Intrepid
Intrepid_HGRAD_PYR_C1_FEMDef.hpp
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1#ifndef INTREPID_HGRAD_PYR_C1_FEMDEF_HPP
2#define INTREPID_HGRAD_PYR_C1_FEMDEF_HPP
3
4#include <limits>
5
6// @HEADER
7// ************************************************************************
8//
9// Intrepid Package
10// Copyright (2007) Sandia Corporation
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12// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
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47// @HEADER
48
54namespace Intrepid {
55
56 template<class Scalar, class ArrayScalar>
58 {
59 this -> basisCardinality_ = 5;
60 this -> basisDegree_ = 1;
61 this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Pyramid<5> >() );
62 this -> basisType_ = BASIS_FEM_DEFAULT;
63 this -> basisCoordinates_ = COORDINATES_CARTESIAN;
64 this -> basisTagsAreSet_ = false;
65 }
66
67
68template<class Scalar, class ArrayScalar>
70
71 // Basis-dependent intializations
72 int tagSize = 4; // size of DoF tag
73 int posScDim = 0; // position in the tag, counting from 0, of the subcell dim
74 int posScOrd = 1; // position in the tag, counting from 0, of the subcell ordinal
75 int posDfOrd = 2; // position in the tag, counting from 0, of DoF ordinal relative to the subcell
76
77 // An array with local DoF tags assigned to basis functions, in the order of their local enumeration
78 int tags[] = { 0, 0, 0, 1,
79 0, 1, 0, 1,
80 0, 2, 0, 1,
81 0, 3, 0, 1,
82 0, 4, 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,z) coordinates of the evaluation point
115 Scalar x = 0.0;
116 Scalar y = 0.0;
117 Scalar z = 0.0;
118 const Scalar eps = std::numeric_limits<Scalar>::epsilon( );
119
120 switch (operatorType) {
121
122 case OPERATOR_VALUE:
123 for (int i0 = 0; i0 < dim0; i0++) {
124 x = inputPoints(i0, 0);
125 y = inputPoints(i0, 1);
126 z = inputPoints(i0, 2);
127
128 //be sure that the basis functions are defined when z is very close to 1.
129 if(fabs(z-1.0) < eps) {
130 if(z <= 1.0) z = 1.0-eps;
131 else z = 1.0+eps;
132 }
133
134
135 Scalar zTerm = 0.25/(1.0 - z);
136
137 // outputValues is a rank-2 array with dimensions (basisCardinality_, dim0)
138 outputValues(0, i0) = (1.0 - x - z) * (1.0 - y - z) * zTerm;
139 outputValues(1, i0) = (1.0 + x - z) * (1.0 - y - z) * zTerm;
140 outputValues(2, i0) = (1.0 + x - z) * (1.0 + y - z) * zTerm;
141 outputValues(3, i0) = (1.0 - x - z) * (1.0 + y - z) * zTerm;
142 outputValues(4, i0) = z;
143 }
144 break;
145
146 case OPERATOR_GRAD:
147 case OPERATOR_D1:
148 for (int i0 = 0; i0 < dim0; i0++) {
149
150 x = inputPoints(i0, 0);
151 y = inputPoints(i0, 1);
152 z = inputPoints(i0, 2);
153
154
155 //be sure that the basis functions are defined when z is very close to 1.
156 //warning, the derivatives are discontinuous in (0, 0, 1)
157 if(fabs(z-1.0) < eps) {
158 if(z <= 1.0) z = 1.0-eps;
159 else z = 1.0+eps;
160 }
161
162
163 Scalar zTerm = 0.25/(1.0 - z);
164 Scalar zTerm2 = 4.0 * zTerm * zTerm;
165
166 // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, spaceDim)
167 outputValues(0, i0, 0) = (y + z - 1.0) * zTerm;
168 outputValues(0, i0, 1) = (x + z - 1.0) * zTerm;
169 outputValues(0, i0, 2) = x * y * zTerm2 - 0.25;
170
171 outputValues(1, i0, 0) = (1.0 - y - z) * zTerm;
172 outputValues(1, i0, 1) = (z - x - 1.0) * zTerm;
173 outputValues(1, i0, 2) = - x*y * zTerm2 - 0.25;
174
175 outputValues(2, i0, 0) = (1.0 + y - z) * zTerm;
176 outputValues(2, i0, 1) = (1.0 + x - z) * zTerm;
177 outputValues(2, i0, 2) = x * y * zTerm2 - 0.25;
178
179 outputValues(3, i0, 0) = (z - y - 1.0) * zTerm;
180 outputValues(3, i0, 1) = (1.0 - x - z) * zTerm;
181 outputValues(3, i0, 2) = - x*y * zTerm2 - 0.25;
182
183 outputValues(4, i0, 0) = 0.0;
184 outputValues(4, i0, 1) = 0.0;
185 outputValues(4, i0, 2) = 1;
186 }
187 break;
188
189 case OPERATOR_CURL:
190 TEUCHOS_TEST_FOR_EXCEPTION( (operatorType == OPERATOR_CURL), std::invalid_argument,
191 ">>> ERROR (Basis_HGRAD_PYR_C1_FEM): CURL is invalid operator for rank-0 (scalar) functions in 3D");
192 break;
193
194 case OPERATOR_DIV:
195 TEUCHOS_TEST_FOR_EXCEPTION( (operatorType == OPERATOR_DIV), std::invalid_argument,
196 ">>> ERROR (Basis_HGRAD_PYR_C1_FEM): DIV is invalid operator for rank-0 (scalar) functions in 3D");
197 break;
198
199 case OPERATOR_D2:
200 for (int i0 = 0; i0 < dim0; i0++) {
201 x = inputPoints(i0,0);
202 y = inputPoints(i0,1);
203 z = inputPoints(i0,2);
204
205 //be sure that the basis functions are defined when z is very close to 1.
