forked from lijiext/lammps
994 lines
35 KiB
C++
994 lines
35 KiB
C++
// ATC header files
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#include "ATC_Error.h"
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#include "FE_Element.h"
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#include "FE_Interpolate.h"
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#include "FE_Quadrature.h"
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// Other headers
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#include <cmath>
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using std::map;
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using std::vector;
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namespace ATC {
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FE_Interpolate::FE_Interpolate(FE_Element *feElement)
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: feElement_(feElement),
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nSD_(feElement->num_dims())
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{
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// Nothing to do here
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}
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FE_Interpolate::~FE_Interpolate()
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{
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if (!feQuadList_.empty()) {
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map<FeIntQuadrature,FE_Quadrature *>::iterator qit;
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for (qit = feQuadList_.begin();
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qit != feQuadList_.end(); ++qit) {
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delete (qit->second);
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}
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}
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}
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void FE_Interpolate::set_quadrature(FeEltGeometry geo,
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FeIntQuadrature quad)
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{
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if (feQuadList_.count(quad) == 0) {
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feQuad_ = new FE_Quadrature(geo,quad);
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feQuadList_[quad] = feQuad_;
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} else {
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feQuad_ = feQuadList_[quad];
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}
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precalculate_shape_functions();
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}
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void FE_Interpolate::precalculate_shape_functions()
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{
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int numEltNodes = feElement_->num_elt_nodes();
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int numFaces = feElement_->num_faces();
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int numFaceNodes = feElement_->num_face_nodes();
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int numIPs = feQuad_->numIPs;
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DENS_MAT &ipCoords = feQuad_->ipCoords;
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int numFaceIPs = feQuad_->numFaceIPs;
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vector<DENS_MAT> &ipFaceCoords = feQuad_->ipFaceCoords;
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DENS_MAT &ipFace2DCoords = feQuad_->ipFace2DCoords;
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// Compute elemental shape functions at ips
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N_.reset(numIPs,numEltNodes);
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dNdr_.assign(numIPs,DENS_MAT(nSD_,numEltNodes));
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for (int ip = 0; ip < numIPs; ip++) {
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CLON_VEC thisIP = column(ipCoords,ip);
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CLON_VEC thisN = row(N_,ip);
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DENS_MAT &thisdNdr = dNdr_[ip];
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compute_N(thisIP,thisN);
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compute_N_dNdr(thisIP,thisN,thisdNdr);
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}
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// Compute face shape functions at ip's
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NFace_.assign(numFaces,DENS_MAT(numFaceIPs,numEltNodes));
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dNdrFace_.resize(numFaces);
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for (int f = 0; f < numFaces; f++) {
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dNdrFace_[f].assign(numIPs,DENS_MAT(nSD_,numEltNodes));
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}
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for (int f = 0; f < numFaces; f++) {
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for (int ip = 0; ip < numFaceIPs; ip++) {
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CLON_VEC thisIP = column(ipFaceCoords[f],ip);
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CLON_VEC thisN = row(NFace_[f],ip);
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DENS_MAT &thisdNdr = dNdrFace_[f][ip];
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compute_N_dNdr(thisIP,thisN,thisdNdr);
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}
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}
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// Compute 2D face shape function derivatives
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dNdrFace2D_.assign(numFaceIPs,DENS_MAT(nSD_-1,numFaceNodes));
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for (int ip = 0; ip < numFaceIPs; ip++) {
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CLON_VEC thisIP = column(ipFace2DCoords,ip);
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DENS_MAT &thisdNdr = dNdrFace2D_[ip];
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compute_dNdr(thisIP,
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numFaceNodes,nSD_-1,feElement_->face_area(),
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thisdNdr);
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}
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}
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//-----------------------------------------------------------------
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// shape function value at a particular point given local coordinates
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//-----------------------------------------------------------------
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void FE_Interpolate::shape_function(const VECTOR &xi,
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DENS_VEC &N)
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{
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int numEltNodes = feElement_->num_elt_nodes();
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N.resize(numEltNodes);
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compute_N(xi,N);
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}
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void FE_Interpolate::shape_function(const DENS_MAT &eltCoords,
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const VECTOR &xi,
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DENS_VEC &N,
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DENS_MAT &dNdx)
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{
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int numEltNodes = feElement_->num_elt_nodes();
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N.resize(numEltNodes);
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DENS_MAT dNdr(nSD_,numEltNodes,false);
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compute_N_dNdr(xi,N,dNdr);
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DENS_MAT eltCoordsT = transpose(eltCoords);
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DENS_MAT dxdr, drdx;
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dxdr = dNdr*eltCoordsT;
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drdx = inv(dxdr);
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dNdx = drdx*dNdr;
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}
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void FE_Interpolate::shape_function_derivatives(const DENS_MAT &eltCoords,
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const VECTOR &xi,
