/usr/include/trilinos/Intrepid_CellToolsDef.hpp is in libtrilinos-intrepid-dev 12.4.2-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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// ************************************************************************
//
// Intrepid Package
// Copyright (2007) Sandia Corporation
//
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
// license for use of this work by or on behalf of the U.S. Government.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// 1. Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// 2. Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// 3. Neither the name of the Corporation nor the names of the
// contributors may be used to endorse or promote products derived from
// this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Questions? Contact Pavel Bochev (pbboche@sandia.gov)
// Denis Ridzal (dridzal@sandia.gov), or
// Kara Peterson (kjpeter@sandia.gov)
//
// ************************************************************************
// @HEADER
/** \file Intrepid_CellToolsDef.hpp
\brief Definition file for the Intrepid::CellTools class.
\author Created by P. Bochev and D. Ridzal.
*/
#ifndef INTREPID_CELLTOOLSDEF_HPP
#define INTREPID_CELLTOOLSDEF_HPP
// disable clang warnings
#if defined (__clang__) && !defined (__INTEL_COMPILER)
#pragma clang system_header
#endif
namespace Intrepid {
template<class Scalar>
const FieldContainer<double>& CellTools<Scalar>::getSubcellParametrization(const int subcellDim,
const shards::CellTopology& parentCell){
#ifdef HAVE_INTREPID_DEBUG
TEUCHOS_TEST_FOR_EXCEPTION( !(hasReferenceCell(parentCell) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getSubcellParametrization): the specified cell topology does not have a reference cell.");
TEUCHOS_TEST_FOR_EXCEPTION( !( (1 <= subcellDim) && (subcellDim <= 2 ) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getSubcellParametrization): parametrization defined only for 1 and 2-dimensional subcells.");
#endif
// Coefficients of the coordinate functions defining the parametrization maps are stored in
// rank-3 arrays with dimensions (SC, PCD, COEF) where:
// - SC is the subcell count of subcells with the specified dimension in the parent cell
// - PCD is Parent Cell Dimension, which gives the number of coordinate functions in the map:
// PCD = 2 for standard 2D cells and non-standard 2D cells: shell line and beam
// PCD = 3 for standard 3D cells and non-standard 3D cells: shell Tri and Quad
// - COEF is number of coefficients needed to specify a coordinate function:
// COEFF = 2 for edge parametrizations
// COEFF = 3 for both Quad and Tri face parametrizations. Because all Quad reference faces
// are affine, the coefficient of the bilinear term u*v is zero and is not stored, i.e.,
// 3 coefficients are sufficient to store Quad face parameterization maps.
//
// Arrays are sized and filled only when parametrization of a particular subcell is requested
// by setSubcellParametrization.
// Edge maps for 2D non-standard cells: ShellLine and Beam
static FieldContainer<double> lineEdges; static int lineEdgesSet = 0;
// Edge maps for 2D standard cells: Triangle and Quadrilateral
static FieldContainer<double> triEdges; static int triEdgesSet = 0;
static FieldContainer<double> quadEdges; static int quadEdgesSet = 0;
// Edge maps for 3D non-standard cells: Shell Tri and Quad
static FieldContainer<double> shellTriEdges; static int shellTriEdgesSet = 0;
static FieldContainer<double> shellQuadEdges; static int shellQuadEdgesSet = 0;
// Edge maps for 3D standard cells:
static FieldContainer<double> tetEdges; static int tetEdgesSet = 0;
static FieldContainer<double> hexEdges; static int hexEdgesSet = 0;
static FieldContainer<double> pyrEdges; static int pyrEdgesSet = 0;
static FieldContainer<double> wedgeEdges; static int wedgeEdgesSet = 0;
// Face maps for 3D non-standard cells: Shell Triangle and Quadrilateral
static FieldContainer<double> shellTriFaces; static int shellTriFacesSet = 0;
static FieldContainer<double> shellQuadFaces; static int shellQuadFacesSet = 0;
// Face maps for 3D standard cells:
static FieldContainer<double> tetFaces; static int tetFacesSet = 0;
static FieldContainer<double> hexFaces; static int hexFacesSet = 0;
static FieldContainer<double> pyrFaces; static int pyrFacesSet = 0;
static FieldContainer<double> wedgeFaces; static int wedgeFacesSet = 0;
// Select subcell parametrization according to its parent cell type
switch(parentCell.getKey() ) {
// Tet cells
case shards::Tetrahedron<4>::key:
case shards::Tetrahedron<8>::key:
case shards::Tetrahedron<10>::key:
case shards::Tetrahedron<11>::key:
if(subcellDim == 2) {
if(!tetFacesSet){
setSubcellParametrization(tetFaces, subcellDim, parentCell);
tetFacesSet = 1;
}
return tetFaces;
}
else if(subcellDim == 1) {
if(!tetEdgesSet){
setSubcellParametrization(tetEdges, subcellDim, parentCell);
tetEdgesSet = 1;
}
return tetEdges;
}
else{
TEUCHOS_TEST_FOR_EXCEPTION( (subcellDim != 1 || subcellDim != 2), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getSubcellParametrization): Tet parametrizations defined for 1 and 2-subcells only");
}
break;
// Hex cells
case shards::Hexahedron<8>::key:
case shards::Hexahedron<20>::key:
case shards::Hexahedron<27>::key:
if(subcellDim == 2) {
if(!hexFacesSet){
setSubcellParametrization(hexFaces, subcellDim, parentCell);
hexFacesSet = 1;
}
return hexFaces;
}
else if(subcellDim == 1) {
if(!hexEdgesSet){
setSubcellParametrization(hexEdges, subcellDim, parentCell);
hexEdgesSet = 1;
}
return hexEdges;
}
else{
TEUCHOS_TEST_FOR_EXCEPTION( (subcellDim != 1 || subcellDim != 2), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getSubcellParametrization): Hex parametrizations defined for 1 and 2-subcells only");
}
break;
// Pyramid cells
case shards::Pyramid<5>::key:
case shards::Pyramid<13>::key:
case shards::Pyramid<14>::key:
if(subcellDim == 2) {
if(!pyrFacesSet){
setSubcellParametrization(pyrFaces, subcellDim, parentCell);
pyrFacesSet = 1;
}
return pyrFaces;
}
else if(subcellDim == 1) {
if(!pyrEdgesSet){
setSubcellParametrization(pyrEdges, subcellDim, parentCell);
pyrEdgesSet = 1;
}
return pyrEdges;
}
else {
TEUCHOS_TEST_FOR_EXCEPTION( (subcellDim != 1 || subcellDim != 2), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getSubcellParametrization): Pyramid parametrizations defined for 1 and 2-subcells only");
}
break;
// Wedge cells
case shards::Wedge<6>::key:
case shards::Wedge<15>::key:
case shards::Wedge<18>::key:
if(subcellDim == 2) {
if(!wedgeFacesSet){
setSubcellParametrization(wedgeFaces, subcellDim, parentCell);
wedgeFacesSet = 1;
}
return wedgeFaces;
}
else if(subcellDim == 1) {
if(!wedgeEdgesSet){
setSubcellParametrization(wedgeEdges, subcellDim, parentCell);
wedgeEdgesSet = 1;
}
return wedgeEdges;
}
else {
TEUCHOS_TEST_FOR_EXCEPTION( (subcellDim != 1 || subcellDim != 2), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getSubcellParametrization): Wedge parametrization defined for 1 and 2-subcells only");
}
break;
//
// Standard 2D cells have only 1-subcells
//
case shards::Triangle<3>::key:
case shards::Triangle<4>::key:
case shards::Triangle<6>::key:
if(subcellDim == 1) {
if(!triEdgesSet){
setSubcellParametrization(triEdges, subcellDim, parentCell);
triEdgesSet = 1;
}
return triEdges;
}
else{
TEUCHOS_TEST_FOR_EXCEPTION( true, std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getSubcellParametrization): Triangle parametrizations defined for 1-subcells only");
}
break;
case shards::Quadrilateral<4>::key:
case shards::Quadrilateral<8>::key:
case shards::Quadrilateral<9>::key:
if(subcellDim == 1) {
if(!quadEdgesSet){
setSubcellParametrization(quadEdges, subcellDim, parentCell);
quadEdgesSet = 1;
}
return quadEdges;
}
else{
TEUCHOS_TEST_FOR_EXCEPTION( true, std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getSubcellParametrization): Quad parametrizations defined for 1-subcells only");
}
break;
//
// Non-standard 3D Shell Tri and Quad cells have 1 and 2-subcells. Because they are 3D cells
// can't reuse edge parametrization arrays for 2D Triangle and Quadrilateral.
//
case shards::ShellTriangle<3>::key:
case shards::ShellTriangle<6>::key:
if(subcellDim == 2) {
if(!shellTriFacesSet){
setSubcellParametrization(shellTriFaces, subcellDim, parentCell);
shellTriFacesSet = 1;
}
return shellTriFaces;
}
else if(subcellDim == 1) {
if(!shellTriEdgesSet){
setSubcellParametrization(shellTriEdges, subcellDim, parentCell);
shellTriEdgesSet = 1;
}
return shellTriEdges;
}
else if( subcellDim != 1 || subcellDim != 2){
TEUCHOS_TEST_FOR_EXCEPTION( true, std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getSubcellParametrization): Shell Triangle parametrizations defined for 1 and 2-subcells only");
}
break;
case shards::ShellQuadrilateral<4>::key:
case shards::ShellQuadrilateral<8>::key:
case shards::ShellQuadrilateral<9>::key:
if(subcellDim == 2) {
if(!shellQuadFacesSet){
setSubcellParametrization(shellQuadFaces, subcellDim, parentCell);
shellQuadFacesSet = 1;
}
return shellQuadFaces;
}
else if(subcellDim == 1) {
if(!shellQuadEdgesSet){
setSubcellParametrization(shellQuadEdges, subcellDim, parentCell);
shellQuadEdgesSet = 1;
}
return shellQuadEdges;
}
else if( subcellDim != 1 || subcellDim != 2){
TEUCHOS_TEST_FOR_EXCEPTION( true, std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getSubcellParametrization): Shell Quad parametrizations defined for 1 and 2-subcells only");
}
break;
//
// Non-standard 2D cells: Shell Lines and Beams have 1-subcells
//
case shards::ShellLine<2>::key:
case shards::ShellLine<3>::key:
case shards::Beam<2>::key:
case shards::Beam<3>::key:
if(subcellDim == 1) {
if(!lineEdgesSet){
setSubcellParametrization(lineEdges, subcellDim, parentCell);
lineEdgesSet = 1;
}
return lineEdges;
}
else{
TEUCHOS_TEST_FOR_EXCEPTION( true, std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getSubcellParametrization): shell line/beam parametrizations defined for 1-subcells only");
}
break;
default:
TEUCHOS_TEST_FOR_EXCEPTION( true, std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getSubcellParametrization): invalid cell topology.");
}//cell key
// To disable compiler warning, should never be reached
return lineEdges;
}
template<class Scalar>
void CellTools<Scalar>::setSubcellParametrization(FieldContainer<double>& subcellParametrization,
const int subcellDim,
const shards::CellTopology& parentCell)
{
#ifdef HAVE_INTREPID_DEBUG
TEUCHOS_TEST_FOR_EXCEPTION( !(hasReferenceCell(parentCell) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::setSubcellParametrization): the specified cell topology does not have a reference cell.");
TEUCHOS_TEST_FOR_EXCEPTION( !( (1 <= subcellDim) && (subcellDim <= 2 ) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::setSubcellParametrization): parametrization defined only for 1 and 2-dimensional subcells.");
#endif
// subcellParametrization is rank-3 FieldContainer with dimensions (SC, PCD, COEF) where:
// - SC is the subcell count of subcells with the specified dimension in the parent cell
// - PCD is Parent Cell Dimension, which gives the number of coordinate functions in the map
// PCD = 2 for standard 2D cells and non-standard 2D cells: shell line and beam
// PCD = 3 for standard 3D cells and non-standard 3D cells: shell Tri and Quad
// - COEF is number of coefficients needed to specify a coordinate function:
// COEFF = 2 for edge parametrizations
// COEFF = 3 for both Quad and Tri face parametrizations. Because all Quad reference faces
// are affine, the coefficient of the bilinear term u*v is zero and is not stored, i.e.,
// 3 coefficients are sufficient to store Quad face parameterization maps.
//
// Edge parametrization maps [-1,1] to edge defined by (v0, v1)
// Face parametrization maps [-1,1]^2 to quadrilateral face (v0, v1, v2, v3), or
// standard 2-simplex {(0,0),(1,0),(0,1)} to traingle face (v0, v1, v2).
// This defines orientation-preserving parametrizations with respect to reference edge and
// face orientations induced by their vertex order.
// get subcellParametrization dimensions: (sc, pcd, coeff)
unsigned sc = parentCell.getSubcellCount(subcellDim);
unsigned pcd = parentCell.getDimension();
unsigned coeff = (subcellDim == 1) ? 2 : 3;
// Resize container
subcellParametrization.resize(sc, pcd, coeff);
// Edge parametrizations of 2D and 3D cells (shell lines and beams are 2D cells with edges)
if(subcellDim == 1){
for(unsigned subcellOrd = 0; subcellOrd < sc; subcellOrd++){
int v0ord = parentCell.getNodeMap(subcellDim, subcellOrd, 0);
int v1ord = parentCell.getNodeMap(subcellDim, subcellOrd, 1);
// vertexK[0] = x_k; vertexK[1] = y_k; vertexK[2] = z_k; z_k = 0 for 2D cells
// Note that ShellLine and Beam are 2D cells!
const double* v0 = getReferenceVertex(parentCell, v0ord);
const double* v1 = getReferenceVertex(parentCell, v1ord);
// x(t) = (x0 + x1)/2 + t*(x1 - x0)/2
subcellParametrization(subcellOrd, 0, 0) = (v0[0] + v1[0])/2.0;
subcellParametrization(subcellOrd, 0, 1) = (v1[0] - v0[0])/2.0;
// y(t) = (y0 + y1)/2 + t*(y1 - y0)/2
subcellParametrization(subcellOrd, 1, 0) = (v0[1] + v1[1])/2.0;
subcellParametrization(subcellOrd, 1, 1) = (v1[1] - v0[1])/2.0;
if( pcd == 3 ) {
// z(t) = (z0 + z1)/2 + t*(z1 - z0)/2
subcellParametrization(subcellOrd, 2, 0) = (v0[2] + v1[2])/2.0;
subcellParametrization(subcellOrd, 2, 1) = (v1[2] - v0[2])/2.0;
}
}// for loop over 1-subcells
}
// Face parametrizations of 3D cells: (shell Tri and Quad are 3D cells with faces)
// A 3D cell can have both Tri and Quad faces, but because they are affine images of the
// parametrization domain, 3 coefficients are enough to store them in both cases.
