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Contents of /trunk/finley/src/Quadrature.c

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Revision 964 - (show annotations)
Tue Feb 13 05:10:26 2007 UTC (12 years, 8 months ago) by gross
File MIME type: text/plain
File size: 16607 byte(s)
The set/getRefVal functions of Data objects have been removed (mainly to avoid later problems with MPI).
Moreover, a faster access to the reference id of samples has been introduced. I don't think that anybody will
profit form this at this stage but it will allow a faster dump of data objects.


1 /*
2 ************************************************************
3 * Copyright 2006 by ACcESS MNRF *
4 * *
5 * http://www.access.edu.au *
6 * Primary Business: Queensland, Australia *
7 * Licensed under the Open Software License version 3.0 *
8 * http://www.opensource.org/licenses/osl-3.0.php *
9 * *
10 ************************************************************
11 */
12
13 /**************************************************************/
14
15 /* Finley: */
16
17 /**************************************************************/
18
19 /* Author: gross@access.edu.au */
20 /* Version: $Id$ */
21
22 /**************************************************************/
23
24 #include "Quadrature.h"
25
26 #define QUADNODES(_K_,_I_) quadNodes[INDEX2(_K_,_I_,DIM)]
27 #define QUADWEIGHTS(_I_) quadWeights[_I_]
28
29 /**************************************************************/
30
31 /* get a quadrature scheme with numQuadNodes quadrature nodes for the tri */
32 /* as a queezed scheme on a quad [0,1]^2 */
33
34 void Finley_Quad_getNodesTri(int numQuadNodes,double* quadNodes,double* quadWeights) {
35 int i;
36 double Q1,Q2;
37 #define DIM 2
38
39 /* the easy case: */
40
41 if (numQuadNodes==1) {
42 QUADNODES(0,0)=1./3.;
43 QUADNODES(1,0)=1./3.;
44 QUADWEIGHTS(0)= .5;
45 } else {
46
47 /* get scheme on [0.1]^2 */
48
49 Finley_Quad_getNodesRec(numQuadNodes,quadNodes,quadWeights);
50 if (! Finley_noError()) return;
51
52 /* squeeze it: */
53
54 for (i=0;i<numQuadNodes;i++) {
55 Q1=QUADNODES(0,i);
56 Q2=QUADNODES(1,i);
57 QUADWEIGHTS(i)=QUADWEIGHTS(i)*(1.-(1./2.)*(Q1+Q2));
58 QUADNODES(0,i)=Q1*(1.-(1./2.)*Q2);
59 QUADNODES(1,i)=Q2*(1.-(1./2.)*Q1);
60 }
61 }
62 #undef DIM
63 }
64
65 /**************************************************************/
66
67 /* get a quadrature scheme with numQuadNodes quadrature nodes for the tet */
68 /* as a queezed scheme on a hex [0,1]^3 */
69
70 void Finley_Quad_getNodesTet(int numQuadNodes,double* quadNodes,double* quadWeights) {
71 int i;
72 double Q1,Q2,Q3,JA11,JA12,JA13,JA21,JA22,JA23,JA31,JA32,JA33,DET;
73 #define DIM 3
74
75 /* the easy case: */
76
77 if (numQuadNodes==1) {
78 QUADNODES(0,0)= .25;
79 QUADNODES(1,0)= .25;
80 QUADNODES(2,0)= .25;
81 QUADWEIGHTS(0)=1./6.;
82 } else {
83
84 /* get scheme on [0.1]^3 */
85
86 Finley_Quad_getNodesHex(numQuadNodes,quadNodes,quadWeights);
87 if (! Finley_noError()) return;
88
89 /* squeeze it: */
90
91 for (i=0;i<numQuadNodes;i++) {
92 Q1=QUADNODES(0,i);
93 Q2=QUADNODES(1,i);
94 Q3=QUADNODES(2,i);
95
96 JA11= (1./3.)*Q2*Q3-(1./2.)*(Q2+Q3) +1.;
97 JA12= (1./3.)*Q1*Q3-(1./2.)*Q1;
98 JA13= (1./3.)*Q1*Q2-(1./2.)*Q1;
99 JA21= (1./3.)*Q2*Q3-(1./2.)*Q2;
100 JA22= (1./3.)*Q1*Q3-(1./2.)*(Q1+Q3) +1.;
