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 
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48 
54 namespace Intrepid {
55 
56  template<class Scalar, class ArrayScalar>
57  Basis_HGRAD_PYR_C1_FEM<Scalar, ArrayScalar>::Basis_HGRAD_PYR_C1_FEM()
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 
68 template<class Scalar, class ArrayScalar>
69 void Basis_HGRAD_PYR_C1_FEM<Scalar, ArrayScalar>::initializeTags() {
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 
97 template<class Scalar, class ArrayScalar>
98 void Basis_HGRAD_PYR_C1_FEM<Scalar, ArrayScalar>::getValues(ArrayScalar & outputValues,
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 
284 template<class Scalar, class ArrayScalar>
285 void Basis_HGRAD_PYR_C1_FEM<Scalar, ArrayScalar>::getValues(ArrayScalar& outputValues,
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
Intrepid::Basis_HGRAD_PYR_C1_FEM::getValues
void getValues(ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
FEM basis evaluation on a reference Pyramid cell.
Definition: Intrepid_HGRAD_PYR_C1_FEMDef.hpp:98
Intrepid::Basis_HGRAD_PYR_C1_FEM::initializeTags
void initializeTags()
Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays.
Definition: Intrepid_HGRAD_PYR_C1_FEMDef.hpp:69
Intrepid::Basis_HGRAD_PYR_C1_FEM::Basis_HGRAD_PYR_C1_FEM
Basis_HGRAD_PYR_C1_FEM()
Constructor.
Definition: Intrepid_HGRAD_PYR_C1_FEMDef.hpp:57
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