else if(subcellDim == 2) {
for(unsigned subcellOrd = 0; subcellOrd < sc; subcellOrd++){
switch(parentCell.getKey(subcellDim,subcellOrd)){
// Admissible triangular faces for 3D cells in Shards:
case shards::Triangle<3>::key:
case shards::Triangle<4>::key:
case shards::Triangle<6>::key:
{
int v0ord = parentCell.getNodeMap(subcellDim, subcellOrd, 0);
int v1ord = parentCell.getNodeMap(subcellDim, subcellOrd, 1);
int v2ord = parentCell.getNodeMap(subcellDim, subcellOrd, 2);
const double* v0 = getReferenceVertex(parentCell, v0ord);
const double* v1 = getReferenceVertex(parentCell, v1ord);
const double* v2 = getReferenceVertex(parentCell, v2ord);
// x(u,v) = x0 + (x1 - x0)*u + (x2 - x0)*v
subcellParametrization(subcellOrd, 0, 0) = v0[0];
subcellParametrization(subcellOrd, 0, 1) = v1[0] - v0[0];
subcellParametrization(subcellOrd, 0, 2) = v2[0] - v0[0];
// y(u,v) = y0 + (y1 - y0)*u + (y2 - y0)*v
subcellParametrization(subcellOrd, 1, 0) = v0[1];
subcellParametrization(subcellOrd, 1, 1) = v1[1] - v0[1];
subcellParametrization(subcellOrd, 1, 2) = v2[1] - v0[1];
// z(u,v) = z0 + (z1 - z0)*u + (z2 - z0)*v
subcellParametrization(subcellOrd, 2, 0) = v0[2];
subcellParametrization(subcellOrd, 2, 1) = v1[2] - v0[2];
subcellParametrization(subcellOrd, 2, 2) = v2[2] - v0[2];
}
break;
// Admissible quadrilateral faces for 3D cells in Shards:
case shards::Quadrilateral<4>::key:
case shards::Quadrilateral<8>::key:
case shards::Quadrilateral<9>::key:
{
int v0ord = parentCell.getNodeMap(subcellDim, subcellOrd, 0);
int v1ord = parentCell.getNodeMap(subcellDim, subcellOrd, 1);
int v2ord = parentCell.getNodeMap(subcellDim, subcellOrd, 2);
int v3ord = parentCell.getNodeMap(subcellDim, subcellOrd, 3);
const double* v0 = getReferenceVertex(parentCell, v0ord);
const double* v1 = getReferenceVertex(parentCell, v1ord);
const double* v2 = getReferenceVertex(parentCell, v2ord);
const double* v3 = getReferenceVertex(parentCell, v3ord);
// x(u,v) = (x0+x1+x2+x3)/4+u*(-x0+x1+x2-x3)/4+v*(-x0-x1+x2+x3)/4+uv*(0=x0-x1+x2-x3)/4
subcellParametrization(subcellOrd, 0, 0) = ( v0[0] + v1[0] + v2[0] + v3[0])/4.0;
subcellParametrization(subcellOrd, 0, 1) = (-v0[0] + v1[0] + v2[0] - v3[0])/4.0;
subcellParametrization(subcellOrd, 0, 2) = (-v0[0] - v1[0] + v2[0] + v3[0])/4.0;
// y(u,v) = (y0+y1+y2+y3)/4+u*(-y0+y1+y2-y3)/4+v*(-y0-y1+y2+y3)/4+uv*(0=y0-y1+y2-y3)/4
subcellParametrization(subcellOrd, 1, 0) = ( v0[1] + v1[1] + v2[1] + v3[1])/4.0;
subcellParametrization(subcellOrd, 1, 1) = (-v0[1] + v1[1] + v2[1] - v3[1])/4.0;
subcellParametrization(subcellOrd, 1, 2) = (-v0[1] - v1[1] + v2[1] + v3[1])/4.0;
// z(u,v) = (z0+z1+z2+z3)/4+u*(-z0+z1+z2-z3)/4+v*(-z0-z1+z2+z3)/4+uv*(0=z0-z1+z2-z3)/4
subcellParametrization(subcellOrd, 2, 0) = ( v0[2] + v1[2] + v2[2] + v3[2])/4.0;
subcellParametrization(subcellOrd, 2, 1) = (-v0[2] + v1[2] + v2[2] - v3[2])/4.0;
subcellParametrization(subcellOrd, 2, 2) = (-v0[2] - v1[2] + v2[2] + v3[2])/4.0;
}
break;
default:
TEUCHOS_TEST_FOR_EXCEPTION( true, std::invalid_argument,
">>> ERROR (Intrepid::CellTools::setSubcellParametrization): parametrization not defined for the specified face topology.");
}// switch face topology key
}// for subcellOrd
}
}
template<class Scalar>
const double* CellTools<Scalar>::getReferenceVertex(const shards::CellTopology& cell,
const int vertexOrd){
#ifdef HAVE_INTREPID_DEBUG
TEUCHOS_TEST_FOR_EXCEPTION( !(hasReferenceCell(cell) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceVertex): the specified cell topology does not have a reference cell.");
TEUCHOS_TEST_FOR_EXCEPTION( !( (0 <= vertexOrd) && (vertexOrd < (int)cell.getVertexCount() ) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceVertex): invalid node ordinal for the specified cell topology. ");
#endif
// Simply call getReferenceNode with the base topology of the cell
return getReferenceNode(cell.getBaseCellTopologyData(), vertexOrd);
}
template<class Scalar>
template<class ArraySubcellVert>
void CellTools<Scalar>::getReferenceSubcellVertices(ArraySubcellVert & subcellVertices,
const int subcellDim,
const int subcellOrd,
const shards::CellTopology& parentCell){
#ifdef HAVE_INTREPID_DEBUG
TEUCHOS_TEST_FOR_EXCEPTION( !(hasReferenceCell(parentCell) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceSubcellVertices): the specified cell topology does not have a reference cell.");
// subcellDim can equal the cell dimension because the cell itself is a valid subcell! In this case
// the method will return all cell cellWorkset.
TEUCHOS_TEST_FOR_EXCEPTION( !( (0 <= subcellDim) && (subcellDim <= (int)parentCell.getDimension()) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceSubcellVertices): subcell dimension out of range.");
TEUCHOS_TEST_FOR_EXCEPTION( !( (0 <= subcellOrd) && (subcellOrd < (int)parentCell.getSubcellCount(subcellDim) ) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceSubcellVertices): subcell ordinal out of range.");
// Verify subcellVertices rank and dimensions
{
std::string errmsg = ">>> ERROR (Intrepid::CellTools::getReferenceSubcellVertices):";
TEUCHOS_TEST_FOR_EXCEPTION( !( requireRankRange(errmsg, subcellVertices, 2, 2) ), std::invalid_argument, errmsg);
int subcVertexCount = parentCell.getVertexCount(subcellDim, subcellOrd);
int spaceDim = parentCell.getDimension();
TEUCHOS_TEST_FOR_EXCEPTION( !( requireDimensionRange(errmsg, subcellVertices, 0, subcVertexCount, subcVertexCount) ),
std::invalid_argument, errmsg);
TEUCHOS_TEST_FOR_EXCEPTION( !( requireDimensionRange(errmsg, subcellVertices, 1, spaceDim, spaceDim) ),
std::invalid_argument, errmsg);
}
#endif
// Simply call getReferenceNodes with the base topology
getReferenceSubcellNodes(subcellVertices, subcellDim, subcellOrd, parentCell.getBaseCellTopologyData() );
}
template<class Scalar>
const double* CellTools<Scalar>::getReferenceNode(const shards::CellTopology& cell,
const int nodeOrd){
#ifdef HAVE_INTREPID_DEBUG
TEUCHOS_TEST_FOR_EXCEPTION( !(hasReferenceCell(cell) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceNode): the specified cell topology does not have a reference cell.");
TEUCHOS_TEST_FOR_EXCEPTION( !( (0 <= nodeOrd) && (nodeOrd < (int)cell.getNodeCount() ) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceNode): invalid node ordinal for the specified cell topology. ");
#endif
// Cartesian coordinates of supported reference cell cellWorkset, padded to three-dimensions.
// Node order follows cell topology definition in Shards
static const double line[2][3] ={
{-1.0, 0.0, 0.0}, { 1.0, 0.0, 0.0}
};
static const double line_3[3][3] = {
{-1.0, 0.0, 0.0}, { 1.0, 0.0, 0.0},
// Extension node: edge midpoint
{ 0.0, 0.0, 0.0}
};
// Triangle topologies
static const double triangle[3][3] = {
{ 0.0, 0.0, 0.0}, { 1.0, 0.0, 0.0}, { 0.0, 1.0, 0.0}
};
static const double triangle_4[4][3] = {
{ 0.0, 0.0, 0.0}, { 1.0, 0.0, 0.0}, { 0.0, 1.0, 0.0},
// Extension node: cell center
{ 1/3, 1/3, 0.0}
};
static const double triangle_6[6][3] = {
{ 0.0, 0.0, 0.0}, { 1.0, 0.0, 0.0}, { 0.0, 1.0, 0.0},
// Extension cellWorkset: 3 edge midpoints
{ 0.5, 0.0, 0.0}, { 0.5, 0.5, 0.0}, { 0.0, 0.5, 0.0}
};
// Quadrilateral topologies
static const double quadrilateral[4][3] = {
{-1.0,-1.0, 0.0}, { 1.0,-1.0, 0.0}, { 1.0, 1.0, 0.0}, {-1.0, 1.0, 0.0}
};
static const double quadrilateral_8[8][3] = {
{-1.0,-1.0, 0.0}, { 1.0,-1.0, 0.0}, { 1.0, 1.0, 0.0}, {-1.0, 1.0, 0.0},
// Extension cellWorkset: 4 edge midpoints
{ 0.0,-1.0, 0.0}, { 1.0, 0.0, 0.0}, { 0.0, 1.0, 0.0}, {-1.0, 0.0, 0.0}
};
static const double quadrilateral_9[9][3] = {
{-1.0,-1.0, 0.0}, { 1.0,-1.0, 0.0}, { 1.0, 1.0, 0.0}, {-1.0, 1.0, 0.0},
// Extension cellWorkset: 4 edge midpoints + 1 cell center
{ 0.0,-1.0, 0.0}, { 1.0, 0.0, 0.0}, { 0.0, 1.0, 0.0}, {-1.0, 0.0, 0.0}, { 0.0, 0.0, 0.0}
};
// Tetrahedron topologies
static const double tetrahedron[4][3] = {
{ 0.0, 0.0, 0.0}, { 1.0, 0.0, 0.0}, { 0.0, 1.0, 0.0}, { 0.0, 0.0, 1.0}
};
static const double tetrahedron_8[8][3] = {
{ 0.0, 0.0, 0.0}, { 1.0, 0.0, 0.0}, { 0.0, 1.0, 0.0}, { 0.0, 0.0, 1.0},
// Extension cellWorkset: 4 face centers (do not follow natural face order - see the cell topology!)
{ 1/3, 0.0, 1/3}, { 1/3, 1/3, 1/3}, { 1/3, 1/3, 0.0}, { 0.0, 1/3, 1/3}
};
static const double tetrahedron_10[10][3] = {
{ 0.0, 0.0, 0.0}, { 1.0, 0.0, 0.0}, { 0.0, 1.0, 0.0}, { 0.0, 0.0, 1.0},
// Extension cellWorkset: 6 edge midpoints
{ 0.5, 0.0, 0.0}, { 0.5, 0.5, 0.0}, { 0.0, 0.5, 0.0}, { 0.0, 0.0, 0.5}, { 0.5, 0.0, 0.5}, { 0.0, 0.5, 0.5}
};
static const double tetrahedron_11[10][3] = {
{ 0.0, 0.0, 0.0}, { 1.0, 0.0, 0.0}, { 0.0, 1.0, 0.0}, { 0.0, 0.0, 1.0},
// Extension cellWorkset: 6 edge midpoints
{ 0.5, 0.0, 0.0}, { 0.5, 0.5, 0.0}, { 0.0, 0.5, 0.0}, { 0.0, 0.0, 0.5}, { 0.5, 0.0, 0.5}, { 0.0, 0.5, 0.5}
};
// Hexahedron topologies
static const double hexahedron[8][3] = {
{-1.0,-1.0,-1.0}, { 1.0,-1.0,-1.0}, { 1.0, 1.0,-1.0}, {-1.0, 1.0,-1.0},
{-1.0,-1.0, 1.0}, { 1.0,-1.0, 1.0}, { 1.0, 1.0, 1.0}, {-1.0, 1.0, 1.0}
};
static const double hexahedron_20[20][3] = {
{-1.0,-1.0,-1.0}, { 1.0,-1.0,-1.0}, { 1.0, 1.0,-1.0}, {-1.0, 1.0,-1.0},
{-1.0,-1.0, 1.0}, { 1.0,-1.0, 1.0}, { 1.0, 1.0, 1.0}, {-1.0, 1.0, 1.0},
// Extension cellWorkset: 12 edge midpoints (do not follow natural edge order - see cell topology!)
{ 0.0,-1.0,-1.0}, { 1.0, 0.0,-1.0}, { 0.0, 1.0,-1.0}, {-1.0, 0.0,-1.0},
{-1.0,-1.0, 0.0}, { 1.0,-1.0, 0.0}, { 1.0, 1.0, 0.0}, {-1.0, 1.0, 0.0},
{ 0.0,-1.0, 1.0}, { 1.0, 0.0, 1.0}, { 0.0, 1.0, 1.0}, {-1.0, 0.0, 1.0}
};
static const double hexahedron_27[27][3] = {
{-1.0,-1.0,-1.0}, { 1.0,-1.0,-1.0}, { 1.0, 1.0,-1.0}, {-1.0, 1.0,-1.0},
{-1.0,-1.0, 1.0}, { 1.0,-1.0, 1.0}, { 1.0, 1.0, 1.0}, {-1.0, 1.0, 1.0},
// Extension cellWorkset: 12 edge midpoints + 1 cell center + 6 face centers (do not follow natural subcell order!)
{ 0.0,-1.0,-1.0}, { 1.0, 0.0,-1.0}, { 0.0, 1.0,-1.0}, {-1.0, 0.0,-1.0},
{-1.0,-1.0, 0.0}, { 1.0,-1.0, 0.0}, { 1.0, 1.0, 0.0}, {-1.0, 1.0, 0.0},
{ 0.0,-1.0, 1.0}, { 1.0, 0.0, 1.0}, { 0.0, 1.0, 1.0}, {-1.0, 0.0, 1.0},
{ 0.0, 0.0, 0.0},
{ 0.0, 0.0,-1.0}, { 0.0, 0.0, 1.0}, {-1.0, 0.0, 0.0}, { 1.0, 0.0, 0.0}, {0.0,-1.0, 0.0}, {0.0, 1.0, 0.0}
};
// Pyramid topologies
static const double pyramid[5][3] = {
{-1.0,-1.0, 0.0}, { 1.0,-1.0, 0.0}, { 1.0, 1.0, 0.0}, {-1.0, 1.0, 0.0}, { 0.0, 0.0, 1.0}
};
static const double pyramid_13[13][3] = {
{-1.0,-1.0, 0.0}, { 1.0,-1.0, 0.0}, { 1.0, 1.0, 0.0}, {-1.0, 1.0, 0.0}, { 0.0, 0.0, 1.0},
// Extension cellWorkset: 8 edge midpoints
{ 0.0,-1.0, 0.0}, { 1.0, 0.0, 0.0}, { 0.0, 1.0, 0.0}, {-1.0, 0.0, 0.0},
{-0.5,-0.5, 0.5}, { 0.5,-0.5, 0.5}, { 0.5, 0.5, 0.5}, {-0.5, 0.5, 0.5}
};
static const double pyramid_14[14][3] = {
{-1.0,-1.0, 0.0}, { 1.0,-1.0, 0.0}, { 1.0, 1.0, 0.0}, {-1.0, 1.0, 0.0}, { 0.0, 0.0, 1.0},
// Extension cellWorkset: 8 edge midpoints + quadrilateral face midpoint
{ 0.0,-1.0, 0.0}, { 1.0, 0.0, 0.0}, { 0.0, 1.0, 0.0}, {-1.0, 0.0, 0.0},
{-0.5,-0.5, 0.5}, { 0.5,-0.5, 0.5}, { 0.5, 0.5, 0.5}, {-0.5, 0.5, 0.5}, { 0.0, 0.0, 0.0}
};
// Wedge topologies
static const double wedge[6][3] = {
{ 0.0, 0.0,-1.0}, { 1.0, 0.0,-1.0}, { 0.0, 1.0,-1.0}, { 0.0, 0.0, 1.0}, { 1.0, 0.0, 1.0}, { 0.0, 1.0, 1.0}
};
static const double wedge_15[15][3] = {
{ 0.0, 0.0,-1.0}, { 1.0, 0.0,-1.0}, { 0.0, 1.0,-1.0}, { 0.0, 0.0, 1.0}, { 1.0, 0.0, 1.0}, { 0.0, 1.0, 1.0},
// Extension cellWorkset: 9 edge midpoints (do not follow natural edge order - see cell topology!)
{ 0.5, 0.0,-1.0}, { 0.5, 0.5,-1.0}, { 0.0, 0.5,-1.0}, { 0.0, 0.0, 0.0}, { 1.0, 0.0, 0.0}, { 0.0, 1.0, 0.0},
{ 0.5, 0.0, 1.0}, { 0.5, 0.5, 1.0}, { 0.0, 0.5, 1.0}
};
static const double wedge_18[18][3] = {
{ 0.0, 0.0,-1.0}, { 1.0, 0.0,-1.0}, { 0.0, 1.0,-1.0}, { 0.0, 0.0, 1.0}, { 1.0, 0.0, 1.0}, { 0.0, 1.0, 1.0},
// Extension cellWorkset: 9 edge midpoints + 3 quad face centers (do not follow natural subcell order - see cell topology!)