101 JA23= (1./3.)*Q1*Q2-(1./2.)*Q2;
102 JA31= (1./3.)*Q2*Q3-(1./2.)*Q3;
103 JA32= (1./3.)*Q1*Q3-(1./2.)*Q3;
104 JA33= (1./3.)*Q1*Q2-(1./2.)*(Q1+Q2) +1.;
105 DET=JA11*JA22*JA33+JA12*JA23*JA31+JA13*JA21*JA32-JA13*JA22*JA31-JA11*JA23*JA32-JA12*JA21*JA33;
106 quadWeights[i]=quadWeights[i]*ABS(DET);
107 QUADNODES(0,i)=Q1*((1./3.)*Q2*Q3-(1./2.)*(Q2+Q3)+1.);
108 QUADNODES(1,i)=Q2*((1./3.)*Q1*Q3-(1./2.)*(Q1+Q3)+1.);
109 QUADNODES(2,i)=Q3*((1./3.)*Q1*Q2-(1./2.)*(Q1+Q2)+1.);
110 }
111 }
112 #undef DIM
113 }
114
115 /**************************************************************/
116
117 /* get a quadrature scheme with numQuadNodes quadrature nodes for the quad [0.1]^2 */
118 /* as a X-product of a 1D scheme. */
119
120 void Finley_Quad_getNodesRec(int numQuadNodes,double* quadNodes,double* quadWeights) {
121 char error_msg[LenErrorMsg_MAX];
122 int numQuadNodes1d,i,j,l;
123 double quadNodes1d[numQuadNodes],quadWeights1d[numQuadNodes];
124 #define DIM 2
125
126 /* find numQuadNodes1d with numQuadNodes1d**2==numQuadNodes: */
127
128 for (numQuadNodes1d=1;numQuadNodes1d<=MAX_numQuadNodesLine;numQuadNodes1d++) {
129 if (numQuadNodes1d*numQuadNodes1d==numQuadNodes) {
130
131 /* get 1D scheme: */
132
133 Finley_Quad_getNodesLine(numQuadNodes1d,quadNodes1d,quadWeights1d);
134
135 /* make 2D scheme: */
136
137 if (Finley_noError()) {
138 l=0;
139 for (i=0;i<numQuadNodes1d;i++) {
140 for (j=0;j<numQuadNodes1d;j++) {
141 QUADNODES(0,l)=quadNodes1d[i];
142 QUADNODES(1,l)=quadNodes1d[j];
143 QUADWEIGHTS(l)=quadWeights1d[i]*quadWeights1d[j];
144 l++;
145 }
146 }
147 }
148 return;
149 }
150 }
151 sprintf(error_msg,"Finley_Quad_getNodesRec: Illegal number of quadrature nodes %d on hexahedron.",numQuadNodes);
152 Finley_setError(VALUE_ERROR,error_msg);
153 #undef DIM
154 }
155
156 /**************************************************************/
157
158 /* get a quadrature scheme with numQuadNodes quadrature nodes for the hex [0.1]^3 */
159 /* as a X-product of a 1D scheme. */
160
161 void Finley_Quad_getNodesHex(int numQuadNodes,double* quadNodes,double* quadWeights) {
162 char error_msg[LenErrorMsg_MAX];
163 int numQuadNodes1d,i,j,k,l;
164 double quadNodes1d[numQuadNodes],quadWeights1d[numQuadNodes];
165 #define DIM 3
166
167 /* find numQuadNodes1d with numQuadNodes1d**3==numQuadNodes: */
168
169 for (numQuadNodes1d=1;numQuadNodes1d<=MAX_numQuadNodesLine;numQuadNodes1d++) {
170 if (numQuadNodes1d*numQuadNodes1d*numQuadNodes1d==numQuadNodes) {
171
172 /* get 1D scheme: */
173
174 Finley_Quad_getNodesLine(numQuadNodes1d,quadNodes1d,quadWeights1d);
175
176 /* make 3D scheme: */
177
178 if (Finley_noError()) {
179 l=0;
180 for (i=0;i<numQuadNodes1d;i++) {
181 for (j=0;j<numQuadNodes1d;j++) {
182 for (k=0;k<numQuadNodes1d;k++) {
183 QUADNODES(0,l)=quadNodes1d[i];
184 QUADNODES(1,l)=quadNodes1d[j];
185 QUADNODES(2,l)=quadNodes1d[k];
186 QUADWEIGHTS(l)=quadWeights1d[i]*quadWeights1d[j]*quadWeights1d[k];
187 l++;
188 }
189 }
190 }
191 }
192
193 return;
194 }
195 }
196 sprintf(error_msg,"Finley_Quad_getNodesHex: Illegal number of quadrature nodes %d on hexahedron.",numQuadNodes);
197 Finley_setError(VALUE_ERROR,error_msg);
198 #undef DIM
199 }
200
201 /**************************************************************/
202
203 /* get a quadrature scheme with numQuadNodes quadrature nodes for a point. As there */
