Intrepid
Intrepid_HGRAD_TRI_C2_FEMDef.hpp
1#ifndef INTREPID_HGRAD_TRI_C2_FEMDEF_HPP
2#define INTREPID_HGRAD_TRI_C2_FEMDEF_HPP
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5//
6// Intrepid Package
7// Copyright (2007) Sandia Corporation
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44// @HEADER
45
51namespace Intrepid {
52
53
54template<class Scalar, class ArrayScalar>
56 {
57 this -> basisCardinality_ = 6;
58 this -> basisDegree_ = 2;
59 this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Triangle<3> >() );
60 this -> basisType_ = BASIS_FEM_DEFAULT;
61 this -> basisCoordinates_ = COORDINATES_CARTESIAN;
62 this -> basisTagsAreSet_ = false;
63 }
64
65
66
67template<class Scalar, class ArrayScalar>
69
70 // Basis-dependent initializations
71 int tagSize = 4; // size of DoF tag, i.e., number of fields in the tag
72 int posScDim = 0; // position in the tag, counting from 0, of the subcell dim
73 int posScOrd = 1; // position in the tag, counting from 0, of the subcell ordinal
74 int posDfOrd = 2; // position in the tag, counting from 0, of DoF ordinal relative to the subcell
75
76 // An array with local DoF tags assigned to the basis functions, in the order of their local enumeration
77 int tags[] = { 0, 0, 0, 1,
78 0, 1, 0, 1,
79 0, 2, 0, 1,
80 1, 0, 0, 1,
81 1, 1, 0, 1,
82 1, 2, 0, 1};
83
84 // Basis-independent function sets tag and enum data in tagToOrdinal_ and ordinalToTag_ arrays:
85 Intrepid::setOrdinalTagData(this -> tagToOrdinal_,
86 this -> ordinalToTag_,
87 tags,
88 this -> basisCardinality_,
89 tagSize,
90 posScDim,
91 posScOrd,
92 posDfOrd);
93}
94
95
96
97template<class Scalar, class ArrayScalar>
99 const ArrayScalar & inputPoints,
100 const EOperator operatorType) const {
101
102 // Verify arguments
103#ifdef HAVE_INTREPID_DEBUG
104 Intrepid::getValues_HGRAD_Args<Scalar, ArrayScalar>(outputValues,
105 inputPoints,
106 operatorType,
107 this -> getBaseCellTopology(),
108 this -> getCardinality() );
109#endif
110
111 // Number of evaluation points = dim 0 of inputPoints
112 int dim0 = inputPoints.dimension(0);
113
114 // Temporaries: (x,y) coordinates of the evaluation point
115 Scalar x = 0.0;
116 Scalar y = 0.0;
117
118 switch (operatorType) {
119
120 case OPERATOR_VALUE:
121 for (int i0 = 0; i0 < dim0; i0++) {
122 x = inputPoints(i0, 0);
123 y = inputPoints(i0, 1);
124
125 // outputValues is a rank-2 array with dimensions (basisCardinality_, dim0)
126 outputValues(0, i0) = (x + y - 1.0)*(2.0*x + 2.0*y - 1.0);
127 outputValues(1, i0) = x*(2.0*x - 1.0);
128 outputValues(2, i0) = y*(2.0*y - 1.0);
129 outputValues(3, i0) = -4.0*x*(x + y - 1.0);
130 outputValues(4, i0) = 4.0*x*y;
131 outputValues(5, i0) = -4.0*y*(x + y - 1.0);
132
133 }
134 break;
135
136 case OPERATOR_GRAD:
137 case OPERATOR_D1:
138 for (int i0 = 0; i0 < dim0; i0++) {
139 x = inputPoints(i0, 0);
140 y = inputPoints(i0, 1);