{ 0.5, 0.0,-1.0}, { 0.5, 0.5,-1.0}, { 0.0, 0.5,-1.0}, { 0.0, 0.0, 0.0}, { 1.0, 0.0, 0.0}, { 0.0, 1.0, 0.0},
{ 0.5, 0.0, 1.0}, { 0.5, 0.5, 1.0}, { 0.0, 0.5, 1.0},
{ 0.5, 0.0, 0.0}, { 0.5, 0.5, 0.0}, { 0.0, 0.5, 0.0}
};
switch(cell.getKey() ) {
// Base line topologies
case shards::Line<2>::key:
case shards::ShellLine<2>::key:
case shards::Beam<2>::key:
return line[nodeOrd];
break;
// Extended line topologies
case shards::Line<3>::key:
case shards::ShellLine<3>::key:
case shards::Beam<3>::key:
return line_3[nodeOrd];
break;
// Base triangle topologies
case shards::Triangle<3>::key:
case shards::ShellTriangle<3>::key:
return triangle[nodeOrd];
break;
// Extened Triangle topologies
case shards::Triangle<4>::key:
return triangle_4[nodeOrd];
break;
case shards::Triangle<6>::key:
case shards::ShellTriangle<6>::key:
return triangle_6[nodeOrd];
break;
// Base Quadrilateral topologies
case shards::Quadrilateral<4>::key:
case shards::ShellQuadrilateral<4>::key:
return quadrilateral[nodeOrd];
break;
// Extended Quadrilateral topologies
case shards::Quadrilateral<8>::key:
case shards::ShellQuadrilateral<8>::key:
return quadrilateral_8[nodeOrd];
break;
case shards::Quadrilateral<9>::key:
case shards::ShellQuadrilateral<9>::key:
return quadrilateral_9[nodeOrd];
break;
// Base Tetrahedron topology
case shards::Tetrahedron<4>::key:
return tetrahedron[nodeOrd];
break;
// Extended Tetrahedron topologies
case shards::Tetrahedron<8>::key:
return tetrahedron_8[nodeOrd];
break;
case shards::Tetrahedron<10>::key:
return tetrahedron_10[nodeOrd];
break;
case shards::Tetrahedron<11>::key:
return tetrahedron_11[nodeOrd];
break;
// Base Hexahedron topology
case shards::Hexahedron<8>::key:
return hexahedron[nodeOrd];
break;
// Extended Hexahedron topologies
case shards::Hexahedron<20>::key:
return hexahedron_20[nodeOrd];
break;
case shards::Hexahedron<27>::key:
return hexahedron_27[nodeOrd];
break;
// Base Pyramid topology
case shards::Pyramid<5>::key:
return pyramid[nodeOrd];
break;
// Extended pyramid topologies
case shards::Pyramid<13>::key:
return pyramid_13[nodeOrd];
break;
case shards::Pyramid<14>::key:
return pyramid_14[nodeOrd];
break;
// Base Wedge topology
case shards::Wedge<6>::key:
return wedge[nodeOrd];
break;
// Extended Wedge topologies
case shards::Wedge<15>::key:
return wedge_15[nodeOrd];
break;
case shards::Wedge<18>::key:
return wedge_18[nodeOrd];
break;
default:
TEUCHOS_TEST_FOR_EXCEPTION( true, std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceNode): invalid cell topology.");
}
// To disable compiler warning, should never be reached
return line[0];
}
template<class Scalar>
template<class ArraySubcellNode>
void CellTools<Scalar>::getReferenceSubcellNodes(ArraySubcellNode & subcellNodes,
const int subcellDim,
const int subcellOrd,
const shards::CellTopology& parentCell){
#ifdef HAVE_INTREPID_DEBUG
TEUCHOS_TEST_FOR_EXCEPTION( !(hasReferenceCell(parentCell) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceSubcellNodes): the specified cell topology does not have a reference cell.");
// subcellDim can equal the cell dimension because the cell itself is a valid subcell! In this case
// the method will return all cell cellWorkset.
TEUCHOS_TEST_FOR_EXCEPTION( !( (0 <= subcellDim) && (subcellDim <= (int)parentCell.getDimension()) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceSubcellNodes): subcell dimension out of range.");
TEUCHOS_TEST_FOR_EXCEPTION( !( (0 <= subcellOrd) && (subcellOrd < (int)parentCell.getSubcellCount(subcellDim) ) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceSubcellNodes): subcell ordinal out of range.");
// Verify subcellNodes rank and dimensions
{
std::string errmsg = ">>> ERROR (Intrepid::CellTools::getReferenceSubcellNodes):";
TEUCHOS_TEST_FOR_EXCEPTION( !( requireRankRange(errmsg, subcellNodes, 2, 2) ), std::invalid_argument, errmsg);
int subcNodeCount = parentCell.getNodeCount(subcellDim, subcellOrd);
int spaceDim = parentCell.getDimension();
TEUCHOS_TEST_FOR_EXCEPTION( !( requireDimensionRange(errmsg, subcellNodes, 0, subcNodeCount, subcNodeCount) ),
std::invalid_argument, errmsg);
TEUCHOS_TEST_FOR_EXCEPTION( !( requireDimensionRange(errmsg, subcellNodes, 1, spaceDim, spaceDim) ),
std::invalid_argument, errmsg);
}
#endif
// Find how many cellWorkset does the specified subcell have.
int subcNodeCount = parentCell.getNodeCount(subcellDim, subcellOrd);
// Loop over subcell cellWorkset
for(int subcNodeOrd = 0; subcNodeOrd < subcNodeCount; subcNodeOrd++){
// Get the node number relative to the parent reference cell
int cellNodeOrd = parentCell.getNodeMap(subcellDim, subcellOrd, subcNodeOrd);
// Loop over node's Cartesian coordinates
for(int dim = 0; dim < (int)parentCell.getDimension(); dim++){
subcellNodes(subcNodeOrd, dim) = CellTools::getReferenceNode(parentCell, cellNodeOrd)[dim];
}
}
}
template<class Scalar>
int CellTools<Scalar>::hasReferenceCell(const shards::CellTopology& cell) {
switch(cell.getKey() ) {
case shards::Line<2>::key:
case shards::Line<3>::key:
case shards::ShellLine<2>::key:
case shards::ShellLine<3>::key:
case shards::Beam<2>::key:
case shards::Beam<3>::key:
case shards::Triangle<3>::key:
case shards::Triangle<4>::key:
case shards::Triangle<6>::key:
case shards::ShellTriangle<3>::key:
case shards::ShellTriangle<6>::key:
case shards::Quadrilateral<4>::key:
case shards::Quadrilateral<8>::key:
case shards::Quadrilateral<9>::key:
case shards::ShellQuadrilateral<4>::key:
case shards::ShellQuadrilateral<8>::key:
case shards::ShellQuadrilateral<9>::key:
case shards::Tetrahedron<4>::key:
case shards::Tetrahedron<8>::key:
case shards::Tetrahedron<10>::key:
case shards::Tetrahedron<11>::key:
case shards::Hexahedron<8>::key:
case shards::Hexahedron<20>::key:
case shards::Hexahedron<27>::key:
case shards::Pyramid<5>::key:
case shards::Pyramid<13>::key:
case shards::Pyramid<14>::key:
case shards::Wedge<6>::key:
case shards::Wedge<15>::key:
case shards::Wedge<18>::key:
return 1;
break;
default:
return 0;
}
return 0;
}
//============================================================================================//
// //
// Jacobian, inverse Jacobian and Jacobian determinant //
// //
//============================================================================================//
template<class Scalar>
template<class ArrayJac, class ArrayPoint, class ArrayCell>
void CellTools<Scalar>::setJacobian(ArrayJac & jacobian,
const ArrayPoint & points,
const ArrayCell & cellWorkset,
const shards::CellTopology & cellTopo,
const int & whichCell)
{
INTREPID_VALIDATE( validateArguments_setJacobian(jacobian, points, cellWorkset, whichCell, cellTopo) );
ArrayWrapper<Scalar,ArrayJac, Rank<ArrayJac >::value, false>jacobianWrap(jacobian);
ArrayWrapper<Scalar,ArrayPoint, Rank<ArrayPoint >::value, true>pointsWrap(points);
ArrayWrapper<Scalar,ArrayCell, Rank<ArrayCell >::value, true>cellWorksetWrap(cellWorkset);
int spaceDim = (size_t)cellTopo.getDimension();
size_t numCells = static_cast<size_t>(cellWorkset.dimension(0));
//points can be rank-2 (P,D), or rank-3 (C,P,D)
size_t numPoints = (getrank(points) == 2) ? static_cast<size_t>(points.dimension(0)) : static_cast<size_t>(points.dimension(1));
// Jacobian is computed using gradients of an appropriate H(grad) basis function: define RCP to the base class
Teuchos::RCP< Basis< Scalar, FieldContainer<Scalar> > > HGRAD_Basis;
// Choose the H(grad) basis depending on the cell topology. \todo define maps for shells and beams
switch( cellTopo.getKey() ){
// Standard Base topologies (number of cellWorkset = number of vertices)
case shards::Line<2>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_LINE_C1_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Triangle<3>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_TRI_C1_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Quadrilateral<4>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_QUAD_C1_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Tetrahedron<4>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_TET_C1_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Hexahedron<8>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_HEX_C1_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Wedge<6>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_WEDGE_C1_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Pyramid<5>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_PYR_C1_FEM<Scalar, FieldContainer<Scalar> >() );
break;
// Standard Extended topologies
case shards::Triangle<6>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_TRI_C2_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Quadrilateral<9>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_QUAD_C2_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Tetrahedron<10>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_TET_C2_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Tetrahedron<11>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_TET_COMP12_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Hexahedron<20>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_HEX_I2_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Hexahedron<27>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_HEX_C2_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Wedge<15>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_WEDGE_I2_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Wedge<18>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_WEDGE_C2_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Pyramid<13>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_PYR_I2_FEM<Scalar, FieldContainer<Scalar> >() );
break;
// These extended topologies are not used for mapping purposes
case shards::Quadrilateral<8>::key:
TEUCHOS_TEST_FOR_EXCEPTION( (true), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::setJacobian): Cell topology not supported. ");
break;
// Base and Extended Line, Beam and Shell topologies
case shards::Line<3>::key:
case shards::Beam<2>::key:
case shards::Beam<3>::key:
case shards::ShellLine<2>::key:
case shards::ShellLine<3>::key:
case shards::ShellTriangle<3>::key:
case shards::ShellTriangle<6>::key:
case shards::ShellQuadrilateral<4>::key:
case shards::ShellQuadrilateral<8>::key:
case shards::ShellQuadrilateral<9>::key:
TEUCHOS_TEST_FOR_EXCEPTION( (true), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::setJacobian): Cell topology not supported. ");
break;
default:
TEUCHOS_TEST_FOR_EXCEPTION( (true), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::setJacobian): Cell topology not supported.");
}// switch
// Temp (F,P,D) array for the values of basis functions gradients at the reference points
int basisCardinality = HGRAD_Basis -> getCardinality();
FieldContainer<Scalar> basisGrads(basisCardinality, numPoints, spaceDim);
if(getrank(jacobian)==4){
for (size_t i=0; i< static_cast<size_t>(jacobian.dimension(0)); i++){
for (size_t j=0; j< static_cast<size_t>(jacobian.dimension(1)); j++){
for (size_t k=0; k< static_cast<size_t>(jacobian.dimension(2)); k++){
for (size_t l=0; l< static_cast<size_t>(jacobian.dimension(3)); l++){
jacobianWrap(i,j,k,l)=0.0;
}
}
}
}
}
if(getrank(jacobian)==3){
for (size_t i=0; i< static_cast<size_t>(jacobian.dimension(0)); i++){
for (size_t j=0; j< static_cast<size_t>(jacobian.dimension(1)); j++){
for (size_t k=0; k< static_cast<size_t>(jacobian.dimension(2)); k++){
jacobianWrap(i,j,k)=0.0;
}
}
}
}
// Handle separately rank-2 (P,D) and rank-3 (C,P,D) cases of points arrays.
switch(getrank(points)) {
// refPoints is (P,D): a single or multiple cell jacobians computed for a single set of ref. points
case 2:
{
// getValues requires rank-2 (P,D) input array, but points cannot be passed directly as argument because they are a user type
FieldContainer<Scalar> tempPoints( static_cast<size_t>(points.dimension(0)), static_cast<size_t>(points.dimension(1)) );
// Copy point set corresponding to this cell oridinal to the temp (P,D) array
for(size_t pt = 0; pt < static_cast<size_t>(points.dimension(0)); pt++){
for(size_t dm = 0; dm < static_cast<size_t>(points.dimension(1)) ; dm++){
tempPoints(pt, dm) = pointsWrap(pt, dm);
}//dm
}//pt
HGRAD_Basis -> getValues(basisGrads, tempPoints, OPERATOR_GRAD);
// The outer loops select the multi-index of the Jacobian entry: cell, point, row, col
// If whichCell = -1, all jacobians are computed, otherwise a single cell jacobian is computed
size_t cellLoop = (whichCell == -1) ? numCells : 1 ;
if(whichCell == -1) {
for(size_t cellOrd = 0; cellOrd < cellLoop; cellOrd++) {
for(size_t pointOrd = 0; pointOrd < numPoints; pointOrd++) {
for(int row = 0; row < spaceDim; row++){
for(int col = 0; col < spaceDim; col++){
// The entry is computed by contracting the basis index. Number of basis functions and vertices must be the same.
for(int bfOrd = 0; bfOrd < basisCardinality; bfOrd++){
jacobianWrap(cellOrd, pointOrd, row, col) += cellWorksetWrap(cellOrd, bfOrd, row)*basisGrads(bfOrd, pointOrd, col);
} // bfOrd
} // col
} // row
} // pointOrd
} // cellOrd
//}
}
else {
for(size_t cellOrd = 0; cellOrd < cellLoop; cellOrd++) {
for(size_t pointOrd = 0; pointOrd < numPoints; pointOrd++) {
for(int row = 0; row < spaceDim; row++){
for(int col = 0; col < spaceDim; col++){
// The entry is computed by contracting the basis index. Number of basis functions and vertices must be the same.