204 /* in no quadrature scheme for a point any value for numQuadNodes other than 0 throws */
205 /* an error. */
206
207 void Finley_Quad_getNodesPoint(int numQuadNodes,double* quadNodes,double* quadWeights) {
208 if (numQuadNodes!=0) {
209 Finley_setError(VALUE_ERROR,"Finley_Quad_getNodesPoint: There is no quadrature scheme on points.");
210 }
211 }
212
213 /**************************************************************/
214
215 /* get a quadrature scheme with numQuadNodes quadrature nodes on the line [0,1]: */
216 /* The nodes and weights are set from a table. */
217
218 void Finley_Quad_getNodesLine(int numQuadNodes,double* quadNodes,double* quadWeights) {
219 switch(numQuadNodes) {
220 case 1:
221 quadNodes[0]=0.5;
222 quadWeights[0]=1.;
223 break;
224
225 case 2:
226 quadNodes[0]=(1.-.577350269189626)/2.;
227 quadNodes[1]=(1.+.577350269189626)/2.;
228 quadWeights[0]=.5;
229 quadWeights[1]=.5;
230 break;
231
232 case 3:
233 quadNodes[0]=(1.-.774596669241483)/2.;
234 quadNodes[1]=.5;
235 quadNodes[2]=(1.+.774596669241483)/2.;
236 quadWeights[0]=5./18.;
237 quadWeights[1]=4./ 9.;
238 quadWeights[2]=5./18.;
239 break;
240
241 case 4:
242 quadNodes[0]=(1.-.861136311594053)/2.;
243 quadNodes[1]=(1.-.339981043584856)/2.;
244 quadNodes[2]=(1.+.339981043584856)/2.;
245 quadNodes[3]=(1.+.861136311594053)/2.;
246 quadWeights[0]=.347854845137454/2.;
247 quadWeights[1]=.652145154862546/2.;
248 quadWeights[2]=.652145154862546/2.;
249 quadWeights[3]=.347854845137454/2.;
250 break;
251
252 case 5:
253 quadNodes[0]=(1.-.906179845938664)/2.;
254 quadNodes[1]=(1.-.538469310105683)/2.;
255 quadNodes[2]= .5;
256 quadNodes[3]=(1.+.538469310105683)/2.;
257 quadNodes[4]=(1.+.906179845938664)/2.;
258 quadWeights[0]=.236926885056189/2.;
259 quadWeights[1]=.478628670499366/2.;
260 quadWeights[2]=.568888888888889/2.;
261 quadWeights[3]=.478628670499366/2.;
262 quadWeights[4]=.236926885056189/2.;
263 break;
264
265 case 6:
266 quadNodes[0]=(1.-.932469514203152)/2.;
267 quadNodes[1]=(1.-.661209386466265)/2.;
268 quadNodes[2]=(1.-.238619186083197)/2.;
269 quadNodes[3]=(1.+.238619186083197)/2.;
270 quadNodes[4]=(1.+.661209386466265)/2.;
271 quadNodes[5]=(1.+.932469514203152)/2.;
272 quadWeights[0]=.171324492379170/2.;
273 quadWeights[1]=.360761573048139/2.;
274 quadWeights[2]=.467913934572691/2.;
275 quadWeights[3]=.467913934572691/2.;
276 quadWeights[4]=.360761573048139/2.;
277 quadWeights[5]=.171324492379170/2.;
278 break;
279
280 case 7:
281 quadNodes[0]=(1.-.949107912342759)/2.;
282 quadNodes[1]=(1.-.741531185599394)/2.;
283 quadNodes[2]=(1.-.405845151377397)/2.;
284 quadNodes[3]=0.5;
285 quadNodes[4]=(1.+.405845151377397)/2.;
286 quadNodes[5]=(1.+.741531185599394)/2.;
287 quadNodes[6]=(1.+.949107912342759)/2.;
288 quadWeights[0]= .129484966168870/2.;
289 quadWeights[1]= .279705391489277/2.;
290 quadWeights[2]= .381830050505119/2.;
291 quadWeights[3]= .417959183673469/2.;
292 quadWeights[4]= .381830050505119/2.;
293 quadWeights[5]= .279705391489277/2.;
294 quadWeights[6]= .129484966168870/2.;
295 break;
296
297 case 8:
298 quadNodes[0]=(1.-.960289856497536)/2.;
299 quadNodes[1]=(1.-.796666477413627)/2.;
300 quadNodes[2]=(1.-.525532409916329)/2.;
301 quadNodes[3]=(1.-.183434642495650)/2.;
302 quadNodes[4]=(1.+.183434642495650)/2.;
303 quadNodes[5]=(1.+.525532409916329)/2.;
