Chaste Commit::f2ff7ee04e70ac9d06c57344df8d017dbb12b97b
QuadraticBasisFunction.cpp
1/*
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34*/
35
36#include "QuadraticBasisFunction.hpp"
37#include "Exception.hpp"
38#include "UblasIncludes.hpp"
39
49double QuadraticBasisFunction<0>::ComputeBasisFunction(const ChastePoint<0>& rPoint, unsigned basisIndex)
50{
51 assert(basisIndex == 0);
52 return 1.0;
53}
54
62void QuadraticBasisFunction<0>::ComputeBasisFunctions(const ChastePoint<0>& rPoint,
63 c_vector<double, 1>& rReturnValue)
64{
65 rReturnValue(0) = ComputeBasisFunction(rPoint, 0);
66}
67
77template <unsigned ELEMENT_DIM>
78double QuadraticBasisFunction<ELEMENT_DIM>::ComputeBasisFunction(const ChastePoint<ELEMENT_DIM>& rPoint, unsigned basisIndex)
79{
80 assert(ELEMENT_DIM < 4 && ELEMENT_DIM >= 0);
81 double x, y, z;
82 switch (ELEMENT_DIM)
83 {
84 case 0:
85 assert(basisIndex == 0);
86 return 1.0;
87 break;
88
89 case 1:
90 x = rPoint[0];
91 switch (basisIndex)
92 {
93 case 0:
94 return 2.0*(x-1.0)*(x-0.5);
95 break;
96 case 1:
97 return 2.0*x*(x-0.5);
98 break;
99 case 2:
100 return 4.0*x*(1.0-x);
101 break;
102 default:
103 NEVER_REACHED;
104 }
105 break;
106
107 case 2:
108 x = rPoint[0];
109 y = rPoint[1];
110 switch (basisIndex)
111 {
112 case 0: // the node at (0,0)
113 return 2.0 * (1.0 - x - y) * (0.5 - x - y);
114 break;
115 case 1: // the node at (1,0)
116 return 2.0*x*(x-0.5);
117 break;
118 case 2: // the node at (0,1)
119 return 2.0*y*(y-0.5);
120 break;
121 case 3: // the node opposite 0, which is (1/2,1/2)
122 return 4.0 * y * x;
123 break;
124 case 4: // the node opposite 1, which is (0,1/2)
125 return 4.0 * (1.0 - x - y) * y;
126 break;
127 case 5: // the node opposite 2, which is (1/2,0)
128 return 4.0 * (1.0 - x - y) * x;
129 break;
130 default:
131 NEVER_REACHED;
132 }
133 break;
134
135 case 3:
136 x = rPoint[0];
137 y = rPoint[1];
138 z = rPoint[2];
139 switch (basisIndex)
140 {
141 case 0: // the node at (0,0,0)
142 return 2.0 * (1.0 - x - y - z) * (0.5 - x - y - z);
143 break;
144 case 1: // the node at (1,0,0)
145 return 2.0*x*(x-0.5);
146 break;
147 case 2: // the node at (0,1,0)
148 return 2.0*y*(y-0.5);
149 break;
150 case 3: // the node at (0,0,1)
151 return 2.0*z*(z-0.5);
152 break;
153 case 4: // our (tetgen convention), node4 is between nodes 0 and 1, (1/2,0,0)
154 return 4.0 * (1.0 - x - y - z) * x;
155 break;
156 case 5: // our (tetgen convention), node5 is between nodes 1 and 2, (1/2,1/2,0)
157 return 4 * x * y;
158 break;
159 case 6: // our (tetgen convention), node6 is between nodes 0 and 2, (0,1/2,0)
160 return 4.0 * (1.0 - x - y - z) * y;
161 break;
162 case 7: // our (tetgen convention), node7 is between nodes 0 and 3, (0,0,1/2)
163 return 4.0 * (1.0 - x - y - z) * z;
164 break;
165 case 8: // our (tetgen convention), node8 is between nodes 1 and 3, (1/2,0,1/2)