141
142 // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, spaceDim)
143 outputValues(0, i0, 0) = 4.0*x + 4.0*y - 3.0;
144 outputValues(0, i0, 1) = 4.0*x + 4.0*y - 3.0;
145
146 outputValues(1, i0, 0) = 4.0*x - 1.0;
147 outputValues(1, i0, 1) = 0.0;
148
149 outputValues(2, i0, 0) = 0.0;
150 outputValues(2, i0, 1) = 4.0*y - 1.0;
151
152 outputValues(3, i0, 0) = -4.0*(2.0*x + y - 1.0);
153 outputValues(3, i0, 1) = -4.0*x;
154
155 outputValues(4, i0, 0) = 4.0*y;
156 outputValues(4, i0, 1) = 4.0*x;
157
158 outputValues(5, i0, 0) = -4.0*y;
159 outputValues(5, i0, 1) = -4.0*(x + 2.0*y - 1.0);
160 }
161 break;
162
163 case OPERATOR_CURL:
164 for (int i0 = 0; i0 < dim0; i0++) {
165 x = inputPoints(i0, 0);
166 y = inputPoints(i0, 1);
167
168 // CURL(u) = (u_y, -u_x), is rotated GRAD
169 outputValues(0, i0, 1) =-(4.0*x + 4.0*y - 3.0);
170 outputValues(0, i0, 0) = 4.0*x + 4.0*y - 3.0;
171
172 outputValues(1, i0, 1) =-(4.0*x - 1.0);
173 outputValues(1, i0, 0) = 0.0;
174
175 outputValues(2, i0, 1) = 0.0;
176 outputValues(2, i0, 0) = 4.0*y - 1.0;
177
178 outputValues(3, i0, 1) = 4.0*(2.0*x + y - 1.0);
179 outputValues(3, i0, 0) = -4.0*x;
180
181 outputValues(4, i0, 1) = -4.0*y;
182 outputValues(4, i0, 0) = 4.0*x;
183
184 outputValues(5, i0, 1) = 4.0*y;
185 outputValues(5, i0, 0) = -4.0*(x + 2.0*y - 1.0);
186 }
187 break;
188
189 case OPERATOR_DIV:
190 TEUCHOS_TEST_FOR_EXCEPTION( (operatorType == OPERATOR_DIV), std::invalid_argument,
191 ">>> ERROR (Basis_HGRAD_TRI_C2_FEM): DIV is invalid operator for rank-0 (scalar) fields in 2D.");
192 break;
193
194 case OPERATOR_D2:
195 for (int i0 = 0; i0 < dim0; i0++) {
196 // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, DkCardinality)
197 // D2 -> (2,0) -> dx^2.
198 outputValues(0, i0, 0) = 4.0;
199 outputValues(1, i0, 0) = 4.0;
200 outputValues(2, i0, 0) = 0.0;
201 outputValues(3, i0, 0) =-8.0;
202 outputValues(4, i0, 0) = 0.0;
203 outputValues(5, i0, 0) = 0.0;
204
205 // D2 -> (1,1) -> dx dy
206 outputValues(0, i0, 1) = 4.0;
207 outputValues(1, i0, 1) = 0.0;
208 outputValues(2, i0, 1) = 0.0;
209 outputValues(3, i0, 1) =-4.0;
210 outputValues(4, i0, 1) = 4.0;
211 outputValues(5, i0, 1) =-4.0;
212
213 // D2 -> (0,2) -> dy^2
214 outputValues(0, i0, 2) = 4.0;
215 outputValues(1, i0, 2) = 0.0;
216 outputValues(2, i0, 2) = 4.0;
217 outputValues(3, i0, 2) = 0.0;
218 outputValues(4, i0, 2) = 0.0;
219 outputValues(5, i0, 2) =-8.0;
220 }// for i0
221 break;
222
223 case OPERATOR_D3:
224 case OPERATOR_D4:
225 case OPERATOR_D5:
226 case OPERATOR_D6:
227 case OPERATOR_D7:
228 case OPERATOR_D8:
229 case OPERATOR_D9:
230 case OPERATOR_D10:
231 {
232 // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, DkCardinality)
233 int DkCardinality = Intrepid::getDkCardinality(operatorType,
234 this -> basisCellTopology_.getDimension() );
235 for(int dofOrd = 0; dofOrd < this -> basisCardinality_; dofOrd++) {
