Intrepid
Intrepid_HGRAD_QUAD_C2_FEMDef.hpp
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1 #ifndef INTREPID_HGRAD_QUAD_C2_FEMDEF_HPP
2 #define INTREPID_HGRAD_QUAD_C2_FEMDEF_HPP
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45 
51 namespace Intrepid {
52 
53  template<class Scalar, class ArrayScalar>
54  Basis_HGRAD_QUAD_C2_FEM<Scalar, ArrayScalar>::Basis_HGRAD_QUAD_C2_FEM()
55  {
56  this -> basisCardinality_ = 9;
57  this -> basisDegree_ = 2;
58  this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() );
59  this -> basisType_ = BASIS_FEM_DEFAULT;
60  this -> basisCoordinates_ = COORDINATES_CARTESIAN;
61  this -> basisTagsAreSet_ = false;
62  }
63 
64 
65 template<class Scalar, class ArrayScalar>
66 void Basis_HGRAD_QUAD_C2_FEM<Scalar, ArrayScalar>::initializeTags() {
67 
68  // Basis-dependent intializations
69  int tagSize = 4; // size of DoF tag, i.e., number of fields in the tag
70  int posScDim = 0; // position in the tag, counting from 0, of the subcell dim
71  int posScOrd = 1; // position in the tag, counting from 0, of the subcell ordinal
72  int posDfOrd = 2; // position in the tag, counting from 0, of DoF ordinal relative to the subcell
73 
74  // An array with local DoF tags assigned to basis functions, in the order of their local enumeration
75  int tags[] = { 0, 0, 0, 1,
76  0, 1, 0, 1,
77  0, 2, 0, 1,
78  0, 3, 0, 1,
79  // edge midpoints
80  1, 0, 0, 1,
81  1, 1, 0, 1,
82  1, 2, 0, 1,
83  1, 3, 0, 1,
84  // quad center
85  2, 0, 0, 1};
86 
87  // Basis-independent function sets tag and enum data in tagToOrdinal_ and ordinalToTag_ arrays:
88  Intrepid::setOrdinalTagData(this -> tagToOrdinal_,
89  this -> ordinalToTag_,
90  tags,
91  this -> basisCardinality_,
92  tagSize,
93  posScDim,
94  posScOrd,
95  posDfOrd);
96 }
97 
98 
99 
100 template<class Scalar, class ArrayScalar>
101 void Basis_HGRAD_QUAD_C2_FEM<Scalar, ArrayScalar>::getValues(ArrayScalar & outputValues,
102  const ArrayScalar & inputPoints,
103  const EOperator operatorType) const {
104 
105  // Verify arguments
106 #ifdef HAVE_INTREPID_DEBUG
107  Intrepid::getValues_HGRAD_Args<Scalar, ArrayScalar>(outputValues,
108  inputPoints,
109  operatorType,
110  this -> getBaseCellTopology(),
111  this -> getCardinality() );
112 #endif
113 
114  // Number of evaluation points = dim 0 of inputPoints
115  int dim0 = inputPoints.dimension(0);
116 
117  // Temporaries: (x,y) coordinates of the evaluation point
118  Scalar x = 0.0;
119  Scalar y = 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 
128  // outputValues is a rank-2 array with dimensions (basisCardinality_, dim0)
129  outputValues(0, i0) = x*(x - 1.0)*y*(y - 1.0)/4.0;
130  outputValues(1, i0) = x*(x + 1.0)*y*(y - 1.0)/4.0;
131  outputValues(2, i0) = x*(x + 1.0)*y*(y + 1.0)/4.0;
132  outputValues(3, i0) = x*(x - 1.0)*y*(y + 1.0)/4.0;
133  // edge midpoints basis functions
134  outputValues(4, i0) = (1.0 - x)*(1.0 + x)*y*(y - 1.0)/2.0;