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DENS_MAT &dNdx)
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{
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int numEltNodes = feElement_->num_elt_nodes();
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DENS_MAT dNdr(nSD_,numEltNodes,false);
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DENS_VEC N(numEltNodes);
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compute_N_dNdr(xi,N,dNdr);
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DENS_MAT eltCoordsT = transpose(eltCoords);
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DENS_MAT dxdr, drdx;
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dxdr = dNdr*eltCoordsT; // tangents or Jacobian matrix
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drdx = inv(dxdr);
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dNdx = drdx*dNdr; // dN/dx = dN/dxi (dx/dxi)^-1
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}
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void FE_Interpolate::tangents(const DENS_MAT &eltCoords,
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const VECTOR &xi,
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DENS_MAT &dxdr) const
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{
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int numEltNodes = feElement_->num_elt_nodes();
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DENS_MAT dNdr(nSD_,numEltNodes,false);
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DENS_VEC N(numEltNodes);
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compute_N_dNdr(xi,N,dNdr);
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//dNdr.print("dNdr");
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DENS_MAT eltCoordsT = transpose(eltCoords);
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//eltCoordsT.print("elt coords");
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dxdr = dNdr*eltCoordsT;
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//dxdr.print("dxdr");
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}
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void FE_Interpolate::tangents(const DENS_MAT &eltCoords,
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const VECTOR &xi,
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vector<DENS_VEC> & dxdxi,
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const bool normalize) const
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{
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DENS_MAT dxdr;
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tangents(eltCoords,xi,dxdr);
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//dxdr.print("dxdr-post");
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dxdxi.resize(nSD_);
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//for (int i = 0; i < nSD_; ++i) dxdxi[i] = CLON_VEC(dxdr,CLONE_COL,i);
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for (int i = 0; i < nSD_; ++i) {
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dxdxi[i].resize(nSD_);
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for (int j = 0; j < nSD_; ++j) {
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dxdxi[i](j) = dxdr(i,j);
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}
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}
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//dxdxi[0].print("t1");
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//dxdxi[1].print("t2");
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//dxdxi[2].print("t3");
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if (normalize) {
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for (int j = 0; j < nSD_; ++j) {
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double norm = 0;
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VECTOR & t = dxdxi[j];
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for (int i = 0; i < nSD_; ++i) norm += t(i)*t(i);
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norm = 1./sqrt(norm);
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for (int i = 0; i < nSD_; ++i) t(i) *= norm;
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}
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}
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}
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// -------------------------------------------------------------
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// shape_function values at nodes
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// -------------------------------------------------------------
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void FE_Interpolate::shape_function(const DENS_MAT &eltCoords,
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DENS_MAT &N,
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vector<DENS_MAT> &dN,
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DIAG_MAT &weights)
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{
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int numEltNodes = feElement_->num_elt_nodes();
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// Transpose eltCoords
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DENS_MAT eltCoordsT(transpose(eltCoords));
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// Shape functions are simply the canonical element values
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N = N_;
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// Set sizes of matrices and vectors
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if ((int)dN.size() != nSD_) dN.resize(nSD_);
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for (int isd = 0; isd < nSD_; isd++)
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dN[isd].resize(feQuad_->numIPs,numEltNodes);
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weights.resize(feQuad_->numIPs,feQuad_->numIPs);
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// Create some temporary matrices:
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// Jacobian matrix: [dx/dr dy/ds dz/dt | dx/ds ... ]
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DENS_MAT dxdr, drdx, dNdx;
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// Loop over integration points
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for (int ip = 0; ip < feQuad_->numIPs; ip++) {
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// Compute dx/dxi matrix
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dxdr = dNdr_[ip]*eltCoordsT;
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drdx = inv(dxdr);
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// Compute dNdx and fill dN matrix
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dNdx = drdx * dNdr_[ip];
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for (int isd = 0; isd < nSD_; isd++)
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for (int inode = 0; inode < numEltNodes; inode++)
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dN[isd](ip,inode) = dNdx(isd,inode);
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// Compute jacobian determinant of dxdr at this ip
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double J = dxdr(0,0) * (dxdr(1,1)*dxdr(2,2) - dxdr(2,1)*dxdr(1,2))
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- dxdr(0,1) * (dxdr(1,0)*dxdr(2,2) - dxdr(1,2)*dxdr(2,0))
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+ dxdr(0,2) * (dxdr(1,0)*dxdr(2,1) - dxdr(1,1)*dxdr(2,0));
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// Compute ip weight
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weights(ip,ip) = feQuad_->ipWeights(ip)*J;
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}
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}
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//-----------------------------------------------------------------
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// shape functions on a given face
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//-----------------------------------------------------------------
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void FE_Interpolate::face_shape_function(const DENS_MAT &eltCoords,
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const DENS_MAT &faceCoords,
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const int faceID,
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DENS_MAT &N,
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DENS_MAT &n,
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DIAG_MAT &weights)
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{
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int numFaceIPs = feQuad_->numFaceIPs;
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// Transpose eltCoords
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DENS_MAT eltCoordsT = transpose(eltCoords);
