]*(1.0-xr[j]) + vpar[i2+1]*(1.0+xr[j])); // Compute basis function derivatives at current point // using tensor product of one-dimensional Lagrange polynomials if (!Lagrange::computeBasis(fe.N,dNdu,p1,xr[i],p2,xr[j])) ok = false; // Compute Jacobian inverse and derivatives fe.detJxW = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu); // Cartesian coordinates of current integration point X = Xnod * fe.N; X.t = time.t; // Compute the reduced integration terms of the integrand fe.detJxW *= wr[i]*wr[j]; if (!integrand.reducedInt(*A,fe,X)) ok = false; } } // --- Integration loop over all Gauss points in each direction -------- int jp = iel*ng[0]*ng[1]; fe.iGP = firstIp + jp; // Global integration point counter for (int j = 0; j < ng[1]; j++) for (int i = 0; i < ng[0]; i++, fe.iGP++) { // Local element coordinates of current integration point fe.xi = xg[0][i]; fe.eta = xg[1][j]; // Parameter value of current integration point if (!upar.empty()) fe.u = 0.5*(upar[i1]*(1.0-xg[0][i]) + upar[i1+1]*(1.0+xg[0][i])); if (!vpar.empty()) fe.v = 0.5*(vpar[i2]*(1.0-xg[1][j]) + vpar[i2+1]*(1.0+xg[1][j])); // Compute basis function derivatives at current integration point // using tensor product of one-dimensional Lagrange polynomials if (!Lagrange::computeBasis(fe.N,dNdu,p1,xg[0][i],p2,xg[1][j])) ok = false; // Compute Jacobian inverse of coordinate mapping and derivatives fe.detJxW = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu); if (fe.detJxW == 0.0) continue; // skip singular points // Cartesian coordinates of current integration point X = Xnod * fe.N; X.t = time.t; // Evaluate the integrand and accumulate element contributions fe.detJxW *= wg[0][i]*wg[1][j]; if (!integrand.evalInt(*A,fe,time,X)) ok = false; } // Finalize the element quantities if (ok && !integrand.finalizeElement(*A,time,firstIp+jp)) ok = false; // Assembly of global system integral if (ok && !glInt.assemble(A->ref(),fe.iel)) ok = false; A->destruct(); } } } return ok; }
bool ASMs1DSpec::integrate (Integrand& integrand, GlobalIntegral& glInt, const TimeDomain& time) { if (!curv) return true; // silently ignore empty patches // Order of basis (order = degree + 1) const int p1 = curv->order(); const int n1 = nGauss < 1 ? p1 : nGauss; // Evaluate integration points and weights Vector wg1, xg1, points1; if (!Legendre::GLL(wg1,points1,p1)) return false; Matrix D1; if (nGauss < 1) { // We are using the nodal points themselves as integration points if (!Legendre::basisDerivatives(n1,D1)) return false; } else // Using Gauss-Legendre scheme with nGauss points if (!Legendre::GL(wg1,xg1,n1)) return false; FiniteElement fe(p1); Matrix dNdu, Xnod, Jac; Vec4 X; // === Assembly loop over all elements in the patch ========================== const int nel = this->getNoElms(); for (int iel = 1; iel <= nel; iel++) { // Set up control point coordinates for current element if (!this->getElementCoordinates(Xnod,iel)) return false; // Initialize element quantities fe.iel = MLGE[iel-1]; LocalIntegral* A = integrand.getLocalIntegral(p1,fe.iel); if (!integrand.initElement(MNPC[iel-1],*A)) return false; // --- Integration loop over integration points ---------------------------- for (int i = 0; i < n1; i++) { // Compute basis function derivatives at current integration point if (nGauss < 1) { fe.N.fill(0.0); fe.N(i+1) = 1.0; dNdu.fillColumn(1,D1.getRow(i+1)); } else if (!Lagrange::computeBasis(fe.N,&dNdu,points1,xg1[i])) return false; // Compute Jacobian inverse of coordinate mapping and derivatives fe.detJxW = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu); // Cartesian coordinates of current integration point X = Xnod*fe.N; X.t = time.t; // Evaluate the integrand and accumulate element contributions fe.detJxW *= wg1[i]; if (!integrand.evalInt(*A,fe,time,X)) return false; } // Assembly of global system integral if (!glInt.assemble(A->ref(),fe.iel)) return false; A->destruct(); } return true; }
bool ASMs2DSpec::integrate (Integrand& integrand, GlobalIntegral& glInt, const TimeDomain& time) { if (this->empty()) return true; // silently ignore empty patches // Evaluate integration points (= nodal points) and weights Vector wg1,xg1,wg2,xg2; if (!Legendre::GLL(wg1,xg1,p1)) return false; if (!Legendre::GLL(wg2,xg2,p2)) return false; Matrix D1, D2; if (!Legendre::basisDerivatives(p1,D1)) return false; if (!Legendre::basisDerivatives(p2,D2)) return false; // === Assembly loop over all elements in the patch ========================== bool ok = true; for (size_t g = 0; g < threadGroups.size() && ok; g++) { #pragma omp parallel for schedule(static) for (size_t t = 0; t < threadGroups[g].size(); t++) { FiniteElement fe(p1*p2); Matrix dNdu(p1*p2,2), Xnod, Jac; Vec4 X; for (size_t e = 0; e < threadGroups[g][t].size(); e++) { int iel = threadGroups[g][t][e]+1; // Set up control point coordinates for current element if (!this->getElementCoordinates(Xnod,iel)) { ok = false; break; } // Initialize element quantities fe.iel = MLGE[iel-1]; LocalIntegral* A = integrand.getLocalIntegral(fe.N.size(),fe.iel); if (!integrand.initElement(MNPC[iel-1],*A)) { A->destruct(); ok = false; break; } // --- Integration loop over all Gauss points in each direction -------- int count = 1; for (int j = 1; j <= p2; j++) for (int i = 1; i <= p1; i++, count++) { // Evaluate the basis functions and gradients using // tensor product of one-dimensional Lagrange polynomials evalBasis(i,j,p1,p2,D1,D2,fe.N,dNdu); // Compute Jacobian inverse of coordinate mapping and derivatives fe.detJxW = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu); if (fe.detJxW == 0.0) continue; // skip singular points // Cartesian coordinates of current integration point X.x = Xnod(1,count); X.y = Xnod(2,count); X.t = time.t; // Evaluate the integrand and accumulate element contributions fe.detJxW *= wg1(i)*wg2(j); if (!integrand.evalInt(*A,fe,time,X)) ok = false; } // Assembly of global system integral if (ok && !glInt.assemble(A->ref(),fe.iel)) ok = false; A->destruct(); } } } return ok; }