135  outputValues(5, i0) = x*(x + 1.0)*(1.0 - y)*(1.0 + y)/2.0;
136  outputValues(6, i0) = (1.0 - x)*(1.0 + x)*y*(y + 1.0)/2.0;
137  outputValues(7, i0) = x*(x - 1.0)*(1.0 - y)*(1.0 + y)/2.0;
138  // quad bubble basis function
139  outputValues(8, i0) = (1.0 - x)*(1.0 + x)*(1.0 - y)*(1.0 + y);
140  }
141  break;
142 
143  case OPERATOR_GRAD:
144  case OPERATOR_D1:
145  for (int i0 = 0; i0 < dim0; i0++) {
146  x = inputPoints(i0,0);
147  y = inputPoints(i0,1);
148 
149  // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, spaceDim)
150  outputValues(0, i0, 0) = (-0.25 + 0.5*x)*(-1. + y)*y;
151  outputValues(0, i0, 1) = (-1.0 + x)*x*(-0.25 + 0.5*y);
152 
153  outputValues(1, i0, 0) = (0.25 + 0.5*x)*(-1. + y)*y;
154  outputValues(1, i0, 1) = x*(1. + x)*(-0.25 + 0.5*y);
155 
156  outputValues(2, i0, 0) = (0.25 + 0.5*x)*y*(1. + y);
157  outputValues(2, i0, 1) = x*(1. + x)*(0.25 + 0.5*y);
158 
159  outputValues(3, i0, 0) = (-0.25 + 0.5*x)*y*(1. + y);
160  outputValues(3, i0, 1) = (-1. + x)*x*(0.25 + 0.5*y);
161 
162  outputValues(4, i0, 0) = x*(1.0 - y)*y;
163  outputValues(4, i0, 1) = 0.5*(1.0 - x)*(1.0 + x)*(-1.0 + 2.0*y);
164 
165  outputValues(5, i0, 0) = 0.5*(1.0 - y)*(1.0 + y)*(1.0 + 2.0*x);
166  outputValues(5, i0, 1) =-x*(1.0 + x)*y;
167 
168  outputValues(6, i0, 0) =-y*(1.0 + y)*x;
169  outputValues(6, i0, 1) = 0.5*(1.0 - x)*(1.0 + x)*(1.0 + 2.0*y);
170 
171  outputValues(7, i0, 0) = 0.5*(1.0 - y)*(1.0+ y)*(-1.0 + 2.0*x);
172  outputValues(7, i0, 1) = (1.0 - x)*x*y;
173 
174  outputValues(8, i0, 0) =-2.0*(1.0 - y)*(1.0 + y)*x;
175  outputValues(8, i0, 1) =-2.0*(1.0 - x)*(1.0 + x)*y;
176  }
177  break;
178 
179  case OPERATOR_CURL:
180  for (int i0 = 0; i0 < dim0; i0++) {
181  x = inputPoints(i0,0);
182  y = inputPoints(i0,1);
183 
184  // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, spaceDim)
185  // CURL(u) = (u_y, -u_x), is rotated GRAD
186  outputValues(0, i0, 1) =-(-0.25 + 0.5*x)*(-1. + y)*y;
187  outputValues(0, i0, 0) = (-1.0 + x)*x*(-0.25 + 0.5*y);
188 
189  outputValues(1, i0, 1) =-(0.25 + 0.5*x)*(-1. + y)*y;
190  outputValues(1, i0, 0) = x*(1. + x)*(-0.25 + 0.5*y);
191 
192  outputValues(2, i0, 1) =-(0.25 + 0.5*x)*y*(1. + y);
193  outputValues(2, i0, 0) = x*(1. + x)*(0.25 + 0.5*y);
194 
195  outputValues(3, i0, 1) =-(-0.25 + 0.5*x)*y*(1. + y);
196  outputValues(3, i0, 0) = (-1. + x)*x*(0.25 + 0.5*y);
197 
198  outputValues(4, i0, 1) =-x*(1.0 - y)*y;
199  outputValues(4, i0, 0) = 0.5*(1.0 - x)*(1.0 + x)*(-1.0 + 2.0*y);
200 
201  outputValues(5, i0, 1) =-0.5*(1.0 - y)*(1.0 + y)*(1.0 + 2.0*x);
202  outputValues(5, i0, 0) =-x*(1.0 + x)*y;
203 
204  outputValues(6, i0, 1) = y*(1.0 + y)*x;
205  outputValues(6, i0, 0) = 0.5*(1.0 - x)*(1.0 + x)*(1.0 + 2.0*y);
206 
207  outputValues(7, i0, 1) =-0.5*(1.0 - y)*(1.0 + y)*(-1.0 + 2.0*x);
208  outputValues(7, i0, 0) = (1.0 - x)*x*y;
209 
210  outputValues(8, i0, 1) = 2.0*(1.0 - y)*(1.0 + y)*x;
211  outputValues(8, i0, 0) =-2.0*(1.0 - x)*(1.0 + x)*y;