for(int bfOrd = 0; bfOrd < basisCardinality; bfOrd++){
jacobianWrap(pointOrd, row, col) += cellWorksetWrap(whichCell, bfOrd, row)*basisGrads(bfOrd, pointOrd, col);
} // bfOrd
} // col
} // row
} // pointOrd
} // cellOrd
// }
} // if whichcell
}// case 2
break;
// points is (C,P,D): multiple jacobians computed at multiple point sets, one jacobian per cell
case 3:
{
// getValues requires rank-2 (P,D) input array, refPoints cannot be used as argument: need temp (P,D) array
FieldContainer<Scalar> tempPoints( static_cast<size_t>(points.dimension(1)), static_cast<size_t>(points.dimension(2)) );
for(size_t cellOrd = 0; cellOrd < numCells; cellOrd++) {
// Copy point set corresponding to this cell oridinal to the temp (P,D) array
for(size_t pt = 0; pt < static_cast<size_t>(points.dimension(1)); pt++){
for(size_t dm = 0; dm < static_cast<size_t>(points.dimension(2)) ; dm++){
tempPoints(pt, dm) = pointsWrap(cellOrd, pt, dm);
}//dm
}//pt
// Compute gradients of basis functions at this set of ref. points
HGRAD_Basis -> getValues(basisGrads, tempPoints, OPERATOR_GRAD);
// Compute jacobians for the point set corresponding to the current cellordinal
for(size_t pointOrd = 0; pointOrd < numPoints; pointOrd++) {
for(int row = 0; row < spaceDim; row++){
for(int col = 0; col < spaceDim; col++){
// The entry is computed by contracting the basis index. Number of basis functions and vertices must be the same
for(int bfOrd = 0; bfOrd < basisCardinality; bfOrd++){
jacobianWrap(cellOrd, pointOrd, row, col) += cellWorksetWrap(cellOrd, bfOrd, row)*basisGrads(bfOrd, pointOrd, col);
} // bfOrd
} // col
} // row
} // pointOrd
}//cellOrd
// }
}// case 3
break;
default:
TEUCHOS_TEST_FOR_EXCEPTION( !( (getrank(points) == 2) && (getrank(points) == 3) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::setJacobian): rank 2 or 3 required for points array. ");
}//switch
}
template<class Scalar>
template<class ArrayJacInv, class ArrayJac>
void CellTools<Scalar>::setJacobianInv(ArrayJacInv & jacobianInv,
const ArrayJac & jacobian)
{
INTREPID_VALIDATE( validateArguments_setJacobianInv(jacobianInv, jacobian) );
RealSpaceTools<Scalar>::inverse(jacobianInv, jacobian);
}
/*
template<class Scalar>
template<class ArrayJacInv, class ArrayJac>
void CellTools<Scalar>::setJacobianInvTemp(ArrayJacInv & jacobianInv,
const ArrayJac & jacobian)
{
RealSpaceTools<Scalar>::inverseTemp(jacobianInv, jacobian);
}
*/
/*
template<class Scalar>
template<class ArrayJacDet, class ArrayJac>
void CellTools<Scalar>::setJacobianDet(ArrayJacDet & jacobianDet,
const ArrayJac & jacobian)
{
INTREPID_VALIDATE( validateArguments_setJacobianDetArgs(jacobianDet, jacobian) );
RealSpaceTools<Scalar>::det(jacobianDet, jacobian);
}
*/
template<class Scalar>
template<class ArrayJacDet, class ArrayJac>
void CellTools<Scalar>::setJacobianDet(ArrayJacDet & jacobianDet,
const ArrayJac & jacobian)
{
INTREPID_VALIDATE( validateArguments_setJacobianDetArgs(jacobianDet, jacobian) );
RealSpaceTools<Scalar>::det(jacobianDet, jacobian);
}
//============================================================================================//
// //
// Reference-to-physical frame mapping and its inverse //
// //
//============================================================================================//
template<class Scalar>
template<class ArrayPhysPoint, class ArrayRefPoint, class ArrayCell>
void CellTools<Scalar>::mapToPhysicalFrame(ArrayPhysPoint & physPoints,
const ArrayRefPoint & refPoints,
const ArrayCell & cellWorkset,
const shards::CellTopology & cellTopo,
const int & whichCell)
{
INTREPID_VALIDATE(validateArguments_mapToPhysicalFrame( physPoints, refPoints, cellWorkset, cellTopo, whichCell) );
ArrayWrapper<Scalar,ArrayPhysPoint, Rank<ArrayPhysPoint >::value, false>physPointsWrap(physPoints);
ArrayWrapper<Scalar,ArrayRefPoint, Rank<ArrayRefPoint >::value, true>refPointsWrap(refPoints);
ArrayWrapper<Scalar,ArrayCell, Rank<ArrayCell >::value,true>cellWorksetWrap(cellWorkset);
size_t spaceDim = (size_t)cellTopo.getDimension();
size_t numCells = static_cast<size_t>(cellWorkset.dimension(0));
//points can be rank-2 (P,D), or rank-3 (C,P,D)
size_t numPoints = (getrank(refPoints) == 2) ? static_cast<size_t>(refPoints.dimension(0)) : static_cast<size_t>(refPoints.dimension(1));
// Mapping is computed using an appropriate H(grad) basis function: define RCP to the base class
Teuchos::RCP<Basis<Scalar, FieldContainer<Scalar> > > HGRAD_Basis;
// Choose the H(grad) basis depending on the cell topology. \todo define maps for shells and beams
switch( cellTopo.getKey() ){
// Standard Base topologies (number of cellWorkset = number of vertices)
case shards::Line<2>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_LINE_C1_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Triangle<3>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_TRI_C1_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Quadrilateral<4>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_QUAD_C1_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Tetrahedron<4>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_TET_C1_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Hexahedron<8>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_HEX_C1_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Wedge<6>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_WEDGE_C1_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Pyramid<5>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_PYR_C1_FEM<Scalar, FieldContainer<Scalar> >() );
break;
// Standard Extended topologies
case shards::Triangle<6>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_TRI_C2_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Quadrilateral<9>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_QUAD_C2_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Tetrahedron<10>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_TET_C2_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Tetrahedron<11>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_TET_COMP12_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Hexahedron<20>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_HEX_I2_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Hexahedron<27>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_HEX_C2_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Wedge<15>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_WEDGE_I2_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Wedge<18>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_WEDGE_C2_FEM<Scalar, FieldContainer<Scalar> >() );
break;
case shards::Pyramid<13>::key:
HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_PYR_I2_FEM<Scalar, FieldContainer<Scalar> >() );
break;
// These extended topologies are not used for mapping purposes
case shards::Quadrilateral<8>::key:
TEUCHOS_TEST_FOR_EXCEPTION( (true), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::mapToPhysicalFrame): Cell topology not supported. ");
break;
// Base and Extended Line, Beam and Shell topologies
case shards::Line<3>::key:
case shards::Beam<2>::key:
case shards::Beam<3>::key:
case shards::ShellLine<2>::key:
case shards::ShellLine<3>::key:
case shards::ShellTriangle<3>::key:
case shards::ShellTriangle<6>::key:
case shards::ShellQuadrilateral<4>::key:
case shards::ShellQuadrilateral<8>::key:
case shards::ShellQuadrilateral<9>::key:
TEUCHOS_TEST_FOR_EXCEPTION( (true), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::mapToPhysicalFrame): Cell topology not supported. ");
break;
default:
TEUCHOS_TEST_FOR_EXCEPTION( (true), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::mapToPhysicalFrame): Cell topology not supported.");
}// switch
// Temp (F,P) array for the values of nodal basis functions at the reference points
int basisCardinality = HGRAD_Basis -> getCardinality();
FieldContainer<Scalar> basisVals(basisCardinality, numPoints);
//#ifndef HAVE_INTREPID_KOKKOSCORE
// Initialize physPoints
if(getrank(physPoints)==3){
for(size_t i = 0; i < static_cast<size_t>(physPoints.dimension(0)); i++) {
for(size_t j = 0; j < static_cast<size_t>(physPoints.dimension(1)); j++){
for(size_t k = 0; k < static_cast<size_t>(physPoints.dimension(2)); k++){
physPointsWrap(i,j,k) = 0.0;
}
}
}
}else if(getrank(physPoints)==2){
for(size_t i = 0; i < static_cast<size_t>(physPoints.dimension(0)); i++){
for(size_t j = 0; j < static_cast<size_t>(physPoints.dimension(1)); j++){
physPointsWrap(i,j) = 0.0;
}
}
}
//#else
// Kokkos::deep_copy(physPoints.get_kokkos_view(), Scalar(0.0));
//#endif
// handle separately rank-2 (P,D) and rank-3 (C,P,D) cases of refPoints
switch(getrank(refPoints)) {
// refPoints is (P,D): single set of ref. points is mapped to one or multiple physical cells
case 2:
{
// getValues requires rank-2 (P,D) input array, but refPoints cannot be passed directly as argument because they are a user type
FieldContainer<Scalar> tempPoints( static_cast<size_t>(refPoints.dimension(0)), static_cast<size_t>(refPoints.dimension(1)) );
// Copy point set corresponding to this cell oridinal to the temp (P,D) array
for(size_t pt = 0; pt < static_cast<size_t>(refPoints.dimension(0)); pt++){
for(size_t dm = 0; dm < static_cast<size_t>(refPoints.dimension(1)) ; dm++){
tempPoints(pt, dm) = refPointsWrap(pt, dm);
}//dm
}//pt
HGRAD_Basis -> getValues(basisVals, tempPoints, OPERATOR_VALUE);
// If whichCell = -1, ref pt. set is mapped to all cells, otherwise, the set is mapped to one cell only
size_t cellLoop = (whichCell == -1) ? numCells : 1 ;
// Compute the map F(refPoints) = sum node_coordinate*basis(refPoints)
for(size_t cellOrd = 0; cellOrd < cellLoop; cellOrd++) {
for(size_t pointOrd = 0; pointOrd < numPoints; pointOrd++) {
for(size_t dim = 0; dim < spaceDim; dim++){
for(int bfOrd = 0; bfOrd < basisCardinality; bfOrd++){
if(whichCell == -1){
physPointsWrap(cellOrd, pointOrd, dim) += cellWorksetWrap(cellOrd, bfOrd, dim)*basisVals(bfOrd, pointOrd);
}
else{
physPointsWrap(pointOrd, dim) += cellWorksetWrap(whichCell, bfOrd, dim)*basisVals(bfOrd, pointOrd);
}
} // bfOrd
}// dim
}// pointOrd
}//cellOrd
}// case 2
break;
// refPoints is (C,P,D): multiple sets of ref. points are mapped to matching number of physical cells.
case 3:
{
// getValues requires rank-2 (P,D) input array, refPoints cannot be used as argument: need temp (P,D) array
FieldContainer<Scalar> tempPoints( static_cast<size_t>(refPoints.dimension(1)), static_cast<size_t>(refPoints.dimension(2)) );
// Compute the map F(refPoints) = sum node_coordinate*basis(refPoints)
for(size_t cellOrd = 0; cellOrd < numCells; cellOrd++) {
// Copy point set corresponding to this cell oridinal to the temp (P,D) array
for(size_t pt = 0; pt < static_cast<size_t>(refPoints.dimension(1)); pt++){
for(size_t dm = 0; dm < static_cast<size_t>(refPoints.dimension(2)) ; dm++){
tempPoints(pt, dm) = refPointsWrap(cellOrd, pt, dm);
}//dm
}//pt
// Compute basis values for this set of ref. points
HGRAD_Basis -> getValues(basisVals, tempPoints, OPERATOR_VALUE);
for(size_t pointOrd = 0; pointOrd < numPoints; pointOrd++) {
for(size_t dim = 0; dim < spaceDim; dim++){
for(int bfOrd = 0; bfOrd < basisCardinality; bfOrd++){
physPointsWrap(cellOrd, pointOrd, dim) += cellWorksetWrap(cellOrd, bfOrd, dim)*basisVals(bfOrd, pointOrd);
} // bfOrd
}// dim
}// pointOrd
}//cellOrd
}// case 3
break;
}
}
template<class Scalar>
template<class ArrayRefPoint, class ArrayPhysPoint, class ArrayCell>
void CellTools<Scalar>::mapToReferenceFrame(ArrayRefPoint & refPoints,
const ArrayPhysPoint & physPoints,
const ArrayCell & cellWorkset,
const shards::CellTopology & cellTopo,
const int & whichCell)
{
INTREPID_VALIDATE( validateArguments_mapToReferenceFrame(refPoints, physPoints, cellWorkset, cellTopo, whichCell) );
size_t spaceDim = (size_t)cellTopo.getDimension();
size_t numPoints;
size_t numCells;
// Define initial guesses to be the Cell centers of the reference cell topology
FieldContainer<Scalar> cellCenter(spaceDim);
switch( cellTopo.getKey() ){
// Standard Base topologies (number of cellWorkset = number of vertices)
case shards::Line<2>::key:
cellCenter(0) = 0.0; break;
case shards::Triangle<3>::key:
case shards::Triangle<6>::key:
cellCenter(0) = 1./3.; cellCenter(1) = 1./3.; break;
case shards::Quadrilateral<4>::key:
case shards::Quadrilateral<9>::key:
cellCenter(0) = 0.0; cellCenter(1) = 0.0; break;
case shards::Tetrahedron<4>::key:
case shards::Tetrahedron<10>::key:
case shards::Tetrahedron<11>::key:
cellCenter(0) = 1./6.; cellCenter(1) = 1./6.; cellCenter(2) = 1./6.; break;
case shards::Hexahedron<8>::key:
case shards::Hexahedron<20>::key:
case shards::Hexahedron<27>::key:
cellCenter(0) = 0.0; cellCenter(1) = 0.0; cellCenter(2) = 0.0; break;
case shards::Wedge<6>::key:
case shards::Wedge<15>::key:
case shards::Wedge<18>::key:
cellCenter(0) = 1./3.; cellCenter(1) = 1./3.; cellCenter(2) = 0.0; break;
case shards::Pyramid<5>::key:
case shards::Pyramid<13>::key:
cellCenter(0) = 0.; cellCenter(1) = 0.; cellCenter(2) = 0.25; break;
// These extended topologies are not used for mapping purposes
case shards::Quadrilateral<8>::key:
TEUCHOS_TEST_FOR_EXCEPTION( (true), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::mapToReferenceFrame): Cell topology not supported. ");
break;
// Base and Extended Line, Beam and Shell topologies
case shards::Line<3>::key:
case shards::Beam<2>::key:
case shards::Beam<3>::key:
case shards::ShellLine<2>::key:
case shards::ShellLine<3>::key:
case shards::ShellTriangle<3>::key:
case shards::ShellTriangle<6>::key:
case shards::ShellQuadrilateral<4>::key:
case shards::ShellQuadrilateral<8>::key:
case shards::ShellQuadrilateral<9>::key:
TEUCHOS_TEST_FOR_EXCEPTION( (true), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::mapToReferenceFrame): Cell topology not supported. ");
break;
default:
TEUCHOS_TEST_FOR_EXCEPTION( (true), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::mapToReferenceFrame): Cell topology not supported.");
}// switch key
// Resize initial guess depending on the rank of the physical points array
FieldContainer<Scalar> initGuess;
// Default: map (C,P,D) array of physical pt. sets to (C,P,D) array. Requires (C,P,D) initial guess.
if(whichCell == -1){
numPoints = static_cast<size_t>(physPoints.dimension(1));
numCells = static_cast<size_t>(cellWorkset.dimension(0));
initGuess.resize(numCells, numPoints, spaceDim);
// Set initial guess:
for(size_t c = 0; c < numCells; c++){
for(size_t p = 0; p < numPoints; p++){
for(size_t d = 0; d < spaceDim; d++){
initGuess(c, p, d) = cellCenter(d);
}// d
}// p
}// c
}
// Custom: map (P,D) array of physical pts. to (P,D) array. Requires (P,D) initial guess.
else {
numPoints = static_cast<size_t>(physPoints.dimension(0));
initGuess.resize(numPoints, spaceDim);
// Set initial guess:
for(size_t p = 0; p < numPoints; p++){
for(size_t d = 0; d < spaceDim; d++){
initGuess(p, d) = cellCenter(d);
}// d
}// p
}
// Call method with initial guess
mapToReferenceFrameInitGuess(refPoints, initGuess, physPoints, cellWorkset, cellTopo, whichCell);
}
template<class Scalar>
template<class ArrayRefPoint, class ArrayInitGuess, class ArrayPhysPoint, class ArrayCell>
void CellTools<Scalar>::mapToReferenceFrameInitGuess(ArrayRefPoint & refPoints,
const ArrayInitGuess & initGuess,
const ArrayPhysPoint & physPoints,
const ArrayCell & cellWorkset,
const shards::CellTopology & cellTopo,
const int & whichCell)
{
ArrayWrapper<Scalar,ArrayInitGuess, Rank<ArrayInitGuess >::value, true>initGuessWrap(initGuess);
ArrayWrapper<Scalar,ArrayRefPoint, Rank<ArrayRefPoint >::value, false>refPointsWrap(refPoints);
INTREPID_VALIDATE( validateArguments_mapToReferenceFrame(refPoints, initGuess, physPoints, cellWorkset, cellTopo, whichCell) );
size_t spaceDim = (size_t)cellTopo.getDimension();
size_t numPoints;
size_t numCells=0;
// Temp arrays for Newton iterates and Jacobians. Resize according to rank of ref. point array
FieldContainer<Scalar> xOld;
FieldContainer<Scalar> xTem;
FieldContainer<Scalar> jacobian;
FieldContainer<Scalar> jacobInv;
FieldContainer<Scalar> error;
FieldContainer<Scalar> cellCenter(spaceDim);
// Default: map (C,P,D) array of physical pt. sets to (C,P,D) array. Requires (C,P,D) temp arrays and (C,P,D,D) Jacobians.
if(whichCell == -1){
numPoints = static_cast<size_t>(physPoints.dimension(1));
numCells = static_cast<size_t>(cellWorkset.dimension(0));
xOld.resize(numCells, numPoints, spaceDim);
xTem.resize(numCells, numPoints, spaceDim);
jacobian.resize(numCells,numPoints, spaceDim, spaceDim);
jacobInv.resize(numCells,numPoints, spaceDim, spaceDim);
error.resize(numCells,numPoints);
// Set initial guess to xOld
for(size_t c = 0; c < numCells; c++){
for(size_t p = 0; p < numPoints; p++){
for(size_t d = 0; d < spaceDim; d++){
xOld(c, p, d) = initGuessWrap(c, p, d);
}// d
}// p
}// c
}
// Custom: map (P,D) array of physical pts. to (P,D) array. Requires (P,D) temp arrays and (P,D,D) Jacobians.
else {
numPoints = static_cast<size_t>(physPoints.dimension(0));
xOld.resize(numPoints, spaceDim);
xTem.resize(numPoints, spaceDim);
jacobian.resize(numPoints, spaceDim, spaceDim);
jacobInv.resize(numPoints, spaceDim, spaceDim);
error.resize(numPoints);
// Set initial guess to xOld
for(size_t p = 0; p < numPoints; p++){
for(size_t d = 0; d < spaceDim; d++){
xOld(p, d) = initGuessWrap(p, d);
}// d
}// p
}
// Newton method to solve the equation F(refPoints) - physPoints = 0:
// refPoints = xOld - DF^{-1}(xOld)*(F(xOld) - physPoints) = xOld + DF^{-1}(xOld)*(physPoints - F(xOld))
for(int iter = 0; iter < INTREPID_MAX_NEWTON; ++iter) {
// Jacobians at the old iterates and their inverses.
setJacobian(jacobian, xOld, cellWorkset, cellTopo, whichCell);
setJacobianInv(jacobInv, jacobian);
// The Newton step.
mapToPhysicalFrame( xTem, xOld, cellWorkset, cellTopo, whichCell ); // xTem <- F(xOld)
RealSpaceTools<Scalar>::subtract( xTem, physPoints, xTem ); // xTem <- physPoints - F(xOld)
RealSpaceTools<Scalar>::matvec( refPoints, jacobInv, xTem); // refPoints <- DF^{-1}( physPoints - F(xOld) )
RealSpaceTools<Scalar>::add( refPoints, xOld ); // refPoints <- DF^{-1}( physPoints - F(xOld) ) + xOld
// l2 error (Euclidean distance) between old and new iterates: |xOld - xNew|
RealSpaceTools<Scalar>::subtract( xTem, xOld, refPoints );
RealSpaceTools<Scalar>::vectorNorm( error, xTem, NORM_TWO );
// Average L2 error for a multiple sets of physical points: error is rank-2 (C,P) array
Scalar totalError;
if(whichCell == -1) {
FieldContainer<Scalar> cellWiseError(numCells);
// error(C,P) -> cellWiseError(P)
RealSpaceTools<Scalar>::vectorNorm( cellWiseError, error, NORM_ONE );
totalError = RealSpaceTools<Scalar>::vectorNorm( cellWiseError, NORM_ONE );
}
//Average L2 error for a single set of physical points: error is rank-1 (P) array
else{
totalError = RealSpaceTools<Scalar>::vectorNorm( error, NORM_ONE );
totalError = totalError;
}
// Stopping criterion:
if (totalError < INTREPID_TOL) {
break;
}
else if ( iter > INTREPID_MAX_NEWTON) {
INTREPID_VALIDATE(std::cout << " Intrepid::CellTools::mapToReferenceFrameInitGuess failed to converge to desired tolerance within "
<< INTREPID_MAX_NEWTON << " iterations\n" );
break;
}
// initialize next Newton step
// xOld = refPoints;
int refPointsRank=getrank(refPoints);
if (refPointsRank==3){
for(size_t i=0;i<static_cast<size_t>(refPoints.dimension(0));i++){
for(size_t j=0;j<static_cast<size_t>(refPoints.dimension(1));j++){
for(size_t k=0;k<static_cast<size_t>(refPoints.dimension(2));k++){
xOld(i,j,k) = refPointsWrap(i,j,k);
}
}
}
}else if(refPointsRank==2){
for(size_t i=0;i<static_cast<size_t>(refPoints.dimension(0));i++){
for(size_t j=0;j<static_cast<size_t>(refPoints.dimension(1));j++){
xOld(i,j) = refPointsWrap(i,j);
}
}
}
} // for(iter)
}
template<class Scalar>
template<class ArraySubcellPoint, class ArrayParamPoint>
void CellTools<Scalar>::mapToReferenceSubcell(ArraySubcellPoint & refSubcellPoints,
const ArrayParamPoint & paramPoints,
const int subcellDim,
const int subcellOrd,
const shards::CellTopology & parentCell){
int cellDim = parentCell.getDimension();
size_t numPts = static_cast<size_t>(paramPoints.dimension(0));
#ifdef HAVE_INTREPID_DEBUG
TEUCHOS_TEST_FOR_EXCEPTION( !(hasReferenceCell(parentCell) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::mapToReferenceSubcell): the specified cell topology does not have a reference cell.");
TEUCHOS_TEST_FOR_EXCEPTION( !( (1 <= subcellDim) && (subcellDim <= 2 ) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::mapToReferenceSubcell): method defined only for 1 and 2-dimensional subcells.");
TEUCHOS_TEST_FOR_EXCEPTION( !( (0 <= subcellOrd) && (subcellOrd < (int)parentCell.getSubcellCount(subcellDim) ) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::mapToReferenceSubcell): subcell ordinal out of range.");
// refSubcellPoints is rank-2 (P,D1), D1 = cell dimension
std::string errmsg = ">>> ERROR (Intrepid::mapToReferenceSubcell):";
TEUCHOS_TEST_FOR_EXCEPTION( !requireRankRange(errmsg, refSubcellPoints, 2,2), std::invalid_argument, errmsg);
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionRange(errmsg, refSubcellPoints, 1, cellDim, cellDim), std::invalid_argument, errmsg);
// paramPoints is rank-2 (P,D2) with D2 = subcell dimension
TEUCHOS_TEST_FOR_EXCEPTION( !requireRankRange(errmsg, paramPoints, 2,2), std::invalid_argument, errmsg);
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionRange(errmsg, paramPoints, 1, subcellDim, subcellDim), std::invalid_argument, errmsg);
// cross check: refSubcellPoints and paramPoints: dimension 0 must match
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionMatch(errmsg, refSubcellPoints, 0, paramPoints, 0), std::invalid_argument, errmsg);
#endif
// Get the subcell map, i.e., the coefficients of the parametrization function for the subcell
const FieldContainer<double>& subcellMap = getSubcellParametrization(subcellDim, parentCell);
// Apply the parametrization map to every point in parameter domain
if(subcellDim == 2) {
for(size_t pt = 0; pt < numPts; pt++){
double u = paramPoints(pt,0);
double v = paramPoints(pt,1);
// map_dim(u,v) = c_0(dim) + c_1(dim)*u + c_2(dim)*v because both Quad and Tri ref faces are affine!
