Intrepid
Intrepid_CubaturePolygonDef.hpp
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53#include <vector>
54#include <iostream>
55
56namespace Intrepid{
57
58 template<class Scalar, class ArrayPoint, class ArrayWeight>
60 const ArrayPoint& cellVertices,
61 int degree)
62 : degree_(degree), cubDimension_(2), cellTopology_(cellTopology), cellVertices_(cellVertices){
63
64 TEUCHOS_TEST_FOR_EXCEPTION( (degree < 0) || degree > INTREPID_CUBATURE_TRI_DEFAULT_MAX, std::out_of_range,
65 ">>> ERROR (CubaturePolygon): No direct cubature rule implemented for the desired polynomial degree.");
66 // compute area and centroid of polygon
67 Scalar area;
68 std::vector<Scalar> centroid(2,0);
69 int numNodes = cellTopology_.getNodeCount();
70
71 for (int i=0;i<numNodes;i++){
72 int first = cellTopology_.getNodeMap(1,i,0);
73 int second = cellTopology_.getNodeMap(1,i,1);
74 area += cellVertices_(first,0)*cellVertices_(second,1) - cellVertices_(second,0)*cellVertices_(first,1);
75 centroid[0] += (cellVertices_(first,0) + cellVertices_(second,0))*(cellVertices_(first,0)*cellVertices_(second,1) - cellVertices_(second,0)*cellVertices_(first,1));
76 centroid[1] += (cellVertices_(first,1) + cellVertices_(second,1))*(cellVertices_(first,0)*cellVertices_(second,1) - cellVertices_(second,0)*cellVertices_(first,1));
77 }
78 area /= 2;
79 centroid[0] /= (6*area);
80 centroid[1] /= (6*area);
81
82 // get cubature for reference triangle
83 CubatureDirectTriDefault<Scalar,ArrayPoint,ArrayWeight> cubatureTri(degree_);
84 int numCubPointsPerTri = cubatureTri.getNumPoints();
85 int cubDim = cubatureTri.getDimension();
86 cubDimension_ = cubDim;
87 FieldContainer<Scalar> cubatureTriPoints(numCubPointsPerTri,cubDim);
88
89 FieldContainer<Scalar> cubatureTriWeights(numCubPointsPerTri);
90 cubatureTri.getCubature(cubatureTriPoints,cubatureTriWeights);
91
92 // copy into (C,P,D) sized field container where C is the number of triangles in polygon
93 int numCells = cellTopology_.getEdgeCount();
94 FieldContainer<Scalar> cubatureCellPoints(numCells,numCubPointsPerTri,cubDim);
95 for (int k=0;k<numCells;k++){
96 for (int i=0;i<numCubPointsPerTri;i++){
97 for (int j=0;j<cubDim;j++){
98 cubatureCellPoints(k,i,j) = cubatureTriPoints(i,j);
99 }
100 }
101 }
102
103
104 // now map cubature to each triangle cell
105 shards::CellTopology triangleTopology(shards::getCellTopologyData<shards::Triangle<3> >());
106 int totalCubPoints = numCubPointsPerTri*cellTopology_.getEdgeCount();
107 numPoints_ = totalCubPoints;
108 cubaturePoints_.resize(totalCubPoints,cubDim);
109 cubatureWeights_.resize(totalCubPoints);
110
111 FieldContainer<Scalar> physicalPoints(numCells,numCubPointsPerTri,cubDim);
112 FieldContainer<Scalar> trianglePoints(numCells,3,cubDim);
113 int currPoint = 0;
114 for (int i=0;i<numCells;i++){
115 for (int j=0;j<cubDim;j++){
116 trianglePoints(i,0,j) = cellVertices_(cellTopology_.getNodeMap(1,i,0),j);
117 trianglePoints(i,1,j) = cellVertices_(cellTopology_.getNodeMap(1,i,1),j);
118 trianglePoints(i,2,j) = centroid[j];
119 }
120 }
121
122 CellTools<Scalar>::mapToPhysicalFrame(physicalPoints,cubatureTriPoints,trianglePoints,triangleTopology);
123
124 // compute area of each triangle cell -- need when computing new weights
125 FieldContainer<Scalar> jacobians(numCells,numCubPointsPerTri,cubDim,cubDim);
126 FieldContainer<Scalar> detJacobians(numCells, numCubPointsPerTri);
127
128 CellTools<Scalar>::setJacobian(jacobians,physicalPoints,trianglePoints,triangleTopology);