212  }
213  break;
214 
215  case OPERATOR_DIV:
216  TEUCHOS_TEST_FOR_EXCEPTION( (operatorType == OPERATOR_DIV), std::invalid_argument,
217  ">>> ERROR (Basis_HGRAD_QUAD_C2_FEM): DIV is invalid operator for rank-0 (scalar) functions in 2D");
218  break;
219 
220  case OPERATOR_D2:
221  for (int i0 = 0; i0 < dim0; i0++) {
222  x = inputPoints(i0,0);
223  y = inputPoints(i0,1);
224 
225  // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, D2Cardinality=3)
226  outputValues(0, i0, 0) = 0.5*(-1.0 + y)*y;
227  outputValues(0, i0, 1) = 0.25 - 0.5*y + x*(-0.5 + 1.*y);
228  outputValues(0, i0, 2) = 0.5*(-1.0 + x)*x;
229 
230  outputValues(1, i0, 0) = 0.5*(-1.0 + y)*y;
231  outputValues(1, i0, 1) =-0.25 + 0.5*y + x*(-0.5 + 1.*y);
232  outputValues(1, i0, 2) = 0.5*x*(1.0 + x);
233 
234  outputValues(2, i0, 0) = 0.5*y*(1.0 + y);
235  outputValues(2, i0, 1) = 0.25 + 0.5*y + x*(0.5 + 1.*y);
236  outputValues(2, i0, 2) = 0.5*x*(1.0 + x);
237 
238  outputValues(3, i0, 0) = 0.5*y*(1.0 + y);
239  outputValues(3, i0, 1) =-0.25 - 0.5*y + x*(0.5 + 1.*y);
240  outputValues(3, i0, 2) = 0.5*(-1.0 + x)*x;
241 
242  outputValues(4, i0, 0) = (1.0 - y)*y;
243  outputValues(4, i0, 1) = x*(1. - 2.*y);
244  outputValues(4, i0, 2) = (1.0 - x)*(1.0 + x);
245 
246  outputValues(5, i0, 0) = (1.0 - y)*(1.0 + y);
247  outputValues(5, i0, 1) = x*(0. - 2.*y) - 1.*y;
248  outputValues(5, i0, 2) =-x*(1.0 + x);
249 
250  outputValues(6, i0, 0) =-y*(1.0 + y);
251  outputValues(6, i0, 1) = x*(-1. - 2.*y);
252  outputValues(6, i0, 2) = (1.0 - x)*(1.0 + x);
253 
254  outputValues(7, i0, 0) = (1.0 - y)*(1.0 + y);
255  outputValues(7, i0, 1) = x*(0. - 2.*y) + 1.*y;
256  outputValues(7, i0, 2) = (1.0 - x)*x;
257 
258  outputValues(8, i0, 0) =-2.0 + 2.0*y*y;
259  outputValues(8, i0, 1) = 4*x*y;
260  outputValues(8, i0, 2) =-2.0 + 2.0*x*x;
261 
262  }
263  break;
264 
265  case OPERATOR_D3:
266  // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, D3Cardinality=4)
267  for (int i0 = 0; i0 < dim0; i0++) {
268  x = inputPoints(i0,0);
269  y = inputPoints(i0,1);
270 
271  outputValues(0, i0, 0) = 0.0;
272  outputValues(0, i0, 1) =-0.5 + y;
273  outputValues(0, i0, 2) =-0.5 + x;
274  outputValues(0, i0, 3) = 0.0;
275 
276  outputValues(1, i0, 0) = 0.0;
277  outputValues(1, i0, 1) =-0.5 + y;
278  outputValues(1, i0, 2) = 0.5 + x;
279  outputValues(1, i0, 3) = 0.0;
280 
281  outputValues(2, i0, 0) = 0.0;
282  outputValues(2, i0, 1) = 0.5 + y;
283  outputValues(2, i0, 2) = 0.5 + x;
284  outputValues(2, i0, 3) = 0.0;
285 
286  outputValues(3, i0, 0) = 0.0;
287  outputValues(3, i0, 1) = 0.5 + y;
288  outputValues(3, i0, 2) =-0.5 + x;
289  outputValues(3, i0, 3) = 0.0;
290 
291  outputValues(4, i0, 0) = 0.0;
292  outputValues(4, i0, 1) = 1.0 - 2.0*y;
293  outputValues(4, i0, 2) =-2.0*x;
294  outputValues(4, i0, 3) = 0.0;
295 
296  outputValues(5, i0, 0) = 0.0;
297  outputValues(5, i0, 1) =-2.0*y;
298  outputValues(5, i0, 2) =-1.0 - 2.0*x;