for(int dim = 0; dim < cellDim; dim++){
refSubcellPoints(pt, dim) = subcellMap(subcellOrd, dim, 0) + \
subcellMap(subcellOrd, dim, 1)*u + \
subcellMap(subcellOrd, dim, 2)*v;
}
}
}
else if(subcellDim == 1) {
for(size_t pt = 0; pt < numPts; pt++){
for(int dim = 0; dim < cellDim; dim++) {
refSubcellPoints(pt, dim) = subcellMap(subcellOrd, dim, 0) + subcellMap(subcellOrd, dim, 1)*paramPoints(pt,0);
}
}
}
else{
TEUCHOS_TEST_FOR_EXCEPTION( !( (subcellDim == 1) || (subcellDim == 2) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::mapToReferenceSubcell): method defined only for 1 and 2-subcells");
}
}
template<class Scalar>
template<class ArrayEdgeTangent>
void CellTools<Scalar>::getReferenceEdgeTangent(ArrayEdgeTangent & refEdgeTangent,
const int & edgeOrd,
const shards::CellTopology & parentCell){
int spaceDim = parentCell.getDimension();
#ifdef HAVE_INTREPID_DEBUG
TEUCHOS_TEST_FOR_EXCEPTION( !( (spaceDim == 2) || (spaceDim == 3) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceFaceTangents): two or three-dimensional parent cell required");
TEUCHOS_TEST_FOR_EXCEPTION( !( (0 <= edgeOrd) && (edgeOrd < (int)parentCell.getSubcellCount(1) ) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceFaceTangents): edge ordinal out of bounds");
TEUCHOS_TEST_FOR_EXCEPTION( !( refEdgeTangent.size() == spaceDim ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceFaceTangents): output array size is required to match space dimension");
#endif
// Edge parametrizations are computed in setSubcellParametrization and stored in rank-3 array
// (subcOrd, coordinate, coefficient)
const FieldContainer<double>& edgeMap = getSubcellParametrization(1, parentCell);
// All ref. edge maps have affine coordinate functions: f_dim(u) = C_0(dim) + C_1(dim)*u,
// => edge Tangent: -> C_1(*)
refEdgeTangent(0) = edgeMap(edgeOrd, 0, 1);
refEdgeTangent(1) = edgeMap(edgeOrd, 1, 1);
// Skip last coordinate for 2D parent cells
if(spaceDim == 3) {
refEdgeTangent(2) = edgeMap(edgeOrd, 2, 1);
}
}
template<class Scalar>
template<class ArrayFaceTangentU, class ArrayFaceTangentV>
void CellTools<Scalar>::getReferenceFaceTangents(ArrayFaceTangentU & uTan,
ArrayFaceTangentV & vTan,
const int & faceOrd,
const shards::CellTopology & parentCell){
#ifdef HAVE_INTREPID_DEBUG
int spaceDim = parentCell.getDimension();
TEUCHOS_TEST_FOR_EXCEPTION( !(spaceDim == 3), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceFaceTangents): three-dimensional parent cell required");
TEUCHOS_TEST_FOR_EXCEPTION( !( (0 <= faceOrd) && (faceOrd < (int)parentCell.getSubcellCount(2) ) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceFaceTangents): face ordinal out of bounds");
TEUCHOS_TEST_FOR_EXCEPTION( !( (getrank(uTan) == 1) && (getrank(vTan) == 1) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceFaceTangents): rank = 1 required for output arrays");
TEUCHOS_TEST_FOR_EXCEPTION( !( uTan.dimension(0) == spaceDim ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceFaceTangents): dim0 (spatial dim) must match that of parent cell");
TEUCHOS_TEST_FOR_EXCEPTION( !( vTan.dimension(0) == spaceDim ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceFaceTangents): dim0 (spatial dim) must match that of parent cell");
#endif
// Face parametrizations are computed in setSubcellParametrization and stored in rank-3 array
// (subcOrd, coordinate, coefficient): retrieve this array
const FieldContainer<double>& faceMap = getSubcellParametrization(2, parentCell);
/* All ref. face maps have affine coordinate functions: f_dim(u,v) = C_0(dim) + C_1(dim)*u + C_2(dim)*v
* ` => Tangent vectors are: uTan -> C_1(*); vTan -> C_2(*)
*/
// set uTan -> C_1(*)
uTan(0) = faceMap(faceOrd, 0, 1);
uTan(1) = faceMap(faceOrd, 1, 1);
uTan(2) = faceMap(faceOrd, 2, 1);
// set vTan -> C_2(*)
vTan(0) = faceMap(faceOrd, 0, 2);
vTan(1) = faceMap(faceOrd, 1, 2);
vTan(2) = faceMap(faceOrd, 2, 2);
}
template<class Scalar>
template<class ArraySideNormal>
void CellTools<Scalar>::getReferenceSideNormal(ArraySideNormal & refSideNormal,
const int & sideOrd,
const shards::CellTopology & parentCell){
int spaceDim = parentCell.getDimension();
#ifdef HAVE_INTREPID_DEBUG
TEUCHOS_TEST_FOR_EXCEPTION( !( (spaceDim == 2) || (spaceDim == 3) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceSideNormal): two or three-dimensional parent cell required");
// Check side ordinal: by definition side is subcell whose dimension = spaceDim-1
TEUCHOS_TEST_FOR_EXCEPTION( !( (0 <= sideOrd) && (sideOrd < (int)parentCell.getSubcellCount(spaceDim - 1) ) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceSideNormal): side ordinal out of bounds");
#endif
if(spaceDim == 2){
// 2D parent cells: side = 1D subcell (edge), call the edge tangent method and rotate tangents
getReferenceEdgeTangent(refSideNormal, sideOrd, parentCell);
// rotate t(t1, t2) to get n(t2, -t1) so that (n,t) is positively oriented: det(n1,n2/t1,t2)>0
Scalar temp = refSideNormal(0);
refSideNormal(0) = refSideNormal(1);
refSideNormal(1) = -temp;
}
else{
// 3D parent cell: side = 2D subcell (face), call the face normal method.
getReferenceFaceNormal(refSideNormal, sideOrd, parentCell);
}
}
template<class Scalar>
template<class ArrayFaceNormal>
void CellTools<Scalar>::getReferenceFaceNormal(ArrayFaceNormal & refFaceNormal,
const int & faceOrd,
const shards::CellTopology & parentCell){
int spaceDim = parentCell.getDimension();
#ifdef HAVE_INTREPID_DEBUG
TEUCHOS_TEST_FOR_EXCEPTION( !(spaceDim == 3), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceFaceNormal): three-dimensional parent cell required");
TEUCHOS_TEST_FOR_EXCEPTION( !( (0 <= faceOrd) && (faceOrd < (int)parentCell.getSubcellCount(2) ) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceFaceNormal): face ordinal out of bounds");
TEUCHOS_TEST_FOR_EXCEPTION( !( getrank(refFaceNormal) == 1 ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceFaceNormal): rank = 1 required for output array");
TEUCHOS_TEST_FOR_EXCEPTION( !( static_cast<size_t>(refFaceNormal.dimension(0)) == static_cast<size_t>(spaceDim) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getReferenceFaceNormal): dim0 (spatial dim) must match that of parent cell");
#endif
// Reference face normal = vector product of reference face tangents. Allocate temp FC storage:
FieldContainer<Scalar> uTan(spaceDim);
FieldContainer<Scalar> vTan(spaceDim);
getReferenceFaceTangents(uTan, vTan, faceOrd, parentCell);
// Compute the vector product of the reference face tangents:
RealSpaceTools<Scalar>::vecprod(refFaceNormal, uTan, vTan);
}
template<class Scalar>
template<class ArrayEdgeTangent, class ArrayJac>
void CellTools<Scalar>::getPhysicalEdgeTangents(ArrayEdgeTangent & edgeTangents,
const ArrayJac & worksetJacobians,
const int & worksetEdgeOrd,
const shards::CellTopology & parentCell){
size_t worksetSize = static_cast<size_t>(worksetJacobians.dimension(0));
size_t edgePtCount = static_cast<size_t>(worksetJacobians.dimension(1));
int pCellDim = parentCell.getDimension();
#ifdef HAVE_INTREPID_DEBUG
std::string errmsg = ">>> ERROR (Intrepid::CellTools::getPhysicalEdgeTangents):";
TEUCHOS_TEST_FOR_EXCEPTION( !( (pCellDim == 3) || (pCellDim == 2) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getPhysicalEdgeTangents): 2D or 3D parent cell required");
// (1) edgeTangents is rank-3 (C,P,D) and D=2, or 3 is required
TEUCHOS_TEST_FOR_EXCEPTION( !requireRankRange(errmsg, edgeTangents, 3,3), std::invalid_argument, errmsg);
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionRange(errmsg, edgeTangents, 2, 2,3), std::invalid_argument, errmsg);
// (2) worksetJacobians in rank-4 (C,P,D,D) and D=2, or 3 is required
TEUCHOS_TEST_FOR_EXCEPTION( !requireRankRange(errmsg, worksetJacobians, 4,4), std::invalid_argument, errmsg);
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionRange(errmsg, worksetJacobians, 2, 2,3), std::invalid_argument, errmsg);
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionRange(errmsg, worksetJacobians, 3, 2,3), std::invalid_argument, errmsg);
// (4) cross-check array dimensions: edgeTangents (C,P,D) vs. worksetJacobians (C,P,D,D)
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionMatch(errmsg, edgeTangents, 0,1,2,2, worksetJacobians, 0,1,2,3), std::invalid_argument, errmsg);
#endif
// Temp storage for constant reference edge tangent: rank-1 (D) arrays
FieldContainer<double> refEdgeTan(pCellDim);
getReferenceEdgeTangent(refEdgeTan, worksetEdgeOrd, parentCell);
// Loop over workset faces and edge points
for(size_t pCell = 0; pCell < worksetSize; pCell++){
for(size_t pt = 0; pt < edgePtCount; pt++){
// Apply parent cell Jacobian to ref. edge tangent
for(int i = 0; i < pCellDim; i++){
edgeTangents(pCell, pt, i) = 0.0;
for(int j = 0; j < pCellDim; j++){
edgeTangents(pCell, pt, i) += worksetJacobians(pCell, pt, i, j)*refEdgeTan(j);
}// for j
}// for i
}// for pt
}// for pCell
}
template<class Scalar>
template<class ArrayFaceTangentU, class ArrayFaceTangentV, class ArrayJac>
void CellTools<Scalar>::getPhysicalFaceTangents(ArrayFaceTangentU & faceTanU,
ArrayFaceTangentV & faceTanV,
const ArrayJac & worksetJacobians,
const int & worksetFaceOrd,
const shards::CellTopology & parentCell){
size_t worksetSize = static_cast<size_t>(worksetJacobians.dimension(0));
size_t facePtCount = static_cast<size_t>(worksetJacobians.dimension(1));
int pCellDim = parentCell.getDimension();
#ifdef HAVE_INTREPID_DEBUG
std::string errmsg = ">>> ERROR (Intrepid::CellTools::getPhysicalFaceTangents):";
TEUCHOS_TEST_FOR_EXCEPTION( !(pCellDim == 3), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getPhysicalFaceTangents): three-dimensional parent cell required");
// (1) faceTanU and faceTanV are rank-3 (C,P,D) and D=3 is required
TEUCHOS_TEST_FOR_EXCEPTION( !requireRankRange(errmsg, faceTanU, 3,3), std::invalid_argument, errmsg);
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionRange(errmsg, faceTanU, 2, 3,3), std::invalid_argument, errmsg);
TEUCHOS_TEST_FOR_EXCEPTION( !requireRankRange(errmsg, faceTanV, 3,3), std::invalid_argument, errmsg);
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionRange(errmsg, faceTanV, 2, 3,3), std::invalid_argument, errmsg);
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionMatch(errmsg, faceTanU, faceTanV), std::invalid_argument, errmsg);
// (3) worksetJacobians in rank-4 (C,P,D,D) and D=3 is required
TEUCHOS_TEST_FOR_EXCEPTION( !requireRankRange(errmsg, worksetJacobians, 4,4), std::invalid_argument, errmsg);
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionRange(errmsg, worksetJacobians, 2, 3,3), std::invalid_argument, errmsg);
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionRange(errmsg, worksetJacobians, 3, 3,3), std::invalid_argument, errmsg);
// (4) cross-check array dimensions: faceTanU (C,P,D) vs. worksetJacobians (C,P,D,D)
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionMatch(errmsg, faceTanU, 0,1,2,2, worksetJacobians, 0,1,2,3), std::invalid_argument, errmsg);
#endif
// Temp storage for the pair of constant ref. face tangents: rank-1 (D) arrays
FieldContainer<double> refFaceTanU(pCellDim);
FieldContainer<double> refFaceTanV(pCellDim);
getReferenceFaceTangents(refFaceTanU, refFaceTanV, worksetFaceOrd, parentCell);
// Loop over workset faces and face points
for(size_t pCell = 0; pCell < worksetSize; pCell++){
for(size_t pt = 0; pt < facePtCount; pt++){
// Apply parent cell Jacobian to ref. face tangents
for(int dim = 0; dim < pCellDim; dim++){
faceTanU(pCell, pt, dim) = 0.0;
faceTanV(pCell, pt, dim) = 0.0;
// Unroll loops: parent cell dimension can only be 3
faceTanU(pCell, pt, dim) = \
worksetJacobians(pCell, pt, dim, 0)*refFaceTanU(0) + \
worksetJacobians(pCell, pt, dim, 1)*refFaceTanU(1) + \
worksetJacobians(pCell, pt, dim, 2)*refFaceTanU(2);
faceTanV(pCell, pt, dim) = \
worksetJacobians(pCell, pt, dim, 0)*refFaceTanV(0) + \
worksetJacobians(pCell, pt, dim, 1)*refFaceTanV(1) + \
worksetJacobians(pCell, pt, dim, 2)*refFaceTanV(2);
}// for dim
}// for pt
}// for pCell
}
template<class Scalar>
template<class ArraySideNormal, class ArrayJac>
void CellTools<Scalar>::getPhysicalSideNormals(ArraySideNormal & sideNormals,
const ArrayJac & worksetJacobians,
const int & worksetSideOrd,
const shards::CellTopology & parentCell){
size_t worksetSize = static_cast<size_t>(worksetJacobians.dimension(0));
size_t sidePtCount = static_cast<size_t>(worksetJacobians.dimension(1));
int spaceDim = parentCell.getDimension();
#ifdef HAVE_INTREPID_DEBUG
TEUCHOS_TEST_FOR_EXCEPTION( !( (spaceDim == 2) || (spaceDim == 3) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getPhysicalSideNormals): two or three-dimensional parent cell required");
// Check side ordinal: by definition side is subcell whose dimension = spaceDim-1
TEUCHOS_TEST_FOR_EXCEPTION( !( (0 <= worksetSideOrd) && (worksetSideOrd < (int)parentCell.getSubcellCount(spaceDim - 1) ) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getPhysicalSideNormals): side ordinal out of bounds");
#endif
if(spaceDim == 2){
// 2D parent cells: side = 1D subcell (edge), call the edge tangent method and rotate tangents
getPhysicalEdgeTangents(sideNormals, worksetJacobians, worksetSideOrd, parentCell);
// rotate t(t1, t2) to get n(t2, -t1) so that (n,t) is positively oriented: det(n1,n2/t1,t2)>0
for(size_t cell = 0; cell < worksetSize; cell++){
for(size_t pt = 0; pt < sidePtCount; pt++){
Scalar temp = sideNormals(cell, pt, 0);
sideNormals(cell, pt, 0) = sideNormals(cell, pt, 1);
sideNormals(cell, pt, 1) = -temp;
}// for pt
}// for cell
}
else{
// 3D parent cell: side = 2D subcell (face), call the face normal method.