129 CellTools<Scalar>::setJacobianDet(detJacobians,jacobians);
130
131 for (int i=0;i<numCells;i++){
132 for (int j=0;j<numCubPointsPerTri;j++){
133 for (int k=0;k<cubDim;k++){
134 cubaturePoints_(currPoint,k) = physicalPoints(i,j,k);
135 }
136 cubatureWeights_(currPoint++) = cubatureTriWeights(j)*detJacobians(i,j);
137 }
138 }
139 } // end Constructor
140
141
142template<class Scalar, class ArrayPoint, class ArrayWeight>
144 ArrayWeight& cubWeights)const{
145 int numCubPoints = numPoints_;
146 int cellDim = cubDimension_;
147
148 TEUCHOS_TEST_FOR_EXCEPTION ( ( cubPoints.size() < numCubPoints*cellDim || cubWeights.size() < numCubPoints ),
149 std::out_of_range,
150 ">>> ERROR (CubaturePolygon): Insufficient space allocated for cubature points or weights.");
151
152 for (int pointId = 0; pointId < numCubPoints; pointId++){
153 for (int dim = 0; dim < cellDim; dim++){
154 cubPoints(pointId,dim) = cubaturePoints_(pointId,dim);
155 }
156 cubWeights(pointId) = cubatureWeights_(pointId);
157 }
158} // end getCubature
159
160template<class Scalar, class ArrayPoint, class ArrayWeight>
162 ArrayWeight& cubWeights,
163 ArrayPoint& cellCoords) const
164{
165 TEUCHOS_TEST_FOR_EXCEPTION( (true), std::logic_error,
166 ">>> ERROR (CubaturePolygon): Cubature defined in reference space calling method for physical space cubature.");
167}
168
169
170
171template<class Scalar, class ArrayPoint, class ArrayWeight>
173 return numPoints_;
174} // end getNumPoints
175
176template<class Scalar, class ArrayPoint, class ArrayWeight>
178 return cubDimension_;
179} // end getDimension
180
181template<class Scalar, class ArrayPoint, class ArrayWeight>
183 accuracy.assign(1,degree_);
184} // end getAccuracy
185
186} // namespace Intrepid
Header file for the Intrepid::CellTools class.
Header file for the Intrepid::CubatureDirectTriDefault class.
#define INTREPID_CUBATURE_TRI_DEFAULT_MAX
The maximum degree of the polynomial that can be integrated exactly by a direct triangle rule of the ...
Header file for utility class to provide multidimensional containers.
A stateless class for operations on cell data. Provides methods for:
static void mapToPhysicalFrame(ArrayPhysPoint &physPoints, const ArrayRefPoint &refPoints, const ArrayCell &cellWorkset, const shards::CellTopology &cellTopo, const int &whichCell=-1)
Computes F, the reference-to-physical frame map.
static void setJacobianDet(ArrayJacDet &jacobianDet, const ArrayJac &jacobian)
Computes the determinant of the Jacobian matrix DF of the reference-to-physical frame map F.
int getDimension() const
Returns dimension of integration domain.
shards::CellTopology cellTopology_
The topology of the polygon.
FieldContainer< Scalar > cubatureWeights_
Local copy of cubature weights.
void getAccuracy(std::vector< int > &accuracy) const
Returns max. degree of polynomials that are integrated exactly on each triangle. The return vector ha...
int cubDimension_
Dimension of integration domain.
ArrayPoint cellVertices_
The vertices of the polygon.
int getNumPoints() const
Returns the number of cubature points.
int numPoints_
The number of cubature points.
FieldContainer< Scalar > cubaturePoints_
Local copy of cubature points.
int degree_
The degree of the polynomials that are integrated exactly on each triangle.
CubaturePolygon(const shards::CellTopology &cellTopology, const ArrayPoint &cellVertices, int degree)
void getCubature(ArrayPoint &cubPoints, ArrayWeight &cubWeights) const
Returns cubature points and weights (return arrays must be pre-sized/pre-allocated).