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// Shape functions are simply the canonical element values
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N = NFace_[faceID];
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// Create some temporary matrices:
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// Jacobian matrix: [dx/dr dy/ds dz/dt | dx/ds ... ]
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DENS_MAT dxdr, drdx, dNdx;
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// Loop over integration points
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DENS_VEC normal(nSD_);
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n.resize(nSD_,numFaceIPs);
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weights.resize(numFaceIPs,numFaceIPs);
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for (int ip = 0; ip < numFaceIPs; ip++) {
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// Compute 2d jacobian determinant of dxdr at this ip
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double J = face_normal(faceCoords,ip,normal);
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// Copy normal at integration point
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for (int isd = 0; isd < nSD_; isd++) {
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n(isd,ip) = normal(isd);
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}
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// Compute ip weight
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weights(ip,ip) = feQuad_->ipFaceWeights(ip)*J;
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}
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}
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void FE_Interpolate::face_shape_function(const DENS_MAT &eltCoords,
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const DENS_MAT &faceCoords,
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const int faceID,
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DENS_MAT &N,
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vector<DENS_MAT> &dN,
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vector<DENS_MAT> &Nn,
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DIAG_MAT &weights)
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{
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int numEltNodes = feElement_->num_elt_nodes();
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int numFaceIPs = feQuad_->numFaceIPs;
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// Transpose eltCoords
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DENS_MAT eltCoordsT = transpose(eltCoords);
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// Shape functions are simply the canonical element values
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N = NFace_[faceID];
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// Set sizes of matrices and vectors
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if ((int)dN.size() != nSD_) dN.resize(nSD_);
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if ((int)Nn.size() != nSD_) Nn.resize(nSD_);
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for (int isd = 0; isd < nSD_; isd++) {
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dN[isd].resize(numFaceIPs,numEltNodes);
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Nn[isd].resize(numFaceIPs,numEltNodes);
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}
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weights.resize(numFaceIPs,numFaceIPs);
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// Create some temporary matrices:
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// Jacobian matrix: [dx/dr dy/ds dz/dt | dx/ds ... ]
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DENS_MAT dxdr, drdx, dNdx;
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DENS_VEC normal(nSD_);
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// Loop over integration points
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for (int ip = 0; ip < numFaceIPs; ip++) {
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// Compute dx/dxi matrix
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dxdr = dNdrFace_[faceID][ip] * eltCoordsT;
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drdx = inv(dxdr);
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// Compute 2d jacobian determinant of dxdr at this ip
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double J = face_normal(faceCoords,ip,normal);
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// Compute dNdx and fill dN matrix
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dNdx = drdx * dNdrFace_[faceID][ip];
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for (int isd = 0; isd < nSD_; isd++) {
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for (int inode = 0; inode < numEltNodes; inode++) {
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dN[isd](ip,inode) = dNdx(isd,inode);
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Nn[isd](ip,inode) = N(ip,inode)*normal(isd);
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}
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}
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// Compute ip weight
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weights(ip,ip) = feQuad_->ipFaceWeights(ip)*J;
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}
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}
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// -------------------------------------------------------------
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// face normal
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// -------------------------------------------------------------
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double FE_Interpolate::face_normal(const DENS_MAT &faceCoords,
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int ip,
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DENS_VEC &normal)
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{
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// Compute dx/dr for deformed element
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DENS_MAT faceCoordsT = transpose(faceCoords);
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DENS_MAT dxdr = dNdrFace2D_[ip]*faceCoordsT;
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// Normal vector from cross product, hardcoded for 3D, sad
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normal(0) = dxdr(0,1)*dxdr(1,2) - dxdr(0,2)*dxdr(1,1);
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normal(1) = dxdr(0,2)*dxdr(1,0) - dxdr(0,0)*dxdr(1,2);
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normal(2) = dxdr(0,0)*dxdr(1,1) - dxdr(0,1)*dxdr(1,0);
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// Jacobian (3D)
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double J = sqrt(normal(0)*normal(0) +
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normal(1)*normal(1) +
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normal(2)*normal(2));
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double invJ = 1.0/J;
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normal(0) *= invJ;
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normal(1) *= invJ;
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normal(2) *= invJ;
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return J;
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}
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int FE_Interpolate::num_ips() const
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{
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return feQuad_->numIPs;
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}
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int FE_Interpolate::num_face_ips() const
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{
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return feQuad_->numFaceIPs;
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}
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/*********************************************************
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* Class FE_InterpolateCartLagrange
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*
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* For computing Lagrange shape functions using Cartesian
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* coordinate systems (all quads/hexes fall under this
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* category, and any elements derived by degenerating
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* them). Not to be used for serendipity elements, which
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* should be implemented for SPEED.