getPhysicalFaceNormals(sideNormals, worksetJacobians, worksetSideOrd, parentCell);
}
}
template<class Scalar>
template<class ArrayFaceNormal, class ArrayJac>
void CellTools<Scalar>::getPhysicalFaceNormals(ArrayFaceNormal & faceNormals,
const ArrayJac & worksetJacobians,
const int & worksetFaceOrd,
const shards::CellTopology & parentCell){
size_t worksetSize = static_cast<size_t>(worksetJacobians.dimension(0));
size_t facePtCount = static_cast<size_t>(worksetJacobians.dimension(1));
int pCellDim = parentCell.getDimension();
#ifdef HAVE_INTREPID_DEBUG
std::string errmsg = ">>> ERROR (Intrepid::CellTools::getPhysicalFaceNormals):";
TEUCHOS_TEST_FOR_EXCEPTION( !(pCellDim == 3), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::getPhysicalFaceNormals): three-dimensional parent cell required");
// (1) faceNormals is rank-3 (C,P,D) and D=3 is required
TEUCHOS_TEST_FOR_EXCEPTION( !requireRankRange(errmsg, faceNormals, 3,3), std::invalid_argument, errmsg);
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionRange(errmsg, faceNormals, 2, 3,3), std::invalid_argument, errmsg);
// (3) worksetJacobians in rank-4 (C,P,D,D) and D=3 is required
TEUCHOS_TEST_FOR_EXCEPTION( !requireRankRange(errmsg, worksetJacobians, 4,4), std::invalid_argument, errmsg);
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionRange(errmsg, worksetJacobians, 2, 3,3), std::invalid_argument, errmsg);
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionRange(errmsg, worksetJacobians, 3, 3,3), std::invalid_argument, errmsg);
// (4) cross-check array dimensions: faceNormals (C,P,D) vs. worksetJacobians (C,P,D,D)
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionMatch(errmsg, faceNormals, 0,1,2,2, worksetJacobians, 0,1,2,3), std::invalid_argument, errmsg);
#endif
// Temp storage for physical face tangents: rank-3 (C,P,D) arrays
FieldContainer<Scalar> faceTanU(worksetSize, facePtCount, pCellDim);
FieldContainer<Scalar> faceTanV(worksetSize, facePtCount, pCellDim);
getPhysicalFaceTangents(faceTanU, faceTanV, worksetJacobians, worksetFaceOrd, parentCell);
// Compute the vector product of the physical face tangents:
RealSpaceTools<Scalar>::vecprod(faceNormals, faceTanU, faceTanV);
}
//============================================================================================//
// //
// Inclusion tests //
// //
//============================================================================================//
template<class Scalar>
int CellTools<Scalar>::checkPointInclusion(const Scalar* point,
const int pointDim,
const shards::CellTopology & cellTopo,
const double & threshold) {
#ifdef HAVE_INTREPID_DEBUG
TEUCHOS_TEST_FOR_EXCEPTION( !(pointDim == (int)cellTopo.getDimension() ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::checkPointInclusion): Point and cell dimensions do not match. ");
#endif
int testResult = 1;
// Using these values in the tests effectievly inflates the reference element to a larger one
double minus_one = -1.0 - threshold;
double plus_one = 1.0 + threshold;
double minus_zero = - threshold;
// A cell with extended topology has the same reference cell as a cell with base topology.
// => testing for inclusion in a reference Triangle<> and a reference Triangle<6> relies on
// on the same set of inequalities. To eliminate unnecessary cases we switch on the base topology
unsigned key = cellTopo.getBaseCellTopologyData() -> key ;
switch( key ) {
case shards::Line<>::key :
if( !(minus_one <= point[0] && point[0] <= plus_one)) testResult = 0;
break;
case shards::Triangle<>::key : {
Scalar distance = std::max( std::max( -point[0], -point[1] ), point[0] + point[1] - 1.0 );
if( distance > threshold ) testResult = 0;
break;
}
case shards::Quadrilateral<>::key :
if(!( (minus_one <= point[0] && point[0] <= plus_one) && \
(minus_one <= point[1] && point[1] <= plus_one) ) ) testResult = 0;
break;
case shards::Tetrahedron<>::key : {
Scalar distance = std::max( std::max(-point[0],-point[1]), \
std::max(-point[2], point[0] + point[1] + point[2] - 1) );
if( distance > threshold ) testResult = 0;
break;
}
case shards::Hexahedron<>::key :
if(!((minus_one <= point[0] && point[0] <= plus_one) && \
(minus_one <= point[1] && point[1] <= plus_one) && \
(minus_one <= point[2] && point[2] <= plus_one))) \
testResult = 0;
break;
// The base of the reference prism is the same as the reference triangle => apply triangle test
// to X and Y coordinates and test whether Z is in [-1,1]
case shards::Wedge<>::key : {
Scalar distance = std::max( std::max( -point[0], -point[1] ), point[0] + point[1] - 1 );
if( distance > threshold || \
point[2] < minus_one || point[2] > plus_one) \
testResult = 0;
break;
}
// The base of the reference pyramid is the same as the reference quad cell => a horizontal plane
// through a point P(x,y,z) intersects the pyramid at a quadrilateral that equals the base quad
// scaled by (1-z) => P(x,y,z) is inside the pyramid <=> (x,y) is in [-1+z,1-z]^2 && 0 <= Z <= 1
case shards::Pyramid<>::key : {
Scalar left = minus_one + point[2];
Scalar right = plus_one - point[2];
if(!( (left <= point[0] && point[0] <= right) && \
(left <= point[1] && point[1] <= right) &&
(minus_zero <= point[2] && point[2] <= plus_one) ) ) \
testResult = 0;
break;
}
default:
TEUCHOS_TEST_FOR_EXCEPTION( !( (key == shards::Line<>::key ) ||
(key == shards::Triangle<>::key) ||
(key == shards::Quadrilateral<>::key) ||
(key == shards::Tetrahedron<>::key) ||
(key == shards::Hexahedron<>::key) ||
(key == shards::Wedge<>::key) ||
(key == shards::Pyramid<>::key) ),
std::invalid_argument,
">>> ERROR (Intrepid::CellTools::checkPointInclusion): Invalid cell topology. ");
}
return testResult;
}
template<class Scalar>
template<class ArrayPoint>
int CellTools<Scalar>::checkPointsetInclusion(const ArrayPoint& points,
const shards::CellTopology & cellTopo,
const double & threshold) {
int rank = points.rank();
#ifdef HAVE_INTREPID_DEBUG
TEUCHOS_TEST_FOR_EXCEPTION( !( (1 <=getrank(points) ) && (getrank(points) <= 3) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::checkPointsetInclusion): rank-1, 2 or 3 required for input points array. ");
// The last dimension of points array at (rank - 1) is the spatial dimension. Must equal the cell dimension.
TEUCHOS_TEST_FOR_EXCEPTION( !((size_t) points.dimension(rank - 1) == (size_t)cellTopo.getDimension() ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::checkPointsetInclusion): Point and cell dimensions do not match. ");
#endif
// create temp output array depending on the rank of the input array
FieldContainer<int> inRefCell;
switch(rank) {
case 1: inRefCell.resize(1); break;
case 2: inRefCell.resize( static_cast<size_t>(points.dimension(0)) ); break;
case 3: inRefCell.resize( static_cast<size_t>(points.dimension(0)), static_cast<size_t>(points.dimension(1)) ); break;
}
// Call the inclusion method which returns inclusion results for all points
checkPointwiseInclusion(inRefCell, points, cellTopo, threshold);
// Check if any points were outside, break when finding the first one
int allInside = 1;
for(int i = 0; i < inRefCell.size(); i++ ){
if (inRefCell[i] == 0) {
allInside = 0;
break;
}
}
return allInside;
}
template<class Scalar>
template<class ArrayIncl, class ArrayPoint>
void CellTools<Scalar>::checkPointwiseInclusion(ArrayIncl & inRefCell,
const ArrayPoint & points,
const shards::CellTopology & cellTopo,
const double & threshold) {
int apRank = points.rank();
#ifdef HAVE_INTREPID_DEBUG
// Verify that points and inRefCell have correct ranks and dimensions
std::string errmsg = ">>> ERROR (Intrepid::CellTools::checkPointwiseInclusion):";
if(getrank(points) == 1) {
TEUCHOS_TEST_FOR_EXCEPTION( !(getrank(inRefCell) == 1 ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::checkPointwiseInclusion): rank-1 input array requires rank-1 output array.");
TEUCHOS_TEST_FOR_EXCEPTION( !(static_cast<size_t>(inRefCell.dimension(0)) == 1), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::checkPointwiseInclusion): rank-1 input array requires dim0 = 1 for output array.");
}
else if(getrank(points) == 2){
TEUCHOS_TEST_FOR_EXCEPTION( !(getrank(inRefCell) == 1 ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::checkPointwiseInclusion): rank-2 input array requires rank-1 output array.");
// dimension 0 of the arrays must match
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionMatch( errmsg, inRefCell, 0, points, 0), std::invalid_argument, errmsg);
}
else if (getrank(points) == 3) {
TEUCHOS_TEST_FOR_EXCEPTION( !(getrank(inRefCell) == 2 ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::checkPointwiseInclusion): rank-3 input array requires rank-2 output array.");
// dimensions 0 and 1 of the arrays must match
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionMatch( errmsg, inRefCell, 0,1, points, 0,1), std::invalid_argument, errmsg);
}
else{
TEUCHOS_TEST_FOR_EXCEPTION( !( (getrank(points) == 1) || (getrank(points) == 2) || (getrank(points) == 3) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::checkPointwiseInclusion): rank-1, 2 or 3 required for input points array. ");
}
// The last dimension of points array at (rank - 1) is the spatial dimension. Must equal the cell dimension.
TEUCHOS_TEST_FOR_EXCEPTION( !((size_t)points.dimension(apRank - 1) == (size_t)cellTopo.getDimension() ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::checkPointwiseInclusion): Point and cell dimensions do not match. ");
#endif
// Initializations
int dim0 = 1;
int dim1 = 1;
int pointDim = 0;
switch(apRank) {
case 1:
pointDim = static_cast<size_t>(points.dimension(0));
break;
case 2:
dim1 = static_cast<size_t>(points.dimension(0));
pointDim = static_cast<size_t>(points.dimension(1));
break;
case 3:
dim0 = static_cast<size_t>(points.dimension(0));
dim1 = static_cast<size_t>(points.dimension(1));
pointDim = static_cast<size_t>(points.dimension(2));
break;
default:
TEUCHOS_TEST_FOR_EXCEPTION( !( (1 <= getrank(points) ) && (getrank(points) <= 3) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::checkPointwiseInclusion): rank-1, 2 or 3 required for input points array. ");
}// switch
// This method can handle up to rank-3 input arrays. The spatial dim must be the last dimension.
// The method uses [] accessor because array rank is determined at runtime and the appropriate
// (i,j,..,k) accessor is not known. Use of [] requires the following offsets:
// for input array = i0*dim1*pointDim + i1*dim1 (computed in 2 pieces: inPtr0 and inPtr1, resp)
// for output array = i0*dim1 (computed in one piece: outPtr0)
int inPtr0 = 0;
int inPtr1 = 0;
int outPtr0 = 0;
Scalar point[3] = {0.0, 0.0, 0.0};
for(int i0 = 0; i0 < dim0; i0++){
outPtr0 = i0*dim1;
inPtr0 = outPtr0*pointDim;
for(int i1 = 0; i1 < dim1; i1++) {
inPtr1 = inPtr0 + i1*pointDim;
point[0] = points[inPtr1];
if(pointDim > 1) {
point[1] = points[inPtr1 + 1];
if(pointDim > 2) {
point[2] = points[inPtr1 + 2];
if(pointDim > 3) {
TEUCHOS_TEST_FOR_EXCEPTION( !( (1 <= pointDim) && (pointDim <= 3)), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::checkPointwiseInclusion): Input array specifies invalid point dimension ");
}
}
} //if(pointDim > 1)
inRefCell[outPtr0 + i1] = checkPointInclusion(point, pointDim, cellTopo, threshold);
} // for (i1)
} // for(i2)
}
template<class Scalar>
template<class ArrayIncl, class ArrayPoint, class ArrayCell>
void CellTools<Scalar>::checkPointwiseInclusion(ArrayIncl & inCell,
const ArrayPoint & points,
const ArrayCell & cellWorkset,
const shards::CellTopology & cell,
const int & whichCell,
const double & threshold)
{
INTREPID_VALIDATE( validateArguments_checkPointwiseInclusion(inCell, points, cellWorkset, whichCell, cell) );
// For cell topologies with reference cells this test maps the points back to the reference cell
// and uses the method for reference cells
unsigned baseKey = cell.getBaseCellTopologyData() -> key;
switch(baseKey){
case shards::Line<>::key :
case shards::Triangle<>::key:
case shards::Quadrilateral<>::key :
case shards::Tetrahedron<>::key :
case shards::Hexahedron<>::key :
case shards::Wedge<>::key :
case shards::Pyramid<>::key :
{
FieldContainer<Scalar> refPoints;
if(getrank(points) == 2){
refPoints.resize(static_cast<size_t>(points.dimension(0)), static_cast<size_t>(points.dimension(1)) );
mapToReferenceFrame(refPoints, points, cellWorkset, cell, whichCell);
checkPointwiseInclusion(inCell, refPoints, cell, threshold );
}
else if(getrank(points) == 3){
refPoints.resize(static_cast<size_t>(points.dimension(0)), static_cast<size_t>(points.dimension(1)), static_cast<size_t>(points.dimension(2)) );
mapToReferenceFrame(refPoints, points, cellWorkset, cell, whichCell);
checkPointwiseInclusion(inCell, refPoints, cell, threshold );
}
break;
}
default:
TEUCHOS_TEST_FOR_EXCEPTION( true, std::invalid_argument,
">>> ERROR (Intrepid::CellTools::checkPointwiseInclusion): cell topology not supported");
}// switch
}
//============================================================================================//
// //
// Validation of input/output arguments for CellTools methods //
// //
//============================================================================================//
template<class Scalar>
template<class ArrayJac, class ArrayPoint, class ArrayCell>
void CellTools<Scalar>::validateArguments_setJacobian(const ArrayJac & jacobian,
const ArrayPoint & points,
const ArrayCell & cellWorkset,
const int & whichCell,
const shards::CellTopology & cellTopo){
// Validate cellWorkset array
TEUCHOS_TEST_FOR_EXCEPTION( (getrank(cellWorkset) != 3), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): rank = 3 required for cellWorkset array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(cellWorkset.dimension(0)) <= 0), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 0 (number of cells) >= 1 required for cellWorkset array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(cellWorkset.dimension(1)) != (size_t)cellTopo.getSubcellCount(0) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 1 (number of cell nodes) of cellWorkset array does not match cell topology");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(cellWorkset.dimension(2)) != (size_t)cellTopo.getDimension() ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 2 (spatial dimension) of cellWorkset array does not match cell dimension");
// validate whichCell. It can be either -1 (default value) or a valid cell ordinal.