299  outputValues(5, i0, 3) = 0.0;
300 
301  outputValues(6, i0, 0) = 0.0;
302  outputValues(6, i0, 1) =-1.0 - 2.0*y;
303  outputValues(6, i0, 2) =-2.0*x;
304  outputValues(6, i0, 3) = 0.0;
305 
306  outputValues(7, i0, 0) = 0.0;
307  outputValues(7, i0, 1) =-2.0*y;
308  outputValues(7, i0, 2) = 1.0 - 2.0*x;
309  outputValues(7, i0, 3) = 0.0;
310 
311  outputValues(8, i0, 0) = 0.0;
312  outputValues(8, i0, 1) = 4.0*y;
313  outputValues(8, i0, 2) = 4.0*x;
314  outputValues(8, i0, 3) = 0.0;
315  }
316  break;
317 
318  case OPERATOR_D4:
319  // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, D4Cardinality=5)
320  for (int i0 = 0; i0 < dim0; i0++) {
321 
322  outputValues(0, i0, 0) = 0.0;
323  outputValues(0, i0, 1) = 0.0;
324  outputValues(0, i0, 2) = 1.0;
325  outputValues(0, i0, 3) = 0.0;
326  outputValues(0, i0, 4) = 0.0;
327 
328  outputValues(1, i0, 0) = 0.0;
329  outputValues(1, i0, 1) = 0.0;
330  outputValues(1, i0, 2) = 1.0;
331  outputValues(1, i0, 3) = 0.0;
332  outputValues(1, i0, 4) = 0.0;
333 
334  outputValues(2, i0, 0) = 0.0;
335  outputValues(2, i0, 1) = 0.0;
336  outputValues(2, i0, 2) = 1.0;
337  outputValues(2, i0, 3) = 0.0;
338  outputValues(2, i0, 4) = 0.0;
339 
340  outputValues(3, i0, 0) = 0.0;
341  outputValues(3, i0, 1) = 0.0;
342  outputValues(3, i0, 2) = 1.0;
343  outputValues(3, i0, 3) = 0.0;
344  outputValues(3, i0, 4) = 0.0;
345 
346  outputValues(4, i0, 0) = 0.0;
347  outputValues(4, i0, 1) = 0.0;
348  outputValues(4, i0, 2) =-2.0;
349  outputValues(4, i0, 3) = 0.0;
350  outputValues(4, i0, 4) = 0.0;
351 
352  outputValues(5, i0, 0) = 0.0;
353  outputValues(5, i0, 1) = 0.0;
354  outputValues(5, i0, 2) =-2.0;
355  outputValues(5, i0, 3) = 0.0;
356  outputValues(5, i0, 4) = 0.0;
357 
358  outputValues(6, i0, 0) = 0.0;
359  outputValues(6, i0, 1) = 0.0;
360  outputValues(6, i0, 2) =-2.0;
361  outputValues(6, i0, 3) = 0.0;
362  outputValues(6, i0, 4) = 0.0;
363 
364  outputValues(7, i0, 0) = 0.0;
365  outputValues(7, i0, 1) = 0.0;
366  outputValues(7, i0, 2) =-2.0;
367  outputValues(7, i0, 3) = 0.0;
368  outputValues(7, i0, 4) = 0.0;
369 
370  outputValues(8, i0, 0) = 0.0;
371  outputValues(8, i0, 1) = 0.0;
372  outputValues(8, i0, 2) = 4.0;
373  outputValues(8, i0, 3) = 0.0;
374  outputValues(8, i0, 4) = 0.0;
375  }
376  break;
377 
378  case OPERATOR_D5:
379  case OPERATOR_D6:
380  case OPERATOR_D7:
381  case OPERATOR_D8:
382  case OPERATOR_D9:
383  case OPERATOR_D10:
384  {
385  // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, DkCardinality)
386  int DkCardinality = Intrepid::getDkCardinality(operatorType,
387  this -> basisCellTopology_.getDimension() );
388  for(int dofOrd = 0; dofOrd < this -> basisCardinality_; dofOrd++) {
389  for (int i0 = 0; i0 < dim0; i0++) {
390  for(int dkOrd = 0; dkOrd < DkCardinality; dkOrd++){
391  outputValues(dofOrd, i0, dkOrd) = 0.0;
392  }
393  }
394  }
395  }
396  break;
397 
398  default:
399  TEUCHOS_TEST_FOR_EXCEPTION( !( Intrepid::isValidOperator(operatorType) ), std::invalid_argument,
400  ">>> ERROR (Basis_HGRAD_QUAD_C2_FEM): Invalid operator type");
401  }
402 }
403 
404 
405 
406 template<class Scalar, class ArrayScalar>
407 void Basis_HGRAD_QUAD_C2_FEM<Scalar, ArrayScalar>::getValues(ArrayScalar& outputValues,
408  const ArrayScalar & inputPoints,
409  const ArrayScalar & cellVertices,
410  const EOperator operatorType) const {
411  TEUCHOS_TEST_FOR_EXCEPTION( (true), std::logic_error,
412  ">>> ERROR (Basis_HGRAD_QUAD_C2_FEM): FEM Basis calling an FVD member function");
413 }
414 
415 
416 
417 template<class Scalar, class ArrayScalar>
418 void Basis_HGRAD_QUAD_C2_FEM<Scalar, ArrayScalar>::getDofCoords(ArrayScalar & DofCoords) const {
419 #ifdef HAVE_INTREPID_DEBUG
420  // Verify rank of output array.
421  TEUCHOS_TEST_FOR_EXCEPTION( !(DofCoords.rank() == 2), std::invalid_argument,
422  ">>> ERROR: (Intrepid::Basis_HGRAD_QUAD_C2_FEM::getDofCoords) rank = 2 required for DofCoords array");
423  // Verify 0th dimension of output array.
424  TEUCHOS_TEST_FOR_EXCEPTION( !( DofCoords.dimension(0) == this -> basisCardinality_ ), std::invalid_argument,
425  ">>> ERROR: (Intrepid::Basis_HGRAD_QUAD_C2_FEM::getDofCoords) mismatch in number of DoF and 0th dimension of DofCoords array");
426  // Verify 1st dimension of output array.
427  TEUCHOS_TEST_FOR_EXCEPTION( !( DofCoords.dimension(1) == (int)(this -> basisCellTopology_.getDimension()) ), std::invalid_argument,
428  ">>> ERROR: (Intrepid::Basis_HGRAD_QUAD_C2_FEM::getDofCoords) incorrect reference cell (1st) dimension in DofCoords array");
429 #endif
430 
431  DofCoords(0,0) = -1.0; DofCoords(0,1) = -1.0;
432  DofCoords(1,0) = 1.0; DofCoords(1,1) = -1.0;
433  DofCoords(2,0) = 1.0; DofCoords(2,1) = 1.0;
434  DofCoords(3,0) = -1.0; DofCoords(3,1) = 1.0;
435 
436  DofCoords(4,0) = 0.0; DofCoords(4,1) = -1.0;
437  DofCoords(5,0) = 1.0; DofCoords(5,1) = 0.0;
438  DofCoords(6,0) = 0.0; DofCoords(6,1) = 1.0;
439  DofCoords(7,0) = -1.0; DofCoords(7,1) = 0.0;
440 
441  DofCoords(8,0) = 0.0; DofCoords(8,1) = 0.0;
442 
443 }
444 
445 }// namespace Intrepid
446 #endif
Intrepid::Basis_HGRAD_QUAD_C2_FEM::initializeTags
void initializeTags()
Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays.
Definition: Intrepid_HGRAD_QUAD_C2_FEMDef.hpp:66
Intrepid::Basis_HGRAD_QUAD_C2_FEM::getValues
void getValues(ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
FEM basis evaluation on a reference Quadrilateral cell.
Definition: Intrepid_HGRAD_QUAD_C2_FEMDef.hpp:101
Intrepid::Basis_HGRAD_QUAD_C2_FEM::Basis_HGRAD_QUAD_C2_FEM
Basis_HGRAD_QUAD_C2_FEM()
Constructor.
Definition: Intrepid_HGRAD_QUAD_C2_FEMDef.hpp:54
Intrepid::Basis_HGRAD_QUAD_C2_FEM::getDofCoords
void getDofCoords(ArrayScalar &DofCoords) const
Returns spatial locations (coordinates) of degrees of freedom on a reference Quadrilateral.
Definition: Intrepid_HGRAD_QUAD_C2_FEMDef.hpp:418
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