166 return 4.0 * x * z;
167 break;
168 case 9: // our (tetgen convention), node9 is between nodes 2 and 3, (0,1/2,1/2)
169 return 4.0 * y * z;
170 break;
171 default:
172 NEVER_REACHED;
173 }
174 break;
175 }
176 return 0.0; // Avoid compiler warning
177}
178
189template <unsigned ELEMENT_DIM>
190c_vector<double, ELEMENT_DIM> QuadraticBasisFunction<ELEMENT_DIM>::ComputeBasisFunctionDerivative(const ChastePoint<ELEMENT_DIM>& rPoint, unsigned basisIndex)
191{
192 c_vector<double, ELEMENT_DIM> gradN;
193 assert(ELEMENT_DIM < 4 && ELEMENT_DIM > 0);
194
195 double x, y, z;
196 switch (ELEMENT_DIM)
197 {
198 case 1:
199 x = rPoint[0];
200 switch (basisIndex)
201 {
202 case 0:
203 gradN(0) = 4.0*x-3.0;
204 break;
205 case 1:
206 gradN(0) = 4.0*x-1.0;
207 break;
208 case 2:
209 gradN(0) = 4.0-8.0*x;
210 break;
211 default:
212 NEVER_REACHED;
213 }
214 break;
215
216 case 2:
217 x = rPoint[0];
218 y = rPoint[1];
219 switch (basisIndex)
220 {
221 case 0:
222 gradN(0) = -3.0 + 4.0*x + 4.0*y;
223 gradN(1) = -3.0 + 4.0*x + 4.0*y;
224 break;
225 case 1:
226 gradN(0) = 4.0*x - 1.0;
227 gradN(1) = 0.0;
228 break;
229 case 2:
230 gradN(0) = 0.0;
231 gradN(1) = 4.0*y - 1.0;
232 break;
233 case 3:
234 gradN(0) = 4.0*y;
235 gradN(1) = 4.0*x;
236 break;
237 case 4:
238 gradN(0) = -4.0*y;
239 gradN(1) = 4.0-4.0*x-8.0*y;
240 break;
241 case 5:
242 gradN(0) = 4.0-8.0*x-4.0*y;
243 gradN(1) = -4.0*x;
244 break;
245 default:
246 NEVER_REACHED;
247 }
248 break;
249
250 case 3:
251 x = rPoint[0];
252 y = rPoint[1];
253 z = rPoint[2];
254 switch (basisIndex)
255 {
256 case 0:
257 gradN(0) = -3.0 + 4.0*(x+y+z);
258 gradN(1) = -3.0 + 4.0*(x+y+z);
259 gradN(2) = -3.0 + 4.0*(x+y+z);
260 break;
261 case 1:
262 gradN(0) = 4.0*x-1.0;
263 gradN(1) = 0;
264 gradN(2) = 0;
265 break;
266 case 2:
267 gradN(0) = 0;
268 gradN(1) = 4.0*y-1.0;
269 gradN(2) = 0;
270 break;
271 case 3:
272 gradN(0) = 0;
273 gradN(1) = 0;
274 gradN(2) = 4.0*z-1.0;
275 break;
276 case 4:
277 gradN(0) = 4.0-8.0*x-4.0*y-4.0*z;
278 gradN(1) = -4.0*x;
279 gradN(2) = -4.0*x;
280 break;
281 case 5:
282 gradN(0) = 4.0*y;
283 gradN(1) = 4.0*x;
284 gradN(2) = 0.0;
285 break;
286 case 6:
287 gradN(0) = -4.0*y;
288 gradN(1) = 4.0-4.0*x-8.0*y-4.0*z;
289 gradN(2) = -4.0*y;
290 break;
291 case 7:
292 gradN(0) = -4.0*z;
293 gradN(1) = -4.0*z;
294 gradN(2) = 4.0-4.0*x-4.0*y-8.0*z;
295 break;
296 case 8:
297 gradN(0) = 4.0*z;
298 gradN(1) = 0;
299 gradN(2) = 4.0*x;
300 break;
301 case 9:
302 gradN(0) = 0;
303 gradN(1) = 4.0*z;
304 gradN(2) = 4.0*y;
305 break;
306 default:
307 NEVER_REACHED;
308 }
309 break;
310 }
311 return gradN;
312}
313
321template <unsigned ELEMENT_DIM>
322void QuadraticBasisFunction<ELEMENT_DIM>::ComputeBasisFunctions(const ChastePoint<ELEMENT_DIM>& rPoint,
323 c_vector<double, (ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2>& rReturnValue)
324{