TEUCHOS_TEST_FOR_EXCEPTION( !( ( (0 <= whichCell ) && (static_cast<size_t>(whichCell) < static_cast<size_t>(cellWorkset.dimension(0)) ) ) || (whichCell == -1) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): whichCell = -1 or a valid cell ordinal is required.");
// Validate points array: can be rank-2 (P,D) or rank-3 (C,P,D)
// If rank-2: admissible jacobians: rank-3 (P,D,D) or rank-4 (C,P,D,D); admissible whichCell: -1 (default) or cell ordinal.
if(getrank(points) == 2) {
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(points.dimension(0)) <= 0), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 0 (number of points) >= 1 required for points array ");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(points.dimension(1)) != (size_t)cellTopo.getDimension() ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 1 (spatial dimension) of points array does not match cell dimension");
// Validate the output array for the Jacobian: if whichCell == -1 all Jacobians are computed, rank-4 (C,P,D,D) required
if(whichCell == -1) {
TEUCHOS_TEST_FOR_EXCEPTION( (getrank(jacobian) != 4), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): rank = 4 required for jacobian array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(jacobian.dimension(0)) != static_cast<size_t>(cellWorkset.dimension(0))), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 0 (number of cells) of jacobian array must equal dim 0 of cellWorkset array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(jacobian.dimension(1)) != static_cast<size_t>(points.dimension(0))), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 1 (number of points) of jacobian array must equal dim 0 of points array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(jacobian.dimension(2)) != static_cast<size_t>(points.dimension(1))), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 2 (spatial dimension) of jacobian array must equal dim 1 of points array");
TEUCHOS_TEST_FOR_EXCEPTION( !(static_cast<size_t>(jacobian.dimension(2)) == static_cast<size_t>(jacobian.dimension(3)) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 2 = dim 3 (same spatial dimensions) required for jacobian array. ");
TEUCHOS_TEST_FOR_EXCEPTION( !( (0 < static_cast<size_t>(jacobian.dimension(3)) ) && (static_cast<size_t>(jacobian.dimension(3)) < 4) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 2 and dim 3 (spatial dimensions) must be between 1 and 3. ");
}
// A single cell Jacobian is computed when whichCell != -1 (whichCell has been already validated), rank-3 (P,D,D) required
else {
TEUCHOS_TEST_FOR_EXCEPTION( (getrank(jacobian) != 3), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): rank = 3 required for jacobian array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(jacobian.dimension(0)) != static_cast<size_t>(points.dimension(0))), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 0 (number of points) of jacobian array must equal dim 0 of points array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(jacobian.dimension(1)) != static_cast<size_t>(points.dimension(1))), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 1 (spatial dimension) of jacobian array must equal dim 1 of points array");
TEUCHOS_TEST_FOR_EXCEPTION( !(static_cast<size_t>(jacobian.dimension(1)) == static_cast<size_t>(jacobian.dimension(2)) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 1 = dim 2 (same spatial dimensions) required for jacobian array. ");
TEUCHOS_TEST_FOR_EXCEPTION( !( (0 < static_cast<size_t>(jacobian.dimension(1)) ) && (static_cast<size_t>(jacobian.dimension(1)) < 4) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 1 and dim 2 (spatial dimensions) must be between 1 and 3. ");
}
}
// Point array is rank-3 (C,P,D): requires whichCell = -1 and rank-4 (C,P,D,D) jacobians
else if(getrank(points) ==3){
std::string errmsg = ">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian):";
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(points.dimension(0)) != static_cast<size_t>(cellWorkset.dimension(0)) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 0 (number of cells) of points array must equal dim 0 of cellWorkset array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(points.dimension(1)) <= 0), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 1 (number of points) >= 1 required for points array ");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(points.dimension(2)) != (size_t)cellTopo.getDimension() ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 2 (spatial dimension) of points array does not match cell dimension");
TEUCHOS_TEST_FOR_EXCEPTION( (whichCell != -1), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): default value whichCell=-1 required for rank-3 input points");
// rank-4 (C,P,D,D) jacobian required for rank-3 (C,P,D) input points
TEUCHOS_TEST_FOR_EXCEPTION( !requireRankRange(errmsg, jacobian, 4, 4), std::invalid_argument,errmsg);
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(jacobian.dimension(0)) != static_cast<size_t>(points.dimension(0))), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 0 (number of cells) of jacobian array must equal dim 0 of points array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(jacobian.dimension(1)) != static_cast<size_t>(points.dimension(1))), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 1 (number of points) of jacobian array must equal dim 1 of points array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(jacobian.dimension(2)) != static_cast<size_t>(points.dimension(2))), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 2 (spatial dimension) of jacobian array must equal dim 2 of points array");
TEUCHOS_TEST_FOR_EXCEPTION( !(static_cast<size_t>(jacobian.dimension(2)) == static_cast<size_t>(jacobian.dimension(3)) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 2 = dim 3 (same spatial dimensions) required for jacobian array. ");
TEUCHOS_TEST_FOR_EXCEPTION( !( (0 < static_cast<size_t>(jacobian.dimension(3)) ) && (static_cast<size_t>(jacobian.dimension(3)) < 4) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): dim 2 and dim 3 (spatial dimensions) must be between 1 and 3. ");
}
else {
TEUCHOS_TEST_FOR_EXCEPTION( !( (getrank(points) == 2) && (getrank(points) ==3) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobian): rank = 2 or 3 required for points array");
}
}
template<class Scalar>
template<class ArrayJacInv, class ArrayJac>
void CellTools<Scalar>::validateArguments_setJacobianInv(const ArrayJacInv & jacobianInv,
const ArrayJac & jacobian)
{
// Validate input jacobian array: admissible ranks & dimensions are:
// - rank-4 with dimensions (C,P,D,D), or rank-3 with dimensions (P,D,D).
int jacobRank = getrank(jacobian);
TEUCHOS_TEST_FOR_EXCEPTION( !( (jacobRank == 4) || (jacobRank == 3) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobianInv): rank = 4 or 3 required for jacobian array. ");
// Verify correctness of spatial dimensions - they are the last two dimensions of the array: rank-2 and rank-1
TEUCHOS_TEST_FOR_EXCEPTION( !(jacobian.dimension(jacobRank - 1) == jacobian.dimension(jacobRank - 2) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobianInv): dim(rank-2) = dim(rank-2) (same spatial dimensions) required for jacobian array. ");
TEUCHOS_TEST_FOR_EXCEPTION( !( (0 < jacobian.dimension(jacobRank - 1) ) && (jacobian.dimension(jacobRank - 1) < 4) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobianInv): dim(rank-1) and dim(rank-2) (spatial dimensions) must be between 1 and 3. ");
// Validate output jacobianInv array: must have the same rank and dimensions as the input array.
std::string errmsg = ">>> ERROR (Intrepid::CellTools::validateArguments_setJacobianInv):";
TEUCHOS_TEST_FOR_EXCEPTION( !(requireRankMatch(errmsg, jacobianInv, jacobian) ), std::invalid_argument, errmsg);
TEUCHOS_TEST_FOR_EXCEPTION( !(requireDimensionMatch(errmsg, jacobianInv, jacobian) ), std::invalid_argument, errmsg);
}
template<class Scalar>
template<class ArrayJacDet, class ArrayJac>
void CellTools<Scalar>::validateArguments_setJacobianDetArgs(const ArrayJacDet & jacobianDet,
const ArrayJac & jacobian)
{
// Validate input jacobian array: admissible ranks & dimensions are:
// - rank-4 with dimensions (C,P,D,D), or rank-3 with dimensions (P,D,D).
int jacobRank = getrank(jacobian);
TEUCHOS_TEST_FOR_EXCEPTION( !( (jacobRank == 4) || (jacobRank == 3) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobianInv): rank = 4 or 3 required for jacobian array. ");
// Verify correctness of spatial dimensions - they are the last two dimensions of the array: rank-2 and rank-1
TEUCHOS_TEST_FOR_EXCEPTION( !(jacobian.dimension(jacobRank - 1) == jacobian.dimension(jacobRank - 2) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobianInv): dim(rank-2) = dim(rank-2) (same spatial dimensions) required for jacobian array. ");
TEUCHOS_TEST_FOR_EXCEPTION( !( (0 < jacobian.dimension(jacobRank - 1) ) && (jacobian.dimension(jacobRank - 1) < 4) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobianInv): dim(rank-1) and dim(rank-2) (spatial dimensions) must be between 1 and 3. ");
// Validate output jacobianDet array: must be rank-2 with dimensions (C,P) if jacobian was rank-4:
if(jacobRank == 4){
TEUCHOS_TEST_FOR_EXCEPTION( !(getrank(jacobianDet) == 2), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobianDetArgs): rank = 2 required for jacobianDet if jacobian is rank-4. ");
TEUCHOS_TEST_FOR_EXCEPTION( !(static_cast<size_t>(jacobianDet.dimension(0)) == static_cast<size_t>(jacobian.dimension(0)) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobianDetArgs): dim 0 (number of cells) of jacobianDet array must equal dim 0 of jacobian array. ");
TEUCHOS_TEST_FOR_EXCEPTION( !(static_cast<size_t>(jacobianDet.dimension(1)) == static_cast<size_t>(jacobian.dimension(1)) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobianDetArgs): dim 1 (number of points) of jacobianDet array must equal dim 1 of jacobian array.");
}
// must be rank-1 with dimension (P) if jacobian was rank-3
else {
TEUCHOS_TEST_FOR_EXCEPTION( !(getrank(jacobianDet) == 1), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobianDetArgs): rank = 1 required for jacobianDet if jacobian is rank-3. ");
TEUCHOS_TEST_FOR_EXCEPTION( !(static_cast<size_t>(jacobianDet.dimension(0)) == static_cast<size_t>(jacobian.dimension(0)) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_setJacobianDetArgs): dim 0 (number of points) of jacobianDet array must equal dim 0 of jacobian array.");
}
}
template<class Scalar>
template<class ArrayPhysPoint, class ArrayRefPoint, class ArrayCell>
void CellTools<Scalar>::validateArguments_mapToPhysicalFrame(const ArrayPhysPoint & physPoints,
const ArrayRefPoint & refPoints,
const ArrayCell & cellWorkset,
const shards::CellTopology & cellTopo,
const int& whichCell)
{
std::string errmsg = ">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame):";
// Validate cellWorkset array
TEUCHOS_TEST_FOR_EXCEPTION( (getrank(cellWorkset) != 3), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): rank = 3 required for cellWorkset array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(cellWorkset.dimension(0)) <= 0), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): dim 0 (number of cells) >= 1 required for cellWorkset array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(cellWorkset.dimension(1)) != (size_t)cellTopo.getSubcellCount(0) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): dim 1 (number of cell nodes) of cellWorkset array does not match cell topology");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(cellWorkset.dimension(2)) != (size_t)cellTopo.getDimension() ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): dim 2 (spatial dimension) of cellWorkset array does not match cell dimension");
TEUCHOS_TEST_FOR_EXCEPTION( !( ( (0 <= whichCell ) && ((size_t)whichCell < (size_t)cellWorkset.dimension(0) ) ) || (whichCell == -1) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): whichCell = -1 or a valid cell ordinal is required.");
// Validate refPoints array: can be rank-2 (P,D) or rank-3 (C,P,D) array
// If rank-2: admissible output array is (P,D) or (C,P,D); admissible whichCell: -1 (default) or cell ordinal
if(getrank(refPoints) == 2) {
TEUCHOS_TEST_FOR_EXCEPTION( (refPoints.dimension(0) <= 0), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): dim 0 (number of points) >= 1 required for refPoints array ");
TEUCHOS_TEST_FOR_EXCEPTION( ((size_t)refPoints.dimension(1) != (size_t)cellTopo.getDimension() ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): dim 1 (spatial dimension) of refPoints array does not match cell dimension");
// Validate output array: whichCell = -1 requires rank-3 array with dimensions (C,P,D)
if(whichCell == -1) {
TEUCHOS_TEST_FOR_EXCEPTION( ( (getrank(physPoints) != 3) && (whichCell == -1) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): rank = 3 required for physPoints array for the default whichCell value");
TEUCHOS_TEST_FOR_EXCEPTION( ((size_t)physPoints.dimension(0) != (size_t)cellWorkset.dimension(0)), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): dim 0 (number of cells) of physPoints array must equal dim 0 of cellWorkset array");
TEUCHOS_TEST_FOR_EXCEPTION( ((size_t)physPoints.dimension(1) != (size_t)refPoints.dimension(0)), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): dim 1 (number of points) of physPoints array must equal dim 0 of refPoints array");
TEUCHOS_TEST_FOR_EXCEPTION( ((size_t)physPoints.dimension(2) != (size_t)cellTopo.getDimension()), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): dim 2 (spatial dimension) does not match cell dimension ");
}
// 0 <= whichCell < num cells requires rank-2 (P,D) arrays for both refPoints and physPoints
else{
TEUCHOS_TEST_FOR_EXCEPTION( (getrank(physPoints) != 2), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): rank = 2 required for physPoints array");
TEUCHOS_TEST_FOR_EXCEPTION( ((size_t)physPoints.dimension(0) != (size_t)refPoints.dimension(0)), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): dim 0 (number of points) of physPoints array must equal dim 0 of refPoints array");
TEUCHOS_TEST_FOR_EXCEPTION( ((size_t)physPoints.dimension(1) != (size_t)cellTopo.getDimension()), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): dim 1 (spatial dimension) does not match cell dimension ");
}
}
// refPoints is (C,P,D): requires physPoints to be (C,P,D) and whichCell=-1 (because all cell mappings are applied)
else if(getrank(refPoints) == 3) {
// 1. validate refPoints dimensions and rank
TEUCHOS_TEST_FOR_EXCEPTION( ((size_t)refPoints.dimension(0) !=(size_t) cellWorkset.dimension(0) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): dim 0 (number of cells) of refPoints and cellWorkset arraya are required to match ");
TEUCHOS_TEST_FOR_EXCEPTION( (refPoints.dimension(1) <= 0), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): dim 1 (number of points) >= 1 required for refPoints array ");
TEUCHOS_TEST_FOR_EXCEPTION( ((size_t)refPoints.dimension(2) != (size_t)cellTopo.getDimension() ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): dim 2 (spatial dimension) of refPoints array does not match cell dimension");
// 2. whichCell must be -1
TEUCHOS_TEST_FOR_EXCEPTION( (whichCell != -1), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): default value is required for rank-3 refPoints array");
// 3. physPoints must match rank and dimensions of refPoints
TEUCHOS_TEST_FOR_EXCEPTION( !requireRankMatch(errmsg, refPoints, physPoints), std::invalid_argument, errmsg );
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionMatch(errmsg, refPoints, physPoints), std::invalid_argument, errmsg);
}
// if rank is not 2 or 3 throw exception
else {
TEUCHOS_TEST_FOR_EXCEPTION( !( (getrank(refPoints) == 2) || (getrank(refPoints) == 3) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToPhysicalFrame): rank = 2 or 3 required for refPoints array");
}
}
template<class Scalar>
template<class ArrayRefPoint, class ArrayPhysPoint, class ArrayCell>
void CellTools<Scalar>::validateArguments_mapToReferenceFrame(const ArrayRefPoint & refPoints,
const ArrayPhysPoint & physPoints,
const ArrayCell & cellWorkset,
const shards::CellTopology & cellTopo,
const int& whichCell)
{
std::string errmsg = ">>> ERROR (Intrepid::CellTools::validateArguments_mapToReferenceFrame):";
std::string errmsg1 = ">>> ERROR (Intrepid::CellTools::validateArguments_mapToReferenceFrame):";
// Validate cellWorkset array
TEUCHOS_TEST_FOR_EXCEPTION( (getrank(cellWorkset) != 3), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToReferenceFrame): rank = 3 required for cellWorkset array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(cellWorkset.dimension(0)) <= 0), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToReferenceFrame): dim 0 (number of cells) >= 1 required for cellWorkset array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(cellWorkset.dimension(1)) != (size_t)cellTopo.getSubcellCount(0) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToReferenceFrame): dim 1 (number of cell nodes) of cellWorkset array does not match cell topology");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(cellWorkset.dimension(2)) != (size_t)cellTopo.getDimension() ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToReferenceFrame): dim 2 (spatial dimension) of cellWorkset array does not match cell dimension");
// Validate whichCell. It can be either -1 (default value) or a valid celli ordinal.
TEUCHOS_TEST_FOR_EXCEPTION( !( ( (0 <= whichCell ) && ((size_t)whichCell <(size_t) cellWorkset.dimension(0) ) ) || (whichCell == -1) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_mapToReferenceFrame): whichCell = -1 or a valid cell ordinal is required.");
// Admissible ranks and dimensions of refPoints and physPoints depend on whichCell value:
// default is to map multiple sets of points to multiple sets of points. (C,P,D) arrays required
int validRank;
if(whichCell == -1) {
validRank = 3;
errmsg1 += " default value of whichCell requires rank-3 arrays:";
}
// whichCell is valid cell ordinal => we map single set of pts to a single set of pts. (P,D) arrays required
else{
errmsg1 += " rank-2 arrays required when whichCell is valid cell ordinal";
validRank = 2;
}
TEUCHOS_TEST_FOR_EXCEPTION( !requireRankRange(errmsg1, refPoints, validRank,validRank), std::invalid_argument, errmsg1);
TEUCHOS_TEST_FOR_EXCEPTION( !requireRankMatch(errmsg1, physPoints, refPoints), std::invalid_argument, errmsg1);
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionMatch(errmsg1, refPoints, physPoints), std::invalid_argument, errmsg1);
}
template<class Scalar>
template<class ArrayRefPoint, class ArrayInitGuess, class ArrayPhysPoint, class ArrayCell>
void CellTools<Scalar>::validateArguments_mapToReferenceFrame(const ArrayRefPoint & refPoints,
const ArrayInitGuess & initGuess,
const ArrayPhysPoint & physPoints,
const ArrayCell & cellWorkset,
const shards::CellTopology & cellTopo,
const int& whichCell)
{
// Call the method that validates arguments with the default initial guess selection
validateArguments_mapToReferenceFrame(refPoints, physPoints, cellWorkset, cellTopo, whichCell);
// Then check initGuess: its rank and dimensions must match those of physPoints.
std::string errmsg = ">>> ERROR (Intrepid::CellTools::validateArguments_mapToReferenceFrame):";
TEUCHOS_TEST_FOR_EXCEPTION( !requireDimensionMatch(errmsg, initGuess, physPoints), std::invalid_argument, errmsg);
}
template<class Scalar>
template<class ArrayIncl, class ArrayPoint, class ArrayCell>
void CellTools<Scalar>::validateArguments_checkPointwiseInclusion(ArrayIncl & inCell,
const ArrayPoint & physPoints,
const ArrayCell & cellWorkset,
const int & whichCell,
const shards::CellTopology & cell)
{
// Validate cellWorkset array
TEUCHOS_TEST_FOR_EXCEPTION( (getrank(cellWorkset) != 3), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_checkPointwiseInclusion): rank = 3 required for cellWorkset array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(cellWorkset.dimension(0)) <= 0), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_checkPointwiseInclusion): dim 0 (number of cells) >= 1 required for cellWorkset array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(cellWorkset.dimension(1)) != (size_t)cell.getSubcellCount(0) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_checkPointwiseInclusion): dim 1 (number of cell nodes) of cellWorkset array does not match cell topology");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(cellWorkset.dimension(2)) != (size_t)cell.getDimension() ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_checkPointwiseInclusion): dim 2 (spatial dimension) of cellWorkset array does not match cell dimension");
// Validate whichCell It can be either -1 (default value) or a valid cell ordinal.
