Intrepid
Intrepid_HGRAD_HEX_C1_FEMDef.hpp
Go to the documentation of this file.
1#ifndef INTREPID_HGRAD_HEX_C1_FEMDEF_HPP
2#define INTREPID_HGRAD_HEX_C1_FEMDEF_HPP
3// @HEADER
4// ************************************************************************
5//
6// Intrepid Package
7// Copyright (2007) Sandia Corporation
8//
9// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
10// license for use of this work by or on behalf of the U.S. Government.
11//
12// Redistribution and use in source and binary forms, with or without
13// modification, are permitted provided that the following conditions are
14// met:
15//
16// 1. Redistributions of source code must retain the above copyright
17// notice, this list of conditions and the following disclaimer.
18//
19// 2. Redistributions in binary form must reproduce the above copyright
20// notice, this list of conditions and the following disclaimer in the
21// documentation and/or other materials provided with the distribution.
22//
23// 3. Neither the name of the Corporation nor the names of the
24// contributors may be used to endorse or promote products derived from
25// this software without specific prior written permission.
26//
27// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
28// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
29// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
30// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
31// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
32// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
33// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
34// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
35// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
36// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
37// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
38//
39// Questions? Contact Pavel Bochev (pbboche@sandia.gov)
40// Denis Ridzal (dridzal@sandia.gov), or
41// Kara Peterson (kjpeter@sandia.gov)
42//
43// ************************************************************************
44// @HEADER
45
51namespace Intrepid {
52
53
54template<class Scalar, class ArrayScalar>
56 {
57 this -> basisCardinality_ = 8;
58 this -> basisDegree_ = 1;
59 this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Hexahedron<8> >() );
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 intializations
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 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 0, 3, 0, 1,
81 0, 4, 0, 1,
82 0, 5, 0, 1,
83 0, 6, 0, 1,
84 0, 7, 0, 1 };
85
86 // Basis-independent function sets tag and enum data in tagToOrdinal_ and ordinalToTag_ arrays:
87 Intrepid::setOrdinalTagData(this -> tagToOrdinal_,
88 this -> ordinalToTag_,
89 tags,
90 this -> basisCardinality_,
91 tagSize,
92 posScDim,
93 posScOrd,
94 posDfOrd);
95}
96
97
98
99template<class Scalar, class ArrayScalar>
101 const ArrayScalar & inputPoints,
102 const EOperator operatorType) const {
103
104 // Verify arguments