304 quadNodes[6]=(1.+.796666477413627)/2.;
305 quadNodes[7]=(1.+.960289856497536)/2.;
306 quadWeights[0]= .101228536290376/2.;
307 quadWeights[1]= .222381034453374/2.;
308 quadWeights[2]= .313706645877887/2.;
309 quadWeights[3]= .362683783378362/2.;
310 quadWeights[4]= .362683783378362/2.;
311 quadWeights[5]= .313706645877887/2.;
312 quadWeights[6]= .222381034453374/2.;
313 quadWeights[7]= .101228536290376/2.;
314 break;
315
316 case 9:
317 quadNodes[0]=(1.-.968160239507626)/2.;
318 quadNodes[1]=(1.-.836031107326636)/2.;
319 quadNodes[2]=(1.-.613371432700590)/2.;
320 quadNodes[3]=(1.-.324253423403809)/2.;
321 quadNodes[4]= .5;
322 quadNodes[5]=(1.+.324253423403809)/2.;
323 quadNodes[6]=(1.+.613371432700590)/2.;
324 quadNodes[7]=(1.+.836031107326636)/2.;
325 quadNodes[8]=(1.+.968160239507626)/2.;
326 quadWeights[0]= .081274388361574/2.;
327 quadWeights[1]= .180648160694857/2.;
328 quadWeights[2]= .260610696402935/2.;
329 quadWeights[3]= .312347077040003/2.;
330 quadWeights[4]= .330239355001260/2.;
331 quadWeights[5]= .312347077040003/2.;
332 quadWeights[6]= .260610696402935/2.;
333 quadWeights[7]= .180648160694857/2.;
334 quadWeights[8]= .081274388361574/2.;
335 break;
336
337 case 10:
338 quadNodes[0]=(1.-.973906528517172)/2.;
339 quadNodes[1]=(1.-.865063366688985)/2.;
340 quadNodes[2]=(1.-.679409568299024)/2.;
341 quadNodes[3]=(1.-.433395394129247)/2.;
342 quadNodes[4]=(1.-.148874338981631)/2.;
343 quadNodes[5]=(1.+.148874338981631)/2.;
344 quadNodes[6]=(1.+.433395394129247)/2.;
345 quadNodes[7]=(1.+.679409568299024)/2.;
346 quadNodes[8]=(1.+.865063366688985)/2.;
347 quadNodes[9]=(1.+.973906528517172)/2.;
348 quadWeights[0]= .066671344308688/2.;
349 quadWeights[1]= .149451349150581/2.;
350 quadWeights[2]= .219086362515982/2.;
351 quadWeights[3]= .269266719309996/2.;
352 quadWeights[4]= .295524224714753/2.;
353 quadWeights[5]= .295524224714753/2.;
354 quadWeights[6]= .269266719309996/2.;
355 quadWeights[7]= .219086362515982/2.;
356 quadWeights[8]= .149451349150581/2.;
357 quadWeights[9]= .066671344308688/2.;
358 break;
359
360 default:
361 Finley_setError(VALUE_ERROR,"__FILE__: Negative intergration order.");
362 break;
363 }
364 }
365 /**************************************************************/
366 /* */
367 /* the following function are used define the meshes on the surface in the xy-plane */
368
369 /* triangle surface on a tetrahedron */
370 void Finley_Quad_getNodesTriOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) {
371 Finley_Quad_makeNodesOnFace(3,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesTri);
372 }
373 /* rectangular surface on a hexahedron */
374 void Finley_Quad_getNodesRecOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) {
375 Finley_Quad_makeNodesOnFace(3,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesRec);
376 }
377 /* line surface on a triangle or rectangle */
378 void Finley_Quad_getNodesLineOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) {
379 Finley_Quad_makeNodesOnFace(2,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesLine);
380 }
381 /* point surface on a line */
382 void Finley_Quad_getNodesPointOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) {
383 Finley_Quad_makeNodesOnFace(1,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesPoint);
384 }
385