TEUCHOS_TEST_FOR_EXCEPTION( !( ( (0 <= whichCell ) && (whichCell < cellWorkset.dimension(0) ) ) || (whichCell == -1) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_checkPointwiseInclusion): whichCell = -1 or a valid cell ordinal is required.");
// Validate points array: can be rank-2 (P,D) or rank-3 (C,P,D)
// If rank-2: admissible inCell is rank-1 (P); admissible whichCell is valid cell ordinal but not -1.
if(getrank(physPoints) == 2) {
TEUCHOS_TEST_FOR_EXCEPTION( (whichCell == -1), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_checkPointwiseInclusion): whichCell = a valid cell ordinal is required with rank-2 input array.");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(physPoints.dimension(0)) <= 0), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_checkPointwiseInclusion): dim 0 (number of points) >= 1 required for physPoints array ");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(physPoints.dimension(1)) != (size_t)cell.getDimension() ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_checkPointwiseInclusion): dim 1 (spatial dimension) of physPoints array does not match cell dimension");
// Validate inCell
TEUCHOS_TEST_FOR_EXCEPTION( (getrank(inCell) != 1), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_checkPointwiseInclusion): rank = 1 required for inCell array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(inCell.dimension(0)) != static_cast<size_t>(physPoints.dimension(0))), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_checkPointwiseInclusion): dim 0 (number of points) of inCell array must equal dim 0 of physPoints array");
}
// If rank-3: admissible inCell is rank-2 (C,P); admissible whichCell = -1.
else if (getrank(physPoints) == 3){
TEUCHOS_TEST_FOR_EXCEPTION( !(whichCell == -1), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_checkPointwiseInclusion): whichCell = -1 is required with rank-3 input array.");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(physPoints.dimension(0)) != static_cast<size_t>(cellWorkset.dimension(0)) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_checkPointwiseInclusion): dim 0 (number of cells) of physPoints array must equal dim 0 of cellWorkset array ");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(physPoints.dimension(1)) <= 0), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_checkPointwiseInclusion): dim 1 (number of points) >= 1 required for physPoints array ");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(physPoints.dimension(2)) != (size_t)cell.getDimension() ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_checkPointwiseInclusion): dim 2 (spatial dimension) of physPoints array does not match cell dimension");
// Validate inCell
TEUCHOS_TEST_FOR_EXCEPTION( (getrank(inCell) != 2), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_checkPointwiseInclusion): rank = 2 required for inCell array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(inCell.dimension(0)) != static_cast<size_t>(physPoints.dimension(0))), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_checkPointwiseInclusion): dim 0 (number of cells) of inCell array must equal dim 0 of physPoints array");
TEUCHOS_TEST_FOR_EXCEPTION( (static_cast<size_t>(inCell.dimension(1)) != static_cast<size_t>(physPoints.dimension(1))), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_checkPointwiseInclusion): dim 1 (number of points) of inCell array must equal dim 1 of physPoints array");
}
else {
TEUCHOS_TEST_FOR_EXCEPTION( !( (getrank(physPoints) == 2) && (getrank(physPoints) ==3) ), std::invalid_argument,
">>> ERROR (Intrepid::CellTools::validateArguments_checkPointwiseInclusion): rank = 2 or 3 required for points array");
}
}
//============================================================================================//
// //
// Debug //
// //
//============================================================================================//
template<class Scalar>
void CellTools<Scalar>::printSubcellVertices(const int subcellDim,
const int subcellOrd,
const shards::CellTopology & parentCell){
// Get number of vertices for the specified subcell and parent cell dimension
int subcVertexCount = parentCell.getVertexCount(subcellDim, subcellOrd);
int cellDim = parentCell.getDimension();
// Allocate space for the subcell vertex coordinates
FieldContainer<double> subcellVertices(subcVertexCount, cellDim);
// Retrieve the vertex coordinates
getReferenceSubcellVertices(subcellVertices,
subcellDim,
subcellOrd,
parentCell);
// Print the vertices
std::cout
<< " Subcell " << std::setw(2) << subcellOrd
<< " is " << parentCell.getName(subcellDim, subcellOrd) << " with vertices = {";
// Loop over subcell vertices
for(int subcVertOrd = 0; subcVertOrd < subcVertexCount; subcVertOrd++){
std::cout<< "(";
// Loop over vertex Cartesian coordinates
for(int dim = 0; dim < (int)parentCell.getDimension(); dim++){
std::cout << subcellVertices(subcVertOrd, dim);
if(dim < (int)parentCell.getDimension()-1 ) { std::cout << ","; }
}
std::cout<< ")";
if(subcVertOrd < subcVertexCount - 1) { std::cout << ", "; }
}
std::cout << "}\n";
}
template<class Scalar>
template<class ArrayCell>
void CellTools<Scalar>::printWorksetSubcell(const ArrayCell & cellWorkset,
const shards::CellTopology & parentCell,
const int& pCellOrd,
const int& subcellDim,
const int& subcellOrd,
const int& fieldWidth){
// Get the ordinals, relative to reference cell, of subcell cellWorkset
int subcNodeCount = parentCell.getNodeCount(subcellDim, subcellOrd);
int pCellDim = parentCell.getDimension();
std::vector<int> subcNodeOrdinals(subcNodeCount);
for(int i = 0; i < subcNodeCount; i++){
subcNodeOrdinals[i] = parentCell.getNodeMap(subcellDim, subcellOrd, i);
}
// Loop over parent cells and print subcell cellWorkset
std::cout
<< " Subcell " << subcellOrd << " on parent cell " << pCellOrd << " is "
<< parentCell.getName(subcellDim, subcellOrd) << " with node(s) \n ({";
for(int i = 0; i < subcNodeCount; i++){
// print Cartesian coordinates of the node
for(int dim = 0; dim < pCellDim; dim++){
std::cout
<< std::setw(fieldWidth) << std::right << cellWorkset(pCellOrd, subcNodeOrdinals[i], dim);
if(dim < pCellDim - 1){ std::cout << ","; }
}
std::cout << "}";
if(i < subcNodeCount - 1){ std::cout <<", {"; }
}
std::cout << ")\n\n";
}
//============================================================================================//
// //
// Control Volume Coordinates //
// //
//============================================================================================//
template<class Scalar>
template<class ArrayCVCoord, class ArrayCellCoord>
void CellTools<Scalar>::getSubCVCoords(ArrayCVCoord & subCVCoords,
const ArrayCellCoord & cellCoords,
const shards::CellTopology& primaryCell)
{
// get array dimensions
int numCells = cellCoords.dimension(0);
int numNodesPerCell = cellCoords.dimension(1);
int spaceDim = cellCoords.dimension(2);
// num edges per primary cell
int numEdgesPerCell = primaryCell.getEdgeCount();
// num faces per primary cell
int numFacesPerCell = 0;
if (spaceDim > 2){
numFacesPerCell = primaryCell.getFaceCount();
}
// get cell centroids
Intrepid::FieldContainer<Scalar> barycenter(numCells,spaceDim);
getBarycenter(barycenter,cellCoords);
// loop over cells
for (int icell = 0; icell < numCells; icell++){
// get primary edge midpoints
Intrepid::FieldContainer<Scalar> edgeMidpts(numEdgesPerCell,spaceDim);
for (int iedge = 0; iedge < numEdgesPerCell; iedge++){
for (int idim = 0; idim < spaceDim; idim++){
int node0 = primaryCell.getNodeMap(1,iedge,0);
int node1 = primaryCell.getNodeMap(1,iedge,1);
edgeMidpts(iedge,idim) = (cellCoords(icell,node0,idim) +
cellCoords(icell,node1,idim))/2.0;
} // end loop over dimensions
} // end loop over cell edges
// get primary face midpoints in 3-D
int numNodesPerFace;
Intrepid::FieldContainer<Scalar> faceMidpts(numFacesPerCell,spaceDim);
if (spaceDim > 2) {
for (int iface = 0; iface < numFacesPerCell; iface++){
numNodesPerFace = primaryCell.getNodeCount(2,iface);
for (int idim = 0; idim < spaceDim; idim++){
for (int inode0 = 0; inode0 < numNodesPerFace; inode0++) {
int node1 = primaryCell.getNodeMap(2,iface,inode0);
faceMidpts(iface,idim) += cellCoords(icell,node1,idim)/numNodesPerFace;
}
} // end loop over dimensions
} // end loop over cell faces
}
// define coordinates for subcontrol volumes
switch(primaryCell.getKey() ) {
// 2-d parent cells
case shards::Triangle<3>::key:
case shards::Quadrilateral<4>::key:
for (int inode = 0; inode < numNodesPerCell; inode++){
for (int idim = 0; idim < spaceDim; idim++){
// set first node to primary cell node
subCVCoords(icell,inode,0,idim) = cellCoords(icell,inode,idim);
// set second node to adjacent edge midpoint
subCVCoords(icell,inode,1,idim) = edgeMidpts(inode,idim);
// set third node to cell barycenter
subCVCoords(icell,inode,2,idim) = barycenter(icell,idim);
// set fourth node to other adjacent edge midpoint
int jnode = numNodesPerCell-1;
if (inode > 0) jnode = inode - 1;
subCVCoords(icell,inode,3,idim) = edgeMidpts(jnode,idim);
} // dim loop
} // node loop
break;
case shards::Hexahedron<8>::key:
for (int idim = 0; idim < spaceDim; idim++){
// loop over the horizontal quads that define the subcontrol volume coords
for (int icount = 0; icount < 4; icount++){
// set first node of bottom hex to primary cell node
// and fifth node of upper hex
subCVCoords(icell,icount,0,idim) = cellCoords(icell,icount,idim);
subCVCoords(icell,icount+4,4,idim) = cellCoords(icell,icount+4,idim);
// set second node of bottom hex to adjacent edge midpoint
// and sixth node of upper hex
subCVCoords(icell,icount,1,idim) = edgeMidpts(icount,idim);
subCVCoords(icell,icount+4,5,idim) = edgeMidpts(icount+4,idim);
// set third node of bottom hex to bottom face midpoint (number 4)
// and seventh node of upper hex to top face midpoint
subCVCoords(icell,icount,2,idim) = faceMidpts(4,idim);
subCVCoords(icell,icount+4,6,idim) = faceMidpts(5,idim);
// set fourth node of bottom hex to other adjacent edge midpoint
// and eight node of upper hex to other adjacent edge midpoint
int jcount = 3;
if (icount > 0) jcount = icount - 1;
subCVCoords(icell,icount,3,idim) = edgeMidpts(jcount,idim);
subCVCoords(icell,icount+4,7,idim) = edgeMidpts(jcount+4,idim);
// set fifth node to vertical edge
// same as first node of upper hex
subCVCoords(icell,icount,4,idim) = edgeMidpts(icount+numNodesPerCell,idim);
subCVCoords(icell,icount+4,0,idim) = edgeMidpts(icount+numNodesPerCell,idim);
// set sixth node to adjacent face midpoint
// same as second node of upper hex
subCVCoords(icell,icount,5,idim) = faceMidpts(icount,idim);
subCVCoords(icell,icount+4,1,idim) = faceMidpts(icount,idim);
// set seventh node to barycenter
// same as third node of upper hex
subCVCoords(icell,icount,6,idim) = barycenter(icell,idim);
subCVCoords(icell,icount+4,2,idim) = barycenter(icell,idim);
// set eighth node to other adjacent face midpoint
// same as fourth node of upper hex
jcount = 3;
if (icount > 0) jcount = icount - 1;
subCVCoords(icell,icount,7,idim) = faceMidpts(jcount,idim);
subCVCoords(icell,icount+4,3,idim) = faceMidpts(jcount,idim);
} // count loop
} // dim loop
break;
case shards::Tetrahedron<4>::key:
for (int idim = 0; idim < spaceDim; idim++){
// loop over the three bottom nodes
for (int icount = 0; icount < 3; icount++){
// set first node of bottom hex to primary cell node
subCVCoords(icell,icount,0,idim) = cellCoords(icell,icount,idim);
// set second node of bottom hex to adjacent edge midpoint
subCVCoords(icell,icount,1,idim) = edgeMidpts(icount,idim);
// set third node of bottom hex to bottom face midpoint (number 3)
subCVCoords(icell,icount,2,idim) = faceMidpts(3,idim);
// set fourth node of bottom hex to other adjacent edge midpoint
int jcount = 2;
if (icount > 0) jcount = icount - 1;
subCVCoords(icell,icount,3,idim) = edgeMidpts(jcount,idim);
// set fifth node to vertical edge
subCVCoords(icell,icount,4,idim) = edgeMidpts(icount+3,idim);
// set sixth node to adjacent face midpoint
subCVCoords(icell,icount,5,idim) = faceMidpts(icount,idim);
// set seventh node to barycenter
subCVCoords(icell,icount,6,idim) = barycenter(icell,idim);
// set eighth node to other adjacent face midpoint
jcount = 2;
if (icount > 0) jcount = icount - 1;
subCVCoords(icell,icount,7,idim) = faceMidpts(jcount,idim);
} //count loop
// Control volume attached to fourth node
// set first node of bottom hex to primary cell node
subCVCoords(icell,3,0,idim) = cellCoords(icell,3,idim);
// set second node of bottom hex to adjacent edge midpoint
subCVCoords(icell,3,1,idim) = edgeMidpts(3,idim);
// set third node of bottom hex to bottom face midpoint (number 3)
subCVCoords(icell,3,2,idim) = faceMidpts(2,idim);
// set fourth node of bottom hex to other adjacent edge midpoint
subCVCoords(icell,3,3,idim) = edgeMidpts(5,idim);
// set fifth node to vertical edge
subCVCoords(icell,3,4,idim) = edgeMidpts(4,idim);
// set sixth node to adjacent face midpoint
subCVCoords(icell,3,5,idim) = faceMidpts(0,idim);
// set seventh node to barycenter
subCVCoords(icell,3,6,idim) = barycenter(icell,idim);
// set eighth node to other adjacent face midpoint
subCVCoords(icell,3,7,idim) = faceMidpts(1,idim);
} // dim loop
break;
default:
TEUCHOS_TEST_FOR_EXCEPTION( true, std::invalid_argument,
">>> ERROR (getSubCVCoords: invalid cell topology.");
} // cell key
} // cell loop
} // getSubCVCoords
template<class Scalar>
template<class ArrayCent, class ArrayCellCoord>
void CellTools<Scalar>::getBarycenter(ArrayCent & barycenter, const ArrayCellCoord & cellCoords)
{
// get array dimensions
int numCells = cellCoords.dimension(0);
int numVertsPerCell = cellCoords.dimension(1);
int spaceDim = cellCoords.dimension(2);
if (spaceDim == 2)
{
// Method for general polygons
for (int icell = 0; icell < numCells; icell++){
Intrepid::FieldContainer<Scalar> cell_centroid(spaceDim);
Scalar area = 0;
for (int inode = 0; inode < numVertsPerCell; inode++){
int jnode = inode + 1;
if (jnode >= numVertsPerCell) {
jnode = 0;
}
Scalar area_mult = cellCoords(icell,inode,0)*cellCoords(icell,jnode,1)
- cellCoords(icell,jnode,0)*cellCoords(icell,inode,1);
cell_centroid(0) += (cellCoords(icell,inode,0) + cellCoords(icell,jnode,0))*area_mult;
cell_centroid(1) += (cellCoords(icell,inode,1) + cellCoords(icell,jnode,1))*area_mult;
area += 0.5*area_mult;
}
barycenter(icell,0) = cell_centroid(0)/(6.0*area);
barycenter(icell,1) = cell_centroid(1)/(6.0*area);
}
}
else
{
// This method works fine for simplices, but for other 3-d shapes
// is not precisely accurate. Could replace with approximate integration
// perhaps.
for (int icell = 0; icell < numCells; icell++){
Intrepid::FieldContainer<Scalar> cell_centroid(spaceDim);
for (int inode = 0; inode < numVertsPerCell; inode++){
for (int idim = 0; idim < spaceDim; idim++){
cell_centroid(idim) += cellCoords(icell,inode,idim)/numVertsPerCell;
}
}
for (int idim = 0; idim < spaceDim; idim++){
barycenter(icell,idim) = cell_centroid(idim);
}
}
}
} // get Barycenter
} // namespace Intrepid
#endif
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