236 for (int i0 = 0; i0 < dim0; i0++) {
237 for(int dkOrd = 0; dkOrd < DkCardinality; dkOrd++){
238 outputValues(dofOrd, i0, dkOrd) = 0.0;
239 }
240 }
241 }
242 }
243 break;
244
245 default:
246 TEUCHOS_TEST_FOR_EXCEPTION( !( Intrepid::isValidOperator(operatorType) ), std::invalid_argument,
247 ">>> ERROR (Basis_HGRAD_TRI_C2_FEM): Invalid operator type");
248 }
249}
250
251
252
253template<class Scalar, class ArrayScalar>
255 const ArrayScalar & inputPoints,
256 const ArrayScalar & cellVertices,
257 const EOperator operatorType) const {
258 TEUCHOS_TEST_FOR_EXCEPTION( (true), std::logic_error,
259 ">>> ERROR (Basis_HGRAD_TRI_C2_FEM): FEM Basis calling an FVD member function");
260}
261
262template<class Scalar, class ArrayScalar>
264#ifdef HAVE_INTREPID_DEBUG
265 // Verify rank of output array.
266 TEUCHOS_TEST_FOR_EXCEPTION( !(DofCoords.rank() == 2), std::invalid_argument,
267 ">>> ERROR: (Intrepid::Basis_HGRAD_TRI_C2_FEM::getDofCoords) rank = 2 required for DofCoords array");
268 // Verify 0th dimension of output array.
269 TEUCHOS_TEST_FOR_EXCEPTION( !( DofCoords.dimension(0) == this -> basisCardinality_ ), std::invalid_argument,
270 ">>> ERROR: (Intrepid::Basis_HGRAD_TRI_C2_FEM::getDofCoords) mismatch in number of DoF and 0th dimension of DofCoords array");
271 // Verify 1st dimension of output array.
272 TEUCHOS_TEST_FOR_EXCEPTION( !( DofCoords.dimension(1) == (int)(this -> basisCellTopology_.getDimension()) ), std::invalid_argument,
273 ">>> ERROR: (Intrepid::Basis_HGRAD_TRI_C2_FEM::getDofCoords) incorrect reference cell (1st) dimension in DofCoords array");
274#endif
275
276 DofCoords(0,0) = 0.0; DofCoords(0,1) = 0.0;
277 DofCoords(1,0) = 1.0; DofCoords(1,1) = 0.0;
278 DofCoords(2,0) = 0.0; DofCoords(2,1) = 1.0;
279 DofCoords(3,0) = 0.5; DofCoords(3,1) = 0.0;
280 DofCoords(4,0) = 0.5; DofCoords(4,1) = 0.5;
281 DofCoords(5,0) = 0.0; DofCoords(5,1) = 0.5;
282}
283
284}// namespace Intrepid
285#endif
int isValidOperator(const EOperator operatorType)
Verifies validity of an operator enum.
void setOrdinalTagData(std::vector< std::vector< std::vector< int > > > &tagToOrdinal, std::vector< std::vector< int > > &ordinalToTag, const int *tags, const int basisCard, const int tagSize, const int posScDim, const int posScOrd, const int posDfOrd)
Fills ordinalToTag_ and tagToOrdinal_ by basis-specific tag data.
int getDkCardinality(const EOperator operatorType, const int spaceDim)
Returns cardinality of Dk, i.e., the number of all derivatives of order k.
void initializeTags()
Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays.
void getDofCoords(ArrayScalar &DofCoords) const
Returns spatial locations (coordinates) of degrees of freedom on a reference Quadrilateral.
void getValues(ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
Evaluation of a FEM basis on a reference Triangle cell.