105#ifdef HAVE_INTREPID_DEBUG
106 Intrepid::getValues_HGRAD_Args<Scalar, ArrayScalar>(outputValues,
107 inputPoints,
108 operatorType,
109 this -> getBaseCellTopology(),
110 this -> getCardinality() );
111#endif
112
113 // Number of evaluation points = dim 0 of inputPoints
114 int dim0 = inputPoints.dimension(0);
115
116 // Temporaries: (x,y,z) coordinates of the evaluation point
117 Scalar x = 0.0;
118 Scalar y = 0.0;
119 Scalar z = 0.0;
120
121 switch (operatorType) {
122
123 case OPERATOR_VALUE:
124 for (int i0 = 0; i0 < dim0; i0++) {
125 x = inputPoints(i0, 0);
126 y = inputPoints(i0, 1);
127 z = inputPoints(i0, 2);
128
129 // outputValues is a rank-2 array with dimensions (basisCardinality_, dim0)
130 outputValues(0, i0) = (1.0 - x)*(1.0 - y)*(1.0 - z)/8.0;
131 outputValues(1, i0) = (1.0 + x)*(1.0 - y)*(1.0 - z)/8.0;
132 outputValues(2, i0) = (1.0 + x)*(1.0 + y)*(1.0 - z)/8.0;
133 outputValues(3, i0) = (1.0 - x)*(1.0 + y)*(1.0 - z)/8.0;
134
135 outputValues(4, i0) = (1.0 - x)*(1.0 - y)*(1.0 + z)/8.0;
136 outputValues(5, i0) = (1.0 + x)*(1.0 - y)*(1.0 + z)/8.0;
137 outputValues(6, i0) = (1.0 + x)*(1.0 + y)*(1.0 + z)/8.0;
138 outputValues(7, i0) = (1.0 - x)*(1.0 + y)*(1.0 + z)/8.0;
139 }
140 break;
141
142 case OPERATOR_GRAD:
143 case OPERATOR_D1:
144 for (int i0 = 0; i0 < dim0; i0++) {
145 x = inputPoints(i0,0);
146 y = inputPoints(i0,1);
147 z = inputPoints(i0,2);
148
149 // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, spaceDim)
150 outputValues(0, i0, 0) = -(1.0 - y)*(1.0 - z)/8.0;
151 outputValues(0, i0, 1) = -(1.0 - x)*(1.0 - z)/8.0;
152 outputValues(0, i0, 2) = -(1.0 - x)*(1.0 - y)/8.0;
153
154 outputValues(1, i0, 0) = (1.0 - y)*(1.0 - z)/8.0;
155 outputValues(1, i0, 1) = -(1.0 + x)*(1.0 - z)/8.0;
156 outputValues(1, i0, 2) = -(1.0 + x)*(1.0 - y)/8.0;
157
158 outputValues(2, i0, 0) = (1.0 + y)*(1.0 - z)/8.0;
159 outputValues(2, i0, 1) = (1.0 + x)*(1.0 - z)/8.0;
160 outputValues(2, i0, 2) = -(1.0 + x)*(1.0 + y)/8.0;
161
162 outputValues(3, i0, 0) = -(1.0 + y)*(1.0 - z)/8.0;
163 outputValues(3, i0, 1) = (1.0 - x)*(1.0 - z)/8.0;
164 outputValues(3, i0, 2) = -(1.0 - x)*(1.0 + y)/8.0;
165
166 outputValues(4, i0, 0) = -(1.0 - y)*(1.0 + z)/8.0;
167 outputValues(4, i0, 1) = -(1.0 - x)*(1.0 + z)/8.0;
168 outputValues(4, i0, 2) = (1.0 - x)*(1.0 - y)/8.0;
169
170 outputValues(5, i0, 0) = (1.0 - y)*(1.0 + z)/8.0;
171 outputValues(5, i0, 1) = -(1.0 + x)*(1.0 + z)/8.0;
172 outputValues(5, i0, 2) = (1.0 + x)*(1.0 - y)/8.0;
173
174 outputValues(6, i0, 0) = (1.0 + y)*(1.0 + z)/8.0;
175 outputValues(6, i0, 1) = (1.0 + x)*(1.0 + z)/8.0;
176 outputValues(6, i0, 2) = (1.0 + x)*(1.0 + y)/8.0;
177
178 outputValues(7, i0, 0) = -(1.0 + y)*(1.0 + z)/8.0;
179 outputValues(7, i0, 1) = (1.0 - x)*(1.0 + z)/8.0;
180 outputValues(7, i0, 2) = (1.0 - x)*(1.0 + y)/8.0;
181 }
182 break;
183
184 case OPERATOR_CURL:
185 TEUCHOS_TEST_FOR_EXCEPTION( (operatorType == OPERATOR_CURL), std::invalid_argument,
186 ">>> ERROR (Basis_HGRAD_HEX_C1_FEM): CURL is invalid operator for rank-0 (scalar) functions in 3D");