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*
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*********************************************************/
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FE_InterpolateCartLagrange::FE_InterpolateCartLagrange(
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FE_Element *feElement)
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: FE_Interpolate(feElement)
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{
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set_quadrature(HEXA,GAUSS2);
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}
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FE_InterpolateCartLagrange::~FE_InterpolateCartLagrange()
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{
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// Handled by base class
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}
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void FE_InterpolateCartLagrange::compute_N(const VECTOR &point,
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VECTOR &N)
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{
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// *** see comments for compute_N_dNdr ***
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const DENS_VEC &localCoords1d = feElement_->local_coords_1d();
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int numEltNodes = feElement_->num_elt_nodes();
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int numEltNodes1d = feElement_->num_elt_nodes_1d();
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DENS_MAT lagrangeTerms(nSD_,numEltNodes1d);
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DENS_MAT lagrangeDenom(nSD_,numEltNodes1d);
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lagrangeTerms = 1.0;
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lagrangeDenom = 1.0;
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for (int iSD = 0; iSD < nSD_; ++iSD) {
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for (int inode = 0; inode < numEltNodes1d; ++inode) {
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for (int icont = 0; icont < numEltNodes1d; ++icont) {
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if (inode != icont) {
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lagrangeDenom(iSD,inode) *= (localCoords1d(inode) -
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localCoords1d(icont));
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lagrangeTerms(iSD,inode) *= (point(iSD)-localCoords1d(icont));
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}
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}
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}
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}
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for (int iSD=0; iSD<nSD_; ++iSD) {
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for (int inode=0; inode<numEltNodes1d; ++inode) {
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lagrangeTerms(iSD,inode) /= lagrangeDenom(iSD,inode);
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}
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}
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N = 1.0;
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vector<int> mapping(nSD_);
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for (int inode=0; inode<numEltNodes; ++inode) {
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feElement_->mapping(inode,mapping);
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for (int iSD=0; iSD<nSD_; ++iSD) {
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N(inode) *= lagrangeTerms(iSD,mapping[iSD]);
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}
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}
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}
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// Sort of a test-ride for a generic version that can be used for
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// faces too. The only thing that's not "generic" is localCoords,
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// which very magically works in both cases.
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void FE_InterpolateCartLagrange::compute_dNdr(const VECTOR &point,
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const int numNodes,
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const int nD,
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const double,
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DENS_MAT &dNdr)
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{
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// *** see comments for compute_N_dNdr ***
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const DENS_VEC &localCoords1d = feElement_->local_coords_1d();
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int numEltNodes1d = feElement_->num_elt_nodes_1d();
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DENS_MAT lagrangeTerms(nD,numEltNodes1d);
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DENS_MAT lagrangeDenom(nD,numEltNodes1d);
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DENS_MAT lagrangeDeriv(nD,numEltNodes1d);
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lagrangeDenom = 1.0;
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lagrangeTerms = 1.0;
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lagrangeDeriv = 0.0;
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DENS_VEC productRuleVec(numEltNodes1d);
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productRuleVec = 1.0;
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for (int iSD = 0; iSD < nD; ++iSD) {
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for (int inode = 0; inode < numEltNodes1d; ++inode) {
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for (int icont = 0; icont < numEltNodes1d; ++icont) {
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if (inode != icont) {
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lagrangeTerms(iSD,inode) *= (point(iSD)-localCoords1d(icont));
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lagrangeDenom(iSD,inode) *= (localCoords1d(inode) -
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localCoords1d(icont));