206 //warning, the derivatives are discontinuous in (0, 0, 1)
207 if(fabs(z-1.0) < eps) {
208 if(z <= 1.0) z = 1.0-eps;
209 else z = 1.0+eps;
210 }
211
212
213 Scalar zTerm = 0.25/(1.0 - z);
214 Scalar zTerm2 = 4.0 * zTerm * zTerm;
215 Scalar zTerm3 = 8.0 * zTerm * zTerm2;
216
217 // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, D2Cardinality = 6)
218 outputValues(0, i0, 0) = 0.0; // {2, 0, 0}
219 outputValues(0, i0, 1) = zTerm; // {1, 1, 0}
220 outputValues(0, i0, 2) = y*zTerm2; // {1, 0, 1}
221 outputValues(0, i0, 3) = 0.0; // {0, 2, 0}
222 outputValues(0, i0, 4) = x*zTerm2; // {0, 1, 1}
223 outputValues(0, i0, 5) = x*y*zTerm3; // {0, 0, 2}
224
225 outputValues(1, i0, 0) = 0.0; // {2, 0, 0}
226 outputValues(1, i0, 1) = -zTerm; // {1, 1, 0}
227 outputValues(1, i0, 2) = -y*zTerm2; // {1, 0, 1}
228 outputValues(1, i0, 3) = 0.0; // {0, 2, 0}
229 outputValues(1, i0, 4) = -x*zTerm2; // {0, 1, 1}
230 outputValues(1, i0, 5) = -x*y*zTerm3; // {0, 0, 2}
231
232 outputValues(2, i0, 0) = 0.0; // {2, 0, 0}
233 outputValues(2, i0, 1) = zTerm; // {1, 1, 0}
234 outputValues(2, i0, 2) = y*zTerm2; // {1, 0, 1}
235 outputValues(2, i0, 3) = 0.0; // {0, 2, 0}
236 outputValues(2, i0, 4) = x*zTerm2; // {0, 1, 1}
237 outputValues(2, i0, 5) = x*y*zTerm3; // {0, 0, 2}
238
239 outputValues(3, i0, 0) = 0.0; // {2, 0, 0}
240 outputValues(3, i0, 1) = -zTerm; // {1, 1, 0}
241 outputValues(3, i0, 2) = -y*zTerm2; // {1, 0, 1}
242 outputValues(3, i0, 3) = 0.0; // {0, 2, 0}
243 outputValues(3, i0, 4) = -x*zTerm2; // {0, 1, 1}
244 outputValues(3, i0, 5) = -x*y*zTerm3; // {0, 0, 2}
245
246 outputValues(4, i0, 0) = 0.0; // {2, 0, 0}
247 outputValues(4, i0, 1) = 0.0; // {1, 1, 0}
248 outputValues(4, i0, 2) = 0.0; // {1, 0, 1}
249 outputValues(4, i0, 3) = 0.0; // {0, 2, 0}
250 outputValues(4, i0, 4) = 0.0; // {0, 1, 1}
251 outputValues(4, i0, 5) = 0.0; // {0, 0, 2}
252 }
253 break;
254
255 case OPERATOR_D3:
256 case OPERATOR_D4:
257 case OPERATOR_D5:
258 case OPERATOR_D6:
259 case OPERATOR_D7:
260 case OPERATOR_D8:
261 case OPERATOR_D9:
262 case OPERATOR_D10:
263 {
264 // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, DkCardinality)
265 int DkCardinality = Intrepid::getDkCardinality(operatorType,
266 this -> basisCellTopology_.getDimension() );
267 for(int dofOrd = 0; dofOrd < this -> basisCardinality_; dofOrd++) {
268 for (int i0 = 0; i0 < dim0; i0++) {
269 for(int dkOrd = 0; dkOrd < DkCardinality; dkOrd++){
270 outputValues(dofOrd, i0, dkOrd) = 0.0;
271 }
272 }
273 }
274 }
275 break;
276 default:
277 TEUCHOS_TEST_FOR_EXCEPTION( !( Intrepid::isValidOperator(operatorType) ), std::invalid_argument,
278 ">>> ERROR (Basis_HGRAD_PYR_C1_FEM): Invalid operator type");
279 }
280}
281
282
283
284template<class Scalar, class ArrayScalar>
286 const ArrayScalar & inputPoints,
287 const ArrayScalar & cellVertices,
288 const EOperator operatorType) const {
289 TEUCHOS_TEST_FOR_EXCEPTION( (true), std::logic_error,
290 ">>> ERROR (Basis_HGRAD_PYR_C1_FEM): FEM Basis calling an FVD member function");
291}
292}// namespace Intrepid
293#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 getValues(ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
FEM basis evaluation on a reference Pyramid cell.