187 break;
188
189 case OPERATOR_DIV:
190 TEUCHOS_TEST_FOR_EXCEPTION( (operatorType == OPERATOR_DIV), std::invalid_argument,
191 ">>> ERROR (Basis_HGRAD_HEX_C1_FEM): DIV is invalid operator for rank-0 (scalar) functions in 3D");
192 break;
193
194 case OPERATOR_D2:
195 for (int i0 = 0; i0 < dim0; i0++) {
196 x = inputPoints(i0,0);
197 y = inputPoints(i0,1);
198 z = inputPoints(i0,2);
199
200 // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, D2Cardinality = 6)
201 outputValues(0, i0, 0) = 0.0; // {2, 0, 0}
202 outputValues(0, i0, 1) = (1.0 - z)/8.0; // {1, 1, 0}
203 outputValues(0, i0, 2) = (1.0 - y)/8.0; // {1, 0, 1}
204 outputValues(0, i0, 3) = 0.0; // {0, 2, 0}
205 outputValues(0, i0, 4) = (1.0 - x)/8.0; // {0, 1, 1}
206 outputValues(0, i0, 5) = 0.0; // {0, 0, 2}
207
208 outputValues(1, i0, 0) = 0.0; // {2, 0, 0}
209 outputValues(1, i0, 1) = -(1.0 - z)/8.0; // {1, 1, 0}
210 outputValues(1, i0, 2) = -(1.0 - y)/8.0; // {1, 0, 1}
211 outputValues(1, i0, 3) = 0.0; // {0, 2, 0}
212 outputValues(1, i0, 4) = (1.0 + x)/8.0; // {0, 1, 1}
213 outputValues(1, i0, 5) = 0.0; // {0, 0, 2}
214
215 outputValues(2, i0, 0) = 0.0; // {2, 0, 0}
216 outputValues(2, i0, 1) = (1.0 - z)/8.0; // {1, 1, 0}
217 outputValues(2, i0, 2) = -(1.0 + y)/8.0; // {1, 0, 1}
218 outputValues(2, i0, 3) = 0.0; // {0, 2, 0}
219 outputValues(2, i0, 4) = -(1.0 + x)/8.0; // {0, 1, 1}
220 outputValues(2, i0, 5) = 0.0; // {0, 0, 2}
221
222 outputValues(3, i0, 0) = 0.0; // {2, 0, 0}
223 outputValues(3, i0, 1) = -(1.0 - z)/8.0; // {1, 1, 0}
224 outputValues(3, i0, 2) = (1.0 + y)/8.0; // {1, 0, 1}
225 outputValues(3, i0, 3) = 0.0; // {0, 2, 0}
226 outputValues(3, i0, 4) = -(1.0 - x)/8.0; // {0, 1, 1}
227 outputValues(3, i0, 5) = 0.0; // {0, 0, 2}
228
229
230 outputValues(4, i0, 0) = 0.0; // {2, 0, 0}
231 outputValues(4, i0, 1) = (1.0 + z)/8.0; // {1, 1, 0}
232 outputValues(4, i0, 2) = -(1.0 - y)/8.0; // {1, 0, 1}
233 outputValues(4, i0, 3) = 0.0; // {0, 2, 0}
234 outputValues(4, i0, 4) = -(1.0 - x)/8.0; // {0, 1, 1}
235 outputValues(4, i0, 5) = 0.0; // {0, 0, 2}
236
237 outputValues(5, i0, 0) = 0.0; // {2, 0, 0}
238 outputValues(5, i0, 1) = -(1.0 + z)/8.0; // {1, 1, 0}
239 outputValues(5, i0, 2) = (1.0 - y)/8.0; // {1, 0, 1}
240 outputValues(5, i0, 3) = 0.0; // {0, 2, 0}
241 outputValues(5, i0, 4) = -(1.0 + x)/8.0; // {0, 1, 1}
242 outputValues(5, i0, 5) = 0.0; // {0, 0, 2}
243
244 outputValues(6, i0, 0) = 0.0; // {2, 0, 0}
245 outputValues(6, i0, 1) = (1.0 + z)/8.0; // {1, 1, 0}
246 outputValues(6, i0, 2) = (1.0 + y)/8.0; // {1, 0, 1}
247 outputValues(6, i0, 3) = 0.0; // {0, 2, 0}
248 outputValues(6, i0, 4) = (1.0 + x)/8.0; // {0, 1, 1}
249 outputValues(6, i0, 5) = 0.0; // {0, 0, 2}
250
251 outputValues(7, i0, 0) = 0.0; // {2, 0, 0}
252 outputValues(7, i0, 1) = -(1.0 + z)/8.0; // {1, 1, 0}
253 outputValues(7, i0, 2) = -(1.0 + y)/8.0; // {1, 0, 1}
254 outputValues(7, i0, 3) = 0.0; // {0, 2, 0}
255 outputValues(7, i0, 4) = (1.0 - x)/8.0; // {0, 1, 1}