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for (int dcont=0; dcont<numEltNodes1d; ++dcont) {
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if (inode == dcont) {
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productRuleVec(dcont) = 0.0;
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} else if (icont == dcont) {
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} else {
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productRuleVec(dcont) *= (point(iSD)-localCoords1d(icont));
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}
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}
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}
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}
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for (int dcont=0; dcont<numEltNodes1d; ++dcont) {
|
|
lagrangeDeriv(iSD,inode) += productRuleVec(dcont);
|
|
}
|
|
productRuleVec = 1.0;
|
|
}
|
|
}
|
|
for (int iSD=0; iSD<nD; ++iSD) {
|
|
for (int inode=0; inode<numEltNodes1d; ++inode) {
|
|
lagrangeTerms(iSD,inode) /= lagrangeDenom(iSD,inode);
|
|
lagrangeDeriv(iSD,inode) /= lagrangeDenom(iSD,inode);
|
|
}
|
|
}
|
|
|
|
dNdr = 1.0;
|
|
vector<int> mapping(nD);
|
|
for (int inode=0; inode<numNodes; ++inode) {
|
|
feElement_->mapping(inode,mapping);
|
|
for (int iSD=0; iSD<nD; ++iSD) {
|
|
for (int dSD=0; dSD<nD; ++dSD) {
|
|
if (iSD == dSD) {
|
|
dNdr(dSD,inode) *= lagrangeDeriv(iSD,mapping[iSD]);
|
|
} else {
|
|
dNdr(dSD,inode) *= lagrangeTerms(iSD,mapping[iSD]);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void FE_InterpolateCartLagrange::compute_N_dNdr(const VECTOR &point,
|
|
VECTOR &N,
|
|
DENS_MAT &dNdr) const
|
|
{
|
|
// Required data from element class
|
|
const DENS_VEC &localCoords1d = feElement_->local_coords_1d();
|
|
int numEltNodes = feElement_->num_elt_nodes();
|
|
int numEltNodes1d = feElement_->num_elt_nodes_1d();
|
|
|
|
// lagrangeTerms stores the numerator for the various Lagrange polynomials
|
|
// in one dimension, that will be used to produce the three dimensional
|
|
// shape functions
|
|
DENS_MAT lagrangeTerms(nSD_,numEltNodes1d);
|
|
// lagrangeDenom stores the denominator. Stored separately to reduce
|
|
// redundancy, because it will be used for the shape functions and derivs
|
|
DENS_MAT lagrangeDenom(nSD_,numEltNodes1d);
|
|
// lagrangeDeriv stores the numerator for the derivative of the Lagrange
|
|
// polynomials
|
|
DENS_MAT lagrangeDeriv(nSD_,numEltNodes1d);
|
|
// Terms/Denom are products, Deriv will be a sum, so initialize as such:
|
|
lagrangeTerms = 1.0;
|
|
lagrangeDenom = 1.0;
|
|
lagrangeDeriv = 0.0;
|
|
// the derivative requires use of the product rule; to store the prodcuts
|
|
// which make up the terms produced by the product rule, we'll use this
|
|
// vector
|
|
DENS_VEC productRuleVec(numEltNodes1d);
|
|
productRuleVec = 1.0;
|
|
for (int iSD = 0; iSD < nSD_; ++iSD) {
|
|
for (int inode = 0; inode < numEltNodes1d; ++inode) {
|
|
for (int icont = 0; icont < numEltNodes1d; ++icont) {
|
|
if (inode != icont) {
|
|
// each dimension and each 1d node per dimension has a
|
|
// contribution from all nodes besides the current node
|
|
lagrangeTerms(iSD,inode) *= (point(iSD)-localCoords1d(icont));
|
|
lagrangeDenom(iSD,inode) *= (localCoords1d(inode) -
|
|
localCoords1d(icont));
|
|
// complciated; each sum produced by the product rule has one
|
|
// "derivative", and the rest are just identical to the terms
|
|
// above
|
|
for (int dcont=0; dcont<numEltNodes1d; ++dcont) {
|
|
if (inode == dcont) {
|
|
// skip this term, derivative is 0
|
|
productRuleVec(dcont) = 0.0;
|
|
} else if (icont == dcont) {
|
|
// no numerator contribution, derivative is 1
|
|
} else {
|
|
// part of the "constant"
|
|
productRuleVec(dcont) *= (point(iSD)-localCoords1d(icont));
|
|
}
|
|
}
|
|
}
|
|
}
|
|
// sum the terms produced by the product rule and store in Deriv
|
|
for (int dcont=0; dcont<numEltNodes1d; ++dcont) {
|
|
lagrangeDeriv(iSD,inode) += productRuleVec(dcont);
|
|
}
|
|
productRuleVec = 1.0;
|
|
}
|
|
}
|
|
// divide by denom
|
|
for (int iSD=0; iSD<nSD_; ++iSD) {
|
|
for (int inode=0; inode<numEltNodes1d; ++inode) {
|
|
lagrangeTerms(iSD,inode) /= lagrangeDenom(iSD,inode);
|
|
lagrangeDeriv(iSD,inode) /= lagrangeDenom(iSD,inode);
|
|
}
|
|
}
|
|
|
|
N = 1.0;
|
|
dNdr = 1.0;
|
|
// mapping returns the 1d nodes in each dimension that sould be multiplied
|
|
// to achieve the shape functions in 3d
|
|
vector<int> mapping(nSD_);
|
|
for (int inode=0; inode<numEltNodes; ++inode) {
|
|
feElement_->mapping(inode,mapping);
|
|
for (int iSD=0; iSD<nSD_; ++iSD) {
|
|
N(inode) *= lagrangeTerms(iSD,mapping[iSD]);
|
|
for (int dSD=0; dSD<nSD_; ++dSD) {
|
|
// only use Deriv for the dimension in which we're taking the
|
|
// derivative, because the rest is essentially a "constant"
|
|
if (iSD == dSD) {
|
|
dNdr(dSD,inode) *= lagrangeDeriv(iSD,mapping[iSD]);
|
|
} else {
|
|
dNdr(dSD,inode) *= lagrangeTerms(iSD,mapping[iSD]);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/*********************************************************
|
|
* Class FE_InterpolateCartLin
|
|
*
|
|
* For computing linear shape functions using Cartesian
|
|
* coordinate systems (all quads/hexes fall under this
|
|
* category, and any elements derived by degenerating
|
|
* them).
|
|
*
|
|
*********************************************************/
|
|
FE_InterpolateCartLin::FE_InterpolateCartLin(
|
|
FE_Element *feElement)
|
|
: FE_Interpolate(feElement)
|
|
{
|
|
set_quadrature(HEXA,GAUSS2);
|
|
}
|
|
|
|
FE_InterpolateCartLin::~FE_InterpolateCartLin()
|
|
{
|
|
// Handled by base class
|
|
}
|
|
|
|
void FE_InterpolateCartLin::compute_N(const VECTOR &point,
|
|
VECTOR &N)
|
|
{
|
|
// *** see comments for compute_N_dNdr ***
|
|
const DENS_MAT &localCoords = feElement_->local_coords();
|
|
double invVol = 1.0/(feElement_->vol());
|
|
int numEltNodes = feElement_->num_elt_nodes();
|
|
|
|
for (int inode = 0; inode < numEltNodes; ++inode) {
|
|
N(inode) = invVol;
|
|
for (int isd = 0; isd < nSD_; ++isd) {
|
|
N(inode) *= (1.0 + point(isd)*localCoords(isd,inode));
|
|
}
|
|
}
|
|
}
|
|
|
|
// Sort of a test-ride for a generic version that can be used for
|
|
// faces too. The only thing that's not "generic" is localCoords,
|
|
// which very magically works in both cases.
