Intrepid
Intrepid_CubaturePolygonDef.hpp
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43 
52 #include "Intrepid_CellTools.hpp"
53 #include <vector>
54 #include <iostream>
55 
56 namespace Intrepid{
57 
58  template<class Scalar, class ArrayPoint, class ArrayWeight>
59  CubaturePolygon<Scalar,ArrayPoint,ArrayWeight>::CubaturePolygon(const shards::CellTopology& cellTopology,
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
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 
142 template<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 
160 template<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 
171 template<class Scalar, class ArrayPoint, class ArrayWeight>
173  return numPoints_;
174 } // end getNumPoints
175 
176 template<class Scalar, class ArrayPoint, class ArrayWeight>
178  return cubDimension_;
179 } // end getDimension
180 
181 template<class Scalar, class ArrayPoint, class ArrayWeight>
183  accuracy.assign(1,degree_);
184 } // end getAccuracy
185 
186 } // namespace Intrepid
int cubDimension_
Dimension of integration domain.
virtual void getCubature(ArrayPoint &cubPoints, ArrayWeight &cubWeights) const
Returns cubature points and weights (return arrays must be pre-sized/pre-allocated).
Header file for the Intrepid::CellTools class.
int getDimension() const
Returns dimension of integration domain.
Header file for utility class to provide multidimensional containers.
#define INTREPID_CUBATURE_TRI_DEFAULT_MAX
The maximum degree of the polynomial that can be integrated exactly by a direct triangle rule of the ...
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.
virtual int getNumPoints() const
Returns the number of cubature points.
shards::CellTopology cellTopology_
The topology of the polygon.
void getAccuracy(std::vector< int > &accuracy) const
Returns max. degree of polynomials that are integrated exactly on each triangle. The return vector ha...
int degree_
The degree of the polynomials that are integrated exactly on each triangle.
FieldContainer< Scalar > cubatureWeights_
Local copy of cubature weights.
void getCubature(ArrayPoint &cubPoints, ArrayWeight &cubWeights) const
Returns cubature points and weights (return arrays must be pre-sized/pre-allocated).
FieldContainer< Scalar > cubaturePoints_
Local copy of cubature points.
Header file for the Intrepid::CubatureDirectTriDefault class.
virtual int getDimension() const
Returns dimension of integration domain.
void resize(const int dim0)
Resizes FieldContainer to a rank-1 container with the specified dimension, initialized by 0...
Defines direct integration rules on a triangle.
int getNumPoints() const
Returns the number of cubature points.
CubaturePolygon(const shards::CellTopology &cellTopology, const ArrayPoint &cellVertices, int degree)
int numPoints_
The number of cubature points.
A stateless class for operations on cell data. Provides methods for:
static void setJacobianDet(ArrayJacDet &jacobianDet, const ArrayJac &jacobian)
Computes the determinant of the Jacobian matrix DF of the reference-to-physical frame map F...
ArrayPoint cellVertices_
The vertices of the polygon.