386 void Finley_Quad_makeNodesOnFace(int dim, int numQuadNodes,double* quadNodes,double* quadWeights, Finley_Quad_getNodes getFaceNodes) {
387 int q,i;
388 double quadNodesOnFace[numQuadNodes*(dim-1)];
389
390 #define DIM dim
391 getFaceNodes(numQuadNodes,quadNodesOnFace,quadWeights);
392 if (! Finley_noError()) return;
393
394 for (q=0;q<numQuadNodes;q++) {
395 for (i=0;i<dim-1;i++) QUADNODES(i,q)=quadNodesOnFace[INDEX2(i,q,dim-1)];
396 QUADNODES(dim-1,q)=0;
397 }
398 #undef DIM
399 }
400
401 /**************************************************************/
402
403 /* The following functions Finley_Quad_getNumNodes* return the nmber of quadrature points needed to */
404 /* achieve a certain accuracy. Notice that for Tet and Tri the the order is increased */
405 /* to consider the accuracy reduction through the construction process. */
406
407
408 int Finley_Quad_getNumNodesPoint(int order) {
409 if (order <0 ) {
410 Finley_setError(VALUE_ERROR,"Finley_Quad_getNumNodesPoint: Negative intergration order.");
411 return -1;
412 } else {
413 return 0;
414 }
415 }
416
417 int Finley_Quad_getNumNodesLine(int order) {
418 char error_msg[LenErrorMsg_MAX];
419 if (order <0 ) {
420 Finley_setError(VALUE_ERROR,"Finley_Quad_getNumNodesPoint: Negative intergration order.");
421 return -1;
422 } else {
423 if (order > 2*MAX_numQuadNodesLine-1) {
424 sprintf(error_msg,"Finley_Quad_getNumNodesPoint: requested integration order %d on line is too large (>%d).",
425 order,2*MAX_numQuadNodesLine-1);
426 Finley_setError(VALUE_ERROR,error_msg);
427 return -1;
428 } else {
429 Finley_resetError();
430 return order/2+1;
431 }
432 }
433 }
434
435 int Finley_Quad_getNumNodesTri(int order) {
436 int numQuadNodesLine;
437 if (order==1) {
438 return 1;
439 } else {
440 numQuadNodesLine=Finley_Quad_getNumNodesLine(order+1);
441 if (Finley_noError()) {
442 return numQuadNodesLine*numQuadNodesLine;
443 } else {
444 return -1;
445 }
446 }
447 }
448
449 int Finley_Quad_getNumNodesRec(int order) {
450 int numQuadNodesLine;
451 numQuadNodesLine=Finley_Quad_getNumNodesLine(order);
452 if (Finley_noError()) {
453 return numQuadNodesLine*numQuadNodesLine;
454 } else {
455 return -1;
456 }
457 }
458
459 int Finley_Quad_getNumNodesTet(int order) {
460 int numQuadNodesLine;
461 numQuadNodesLine=Finley_Quad_getNumNodesLine(order+2);
462 if (Finley_noError()) {
463 return numQuadNodesLine*numQuadNodesLine*numQuadNodesLine;
464 } else {
465 return -1;
466 }
467 }
468
469 int Finley_Quad_getNumNodesHex(int order) {
470 int numQuadNodesLine;
471 numQuadNodesLine=Finley_Quad_getNumNodesLine(order);
472 if (Finley_noError()) {
473 return numQuadNodesLine*numQuadNodesLine*numQuadNodesLine;
474 } else {
475 return -1;
476 }
477 }
478 /*
479 * $Log$
480 * Revision 1.2 2005/09/15 03:44:23 jgs
481 * Merge of development branch dev-02 back to main trunk on 2005-09-15
482 *
483 * Revision 1.1.1.1.6.1 2005/09/07 06:26:20 gross
484 * the solver from finley are put into the standalone package paso now
485 *
486 * Revision 1.1.1.1 2004/10/26 06:53:57 jgs
487 * initial import of project esys2
488 *
489 * Revision 1.2 2004/08/03 04:49:06 gross
490 * bug in Quadrature.c fixed
491 *
492 * Revision 1.1.1.1 2004/06/24 04:00:40 johng
493 * Initial version of eys using boost-python.
494 *
495 *
496 */

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