|
|
void FE_InterpolateCartLin::compute_dNdr(const VECTOR &point,
|
|
const int numNodes,
|
|
const int nD,
|
|
const double vol,
|
|
DENS_MAT &dNdr)
|
|
{
|
|
// *** see comments for compute_N_dNdr ***
|
|
const DENS_MAT &localCoords = feElement_->local_coords();
|
|
double invVol = 1.0/vol;
|
|
|
|
for (int inode = 0; inode < numNodes; ++inode) {
|
|
for (int idr = 0; idr < nD; ++idr) {
|
|
dNdr(idr,inode) = invVol;
|
|
}
|
|
for (int id = 0; id < nD; ++id) {
|
|
for (int idr = 0; idr < nD; ++idr) {
|
|
if (id == idr) dNdr(idr,inode) *= localCoords(id,inode);
|
|
else dNdr(idr,inode) *= 1.0 +
|
|
point(id)*localCoords(id,inode);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void FE_InterpolateCartLin::compute_N_dNdr(const VECTOR &point,
|
|
VECTOR &N,
|
|
DENS_MAT &dNdr) const
|
|
{
|
|
// Required data from element class
|
|
const DENS_MAT &localCoords = feElement_->local_coords();
|
|
double invVol = 1.0/(feElement_->vol());
|
|
int numEltNodes = feElement_->num_elt_nodes();
|
|
|
|
// Fill in for each node
|
|
for (int inode = 0; inode < numEltNodes; ++inode) {
|
|
// Intiialize shape function and derivatives
|
|
N(inode) = invVol;
|
|
for (int idr = 0; idr < nSD_; ++idr) {
|
|
dNdr(idr,inode) = invVol;
|
|
}
|
|
for (int isd = 0; isd < nSD_; ++isd) {
|
|
// One term for each dimension
|
|
N(inode) *= (1.0 + point(isd)*localCoords(isd,inode));
|
|
// One term for each dimension, only deriv in deriv's dimension
|
|
for (int idr = 0; idr < nSD_; ++idr) {
|
|
if (isd == idr) dNdr(idr,inode) *= localCoords(isd,inode);
|
|
else dNdr(idr,inode) *= 1.0 +
|
|
point(isd)*localCoords(isd,inode);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
/*********************************************************
|
|
* Class FE_InterpolateCartSerendipity
|
|
*
|
|
* For computing shape functions for quadratic serendipity
|
|
* elements, implemented for SPEED.
|
|
*
|
|
*********************************************************/
|
|
FE_InterpolateCartSerendipity::FE_InterpolateCartSerendipity(
|
|
FE_Element *feElement)
|
|
: FE_Interpolate(feElement)
|
|
{
|
|
set_quadrature(HEXA,GAUSS2);
|
|
}
|
|
|
|
FE_InterpolateCartSerendipity::~FE_InterpolateCartSerendipity()
|
|
{
|
|
// Handled by base class
|
|
}
|
|
|
|
void FE_InterpolateCartSerendipity::compute_N(const VECTOR &point,
|
|
VECTOR &N)
|
|
{
|
|
// *** see comments for compute_N_dNdr ***
|
|
const DENS_MAT &localCoords = feElement_->local_coords();
|
|
double invVol = 1.0/(feElement_->vol());
|
|
int numEltNodes = feElement_->num_elt_nodes();
|
|
|
|
for (int inode = 0; inode < numEltNodes; ++inode) {
|
|
N(inode) = invVol;
|
|
for (int isd = 0; isd < nSD_; ++isd) {
|
|
if (((inode == 8 || inode == 10 || inode == 16 || inode == 18) &&
|
|
(isd == 0)) ||
|
|
((inode == 9 || inode == 11 || inode == 17 || inode == 19) &&
|
|
(isd == 1)) ||
|
|
((inode == 12 || inode == 13 || inode == 14 || inode == 15) &&
|
|
(isd == 2))) {
|
|
N(inode) *= (1.0 - pow(point(isd),2))*2;
|
|
} else {
|
|
N(inode) *= (1.0 + point(isd)*localCoords(isd,inode));
|
|
}
|
|
}
|
|
if (inode < 8) {
|
|
N(inode) *= (point(0)*localCoords(0,inode) +
|
|
point(1)*localCoords(1,inode) +
|
|
point(2)*localCoords(2,inode) - 2);
|
|
}
|
|
}
|
|
}
|
|
|
|
// Sort of a test-ride for a generic version that can be used for
|
|
// faces too. The only thing that's not "generic" is localCoords,
|
|
// which very magically works in both cases.