325 assert(ELEMENT_DIM < 4 && ELEMENT_DIM >= 0);
326
327 for (unsigned i=0; i<(ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2; i++)
328 {
329 rReturnValue(i) = ComputeBasisFunction(rPoint, i);
330 }
331}
332
342template <unsigned ELEMENT_DIM>
343void QuadraticBasisFunction<ELEMENT_DIM>::ComputeBasisFunctionDerivatives(const ChastePoint<ELEMENT_DIM>& rPoint,
344 c_matrix<double, ELEMENT_DIM, (ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2>& rReturnValue)
345{
346 assert(ELEMENT_DIM < 4 && ELEMENT_DIM > 0);
347
348 for (unsigned j=0; j<(ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2; j++)
349 {
350 matrix_column<c_matrix<double, ELEMENT_DIM, (ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2> > column(rReturnValue, j);
351 column = ComputeBasisFunctionDerivative(rPoint, j);
352 }
353}
354
368template <unsigned ELEMENT_DIM>
369void QuadraticBasisFunction<ELEMENT_DIM>::ComputeTransformedBasisFunctionDerivatives(const ChastePoint<ELEMENT_DIM>& rPoint,
370 const c_matrix<double, ELEMENT_DIM, ELEMENT_DIM>& rInverseJacobian,
371 c_matrix<double, ELEMENT_DIM, (ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2>& rReturnValue)
372{
373 assert(ELEMENT_DIM < 4 && ELEMENT_DIM > 0);
374
375 ComputeBasisFunctionDerivatives(rPoint, rReturnValue);
376 rReturnValue = prod(trans(rInverseJacobian), rReturnValue);
377}
378
379// Explicit instantiation
380template class QuadraticBasisFunction<1>;
381template class QuadraticBasisFunction<2>;
382template class QuadraticBasisFunction<3>;
NEVER_REACHED
#define NEVER_REACHED
Definition Exception.hpp:219
QuadraticBasisFunction::ComputeBasisFunction
static double ComputeBasisFunction(const ChastePoint< ELEMENT_DIM > &rPoint, unsigned basisIndex)
Definition QuadraticBasisFunction.cpp:78
QuadraticBasisFunction::ComputeBasisFunctionDerivative
static c_vector< double, ELEMENT_DIM > ComputeBasisFunctionDerivative(const ChastePoint< ELEMENT_DIM > &rPoint, unsigned basisIndex)
Definition QuadraticBasisFunction.cpp:190
QuadraticBasisFunction::ComputeBasisFunctions
static void ComputeBasisFunctions(const ChastePoint< ELEMENT_DIM > &rPoint, c_vector< double,(ELEMENT_DIM+1) *(ELEMENT_DIM+2)/2 > &rReturnValue)
Definition QuadraticBasisFunction.cpp:322
QuadraticBasisFunction::ComputeTransformedBasisFunctionDerivatives
static void ComputeTransformedBasisFunctionDerivatives(const ChastePoint< ELEMENT_DIM > &rPoint, const c_matrix< double, ELEMENT_DIM, ELEMENT_DIM > &rInverseJacobian, c_matrix< double, ELEMENT_DIM,(ELEMENT_DIM+1) *(ELEMENT_DIM+2)/2 > &rReturnValue)
Definition QuadraticBasisFunction.cpp:369
QuadraticBasisFunction::ComputeBasisFunctionDerivatives
static void ComputeBasisFunctionDerivatives(const ChastePoint< ELEMENT_DIM > &rPoint, c_matrix< double, ELEMENT_DIM,(ELEMENT_DIM+1) *(ELEMENT_DIM+2)/2 > &rReturnValue)
Definition QuadraticBasisFunction.cpp:343