256 outputValues(7, i0, 5) = 0.0; // {0, 0, 2}
257 }
258 break;
259
260 case OPERATOR_D3:
261 case OPERATOR_D4:
262 case OPERATOR_D5:
263 case OPERATOR_D6:
264 case OPERATOR_D7:
265 case OPERATOR_D8:
266 case OPERATOR_D9:
267 case OPERATOR_D10:
268 {
269 // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, DkCardinality)
270 int DkCardinality = Intrepid::getDkCardinality(operatorType,
271 this -> basisCellTopology_.getDimension() );
272 for(int dofOrd = 0; dofOrd < this -> basisCardinality_; dofOrd++) {
273 for (int i0 = 0; i0 < dim0; i0++) {
274 for(int dkOrd = 0; dkOrd < DkCardinality; dkOrd++){
275 outputValues(dofOrd, i0, dkOrd) = 0.0;
276 }
277 }
278 }
279 }
280 break;
281
282 default:
283 TEUCHOS_TEST_FOR_EXCEPTION( !( Intrepid::isValidOperator(operatorType) ), std::invalid_argument,
284 ">>> ERROR (Basis_HGRAD_HEX_C1_FEM): Invalid operator type");
285 }
286}
287
288
289
290template<class Scalar, class ArrayScalar>
292 const ArrayScalar & inputPoints,
293 const ArrayScalar & cellVertices,
294 const EOperator operatorType) const {
295 TEUCHOS_TEST_FOR_EXCEPTION( (true), std::logic_error,
296 ">>> ERROR (Basis_HGRAD_HEX_C1_FEM): FEM Basis calling an FVD member function");
297 }
298
299template<class Scalar, class ArrayScalar>
301#ifdef HAVE_INTREPID_DEBUG
302 // Verify rank of output array.
303 TEUCHOS_TEST_FOR_EXCEPTION( !(DofCoords.rank() == 2), std::invalid_argument,
304 ">>> ERROR: (Intrepid::Basis_HGRAD_HEX_C1_FEM::getDofCoords) rank = 2 required for DofCoords array");
305 // Verify 0th dimension of output array.
306 TEUCHOS_TEST_FOR_EXCEPTION( !( DofCoords.dimension(0) == this -> basisCardinality_ ), std::invalid_argument,
307 ">>> ERROR: (Intrepid::Basis_HGRAD_HEX_C1_FEM::getDofCoords) mismatch in number of DoF and 0th dimension of DofCoords array");
308 // Verify 1st dimension of output array.
309 TEUCHOS_TEST_FOR_EXCEPTION( !( DofCoords.dimension(1) == (int)(this -> basisCellTopology_.getDimension()) ), std::invalid_argument,
310 ">>> ERROR: (Intrepid::Basis_HGRAD_HEX_C1_FEM::getDofCoords) incorrect reference cell (1st) dimension in DofCoords array");
311#endif
312
313 DofCoords(0,0) = -1.0; DofCoords(0,1) = -1.0; DofCoords(0,2) = -1.0;
314 DofCoords(1,0) = 1.0; DofCoords(1,1) = -1.0; DofCoords(1,2) = -1.0;
315 DofCoords(2,0) = 1.0; DofCoords(2,1) = 1.0; DofCoords(2,2) = -1.0;
316 DofCoords(3,0) = -1.0; DofCoords(3,1) = 1.0; DofCoords(3,2) = -1.0;
317 DofCoords(4,0) = -1.0; DofCoords(4,1) = -1.0; DofCoords(4,2) = 1.0;
318 DofCoords(5,0) = 1.0; DofCoords(5,1) = -1.0; DofCoords(5,2) = 1.0;
319 DofCoords(6,0) = 1.0; DofCoords(6,1) = 1.0; DofCoords(6,2) = 1.0;
320 DofCoords(7,0) = -1.0; DofCoords(7,1) = 1.0; DofCoords(7,2) = 1.0;
321}
322
323}// namespace Intrepid
324
325#endif
326
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
Evaluation of a FEM basis on a reference Hexahedron cell.
void getDofCoords(ArrayScalar &DofCoords) const
Returns spatial locations (coordinates) of degrees of freedom on a reference Quadrilateral.