|
|
void FE_InterpolateCartSerendipity::compute_dNdr(const VECTOR &point,
|
|
const int numNodes,
|
|
const int nD,
|
|
const double vol,
|
|
DENS_MAT &dNdr)
|
|
{
|
|
// *** see comments for compute_N_dNdr ***
|
|
const DENS_MAT &localCoords = feElement_->local_coords();
|
|
double invVol = 1.0/vol;
|
|
bool serendipityNode = false;
|
|
double productRule1 = 0.0;
|
|
double productRule2 = 0.0;
|
|
|
|
if (nD != 3 && nD != 2) {
|
|
ATC_Error("Serendipity dNdr calculations are too hard-wired to do "
|
|
"what you want them to. Only 2D and 3D currently work.");
|
|
}
|
|
|
|
for (int inode = 0; inode < numNodes; ++inode) {
|
|
for (int idr = 0; idr < nD; ++idr) {
|
|
dNdr(idr,inode) = invVol;
|
|
}
|
|
for (int id = 0; id < nD; ++id) {
|
|
for (int idr = 0; idr < nD; ++idr) {
|
|
// identify nodes/dims differently if 3d or 2d case
|
|
if (nD == 3) {
|
|
serendipityNode =
|
|
(((inode == 8 || inode == 10 || inode == 16 || inode == 18) &&
|
|
(id == 0)) ||
|
|
((inode == 9 || inode == 11 || inode == 17 || inode == 19) &&
|
|
(id == 1)) ||
|
|
((inode == 12 || inode == 13 || inode == 14 || inode == 15) &&
|
|
(id == 2)));
|
|
} else if (nD == 2) {
|
|
serendipityNode =
|
|
(((inode == 4 || inode == 6) && (id == 0)) ||
|
|
((inode == 5 || inode == 7) && (id == 1)));
|
|
}
|
|
if (serendipityNode) {
|
|
if (id == idr) {
|
|
dNdr(idr,inode) *= point(id)*(-4);
|
|
} else {
|
|
dNdr(idr,inode) *= (1.0 - pow(point(id),2))*2;
|
|
}
|
|
} else {
|
|
if (id == idr) {
|
|
dNdr(idr,inode) *= localCoords(id,inode);
|
|
} else {
|
|
dNdr(idr,inode) *= (1.0 + point(id)*localCoords(id,inode));
|
|
}
|
|
}
|
|
}
|
|
}
|
|
for (int idr = 0; idr < nD; ++idr) {
|
|
if (inode < 8) {
|
|
// final corner contribution slightly different for 3d and 2d cases
|
|
if (nD == 3) {
|
|
productRule2 = (point(0)*localCoords(0,inode) +
|
|
point(1)*localCoords(1,inode) +
|
|
point(2)*localCoords(2,inode) - 2);
|
|
} else if (nD == 2) {
|
|
productRule2 = (point(0)*localCoords(0,inode) +
|
|
point(1)*localCoords(1,inode) - 1);
|
|
}
|
|
productRule1 = dNdr(idr,inode) *
|
|
(1 + point(idr)*localCoords(idr,inode));
|
|
productRule2 *= dNdr(idr,inode);
|
|
dNdr(idr,inode) = productRule1 + productRule2;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void FE_InterpolateCartSerendipity::compute_N_dNdr(const VECTOR &point,
|
|
VECTOR &N,
|
|
DENS_MAT &dNdr) const
|
|
{
|
|
// Required data from element class
|
|
const DENS_MAT &localCoords = feElement_->local_coords();
|
|
double invVol = 1.0/(feElement_->vol());
|
|
int numEltNodes = feElement_->num_elt_nodes();
|
|
|
|
// Will store terms for product rule derivative for dNdr
|
|
double productRule1;
|
|
double productRule2;
|
|
|
|
// Fill in for each node
|
|
for (int inode = 0; inode < numEltNodes; ++inode) {
|
|
// Initialize shape functions and derivatives
|
|
N(inode) = invVol;
|
|
for (int idr = 0; idr < nSD_; ++idr) {
|
|
dNdr(idr,inode) = invVol;
|
|
}
|
|
// Add components from each dimension
|
|
for (int isd = 0; isd < nSD_; ++isd) {
|
|
for (int idr = 0; idr < nSD_; ++idr) {
|
|
// Check to see if the node is NOT a corner node, and if its
|
|
// "0-coordinate" is in the same dimension as the one we're currently
|
|
// iterating over. If that's the case, we want to contribute to its
|
|
// shape functions and derivatives in a modified way:
|
|
if (((inode == 8 || inode == 10 || inode == 16 || inode == 18) &&
|
|
(isd == 0)) ||
|
|
((inode == 9 || inode == 11 || inode == 17 || inode == 19) &&
|
|
(isd == 1)) ||
|
|
((inode == 12 || inode == 13 || inode == 14 || inode == 15) &&
|
|
(isd == 2))) {
|
|
// If the 1d shape function dimension matches the derivative
|
|
// dimension...
|
|
if (isd == idr) {
|
|
// contribute to N; sloppy, but this is the easiest way to get
|
|
// N to work right without adding extra, arguably unnecessary
|
|
// loops, while also computing the shape functions
|
|
N(inode) *= (1.0 - pow(point(isd),2))*2;
|
|
// contribute to dNdr with the derivative of this shape function
|
|
// contribution
|
|
dNdr(idr,inode) *= point(isd)*(-4);
|
|
} else {
|
|
// otherwise, just use the "constant" contribution to the deriv
|
|
dNdr(idr,inode) *= (1.0 - pow(point(isd),2))*2;
|
|
}
|
|
} else {
|
|
// non-serendipity style contributions
|
|
if (isd == idr) {
|
|
N(inode) *= (1.0 + point(isd)*localCoords(isd,inode));
|
|
dNdr(idr,inode) *= localCoords(isd,inode);
|
|
} else {
|
|
dNdr(idr,inode) *= (1.0 + point(isd)*localCoords(isd,inode));
|
|
}
|
|
}
|
|
}
|
|
}
|
|
// serendipity corner nodes require more extra handling
|
|
if (inode < 8) {
|
|
N(inode) *= (point(0)*localCoords(0,inode) +
|
|
point(1)*localCoords(1,inode) +
|
|
point(2)*localCoords(2,inode) - 2);
|
|
}
|
|
for (int idr = 0; idr < nSD_; ++idr) {
|
|
if (inode < 8) {
|
|
productRule1 = dNdr(idr,inode) *
|
|
(1 + point(idr)*localCoords(idr,inode));
|
|
productRule2 = dNdr(idr,inode) * (point(0)*localCoords(0,inode) +
|
|
point(1)*localCoords(1,inode) +
|
|
point(2)*localCoords(2,inode) - 2);
|
|
dNdr(idr,inode) = productRule1 + productRule2;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
/*********************************************************
|
|
* Class FE_InterpolateSimpLin
|
|
*
|
|
* For computing linear shape functions of simplices,
|
|
* which are rather different from those computed
|
|
* in Cartesian coordinates.
|
|
*
|
|
* Note: degenerating quads/hexes can yield simplices
|
|
* as well, but this class is for computing these
|
|
* shape fucntions _natively_, in their own
|
|
* triangular/tetrahedral coordinate systems.
|
|
*
|
|
*********************************************************/
|
|
FE_InterpolateSimpLin::FE_InterpolateSimpLin(
|
|
FE_Element *feElement)
|
|
: FE_Interpolate(feElement)
|
|
{
|
|
set_quadrature(TETRA,GAUSS2);
|
|
}
|
|
|
|
FE_InterpolateSimpLin::~FE_InterpolateSimpLin()
|
|
{
|
|
// Handled by base class
|
|
}
|
|
|
|
void FE_InterpolateSimpLin::compute_N(const VECTOR &point,
|
|
VECTOR &N)
|
|
{
|
|
int numEltNodes = feElement_->num_elt_nodes();
|
|
|
|
// Fill in for each node
|
|
for (int inode = 0; inode < numEltNodes; ++inode) {
|
|
if (inode == 0) {
|
|
// Fill N...the ips are serving as proxies for "dimensions"
|
|
// since we're in tetrahedral coordinates, except that
|
|
// 0th node = 3rd "dimension" (u or O_o)
|
|
// 1st node = 0th "dimension" (x or r)
|
|
// 2nd node = 1st "dimension" (y or s)
|
|
// 3rd node = 3nd "dimension" (z or t)
|
|
// and remember that u = 1 - r - s - t for tet coords
|
|
N(inode) = 1;
|
|
for (int icont = 0; icont < nSD_; ++icont) {
|
|
N(inode) -= point(icont);
|
|
}
|
|
} else {
|
|
N(inode) = point(inode-1);
|
|
}
|
|
}
|
|
}
|
|
|
|
void FE_InterpolateSimpLin::compute_dNdr(const VECTOR &,
|
|
const int numNodes,
|
|
const int nD,
|
|
const double,
|
|
DENS_MAT &dNdr)
|
|
{
|
|
// Fill in for each node
|
|
for (int inode = 0; inode < numNodes; ++inode) {
|
|
// Fill dNdr_; we want 1 if the dimension of derivative
|
|
// and variable within N correspond. That is, if N == r,
|
|
// we want the 0th dimension to contain (d/dr)r = 1. Of
|
|
// course, (d/di)r = 0 forall i != r, so we need that as
|
|
// well. This is a bit elusively complicated. Also, the 0th
|
|
// integration point contains the term u = 1 - r - s - t.
|
|
// (which map to x, y, and z). Therefore, the derivative in
|
|
// each dimension are -1.
|
|
//
|
|
// The idea is similar for 2 dimensions, which this can
|
|
// handle as well.
|
|
for (int idr = 0; idr < nD; ++idr) {
|
|
if (inode == 0) {
|
|
dNdr(idr,inode) = -1;
|
|
} else {
|
|
dNdr(idr,inode) = (inode == (idr + 1)) ? 1 : 0;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void FE_InterpolateSimpLin::compute_N_dNdr(const VECTOR &point,
|
|
VECTOR &N,
|
|
DENS_MAT &dNdr) const
|
|
{
|
|
int numEltNodes = feElement_->num_elt_nodes();
|
|
|
|
// Fill in for each node
|
|
for (int inode = 0; inode < numEltNodes; ++inode) {
|
|
// Fill N...
|
|
if (inode == 0) {
|
|
N(inode) = 1;
|
|
for (int icont = 0; icont < nSD_; ++icont) {
|
|
N(inode) -= point(icont);
|
|
}
|
|
} else {
|
|
N(inode) = point(inode-1);
|
|
}
|
|
// Fill dNdr...
|
|
for (int idr = 0; idr < nSD_; ++idr) {
|
|
if (inode == 0) {
|
|
dNdr(idr,inode) = -1;
|
|
} else {
|
|
dNdr(idr,inode) = (inode == (idr + 1)) ? 1 : 0;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
} // namespace ATC
|
|
|