/[escript]/trunk/finley/src/Quadrature.cpp
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Contents of /trunk/finley/src/Quadrature.cpp

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Revision 4492 - (show annotations)
Tue Jul 2 01:44:11 2013 UTC (5 years, 9 months ago) by caltinay
File size: 70032 byte(s)
Finley changes that were held back while in release mode - moved more stuff
into finley namespace.

1
2 /*****************************************************************************
3 *
4 * Copyright (c) 2003-2013 by University of Queensland
5 * http://www.uq.edu.au
6 *
7 * Primary Business: Queensland, Australia
8 * Licensed under the Open Software License version 3.0
9 * http://www.opensource.org/licenses/osl-3.0.php
10 *
11 * Development until 2012 by Earth Systems Science Computational Center (ESSCC)
12 * Development since 2012 by School of Earth Sciences
13 *
14 *****************************************************************************/
15
16
17 /****************************************************************************
18
19 Finley: quadrature schemes
20
21 *****************************************************************************/
22
23 #include "Quadrature.h"
24 #include "esysUtils/index.h"
25 #include "esysUtils/mem.h"
26
27
28 #define QUADNODES(_K_,_I_) quadNodes[INDEX2(_K_,_I_,DIM)]
29 #define QUADWEIGHTS(_I_) quadWeights[_I_]
30
31 namespace finley {
32
33 QuadInfo QuadInfoList[]={
34 {PointQuad, "Point", 0, 1, Quad_getNodesPoint, Quad_getNumNodesPoint, Quad_MacroPoint} ,
35 {LineQuad, "Line", 1, 2, Quad_getNodesLine, Quad_getNumNodesLine, Quad_MacroLine} ,
36 {TriQuad, "Tri", 2, 3, Quad_getNodesTri, Quad_getNumNodesTri, Quad_MacroTri},
37 {RecQuad, "Rec", 2, 4, Quad_getNodesRec, Quad_getNumNodesRec, Quad_MacroRec},
38 {TetQuad, "Tet", 3, 4, Quad_getNodesTet, Quad_getNumNodesTet, Quad_MacroTet},
39 {HexQuad, "Hex", 3, 8, Quad_getNodesHex, Quad_getNumNodesHex, Quad_MacroHex},
40 {NoQuad, "NoType", 0, 1, Quad_getNodesPoint, Quad_getNumNodesPoint, Quad_MacroPoint}
41 };
42
43 QuadInfo* QuadInfo_getInfo(QuadTypeId id)
44 {
45 int ptr=0;
46 QuadInfo* out=NULL;
47 while (QuadInfoList[ptr].TypeId!=NoQuad && out==NULL) {
48 if (QuadInfoList[ptr].TypeId==id) out=&(QuadInfoList[ptr]);
49 ptr++;
50 }
51 if (out==NULL) {
52 Finley_setError(VALUE_ERROR,"QuadInfo_getInfo: cannot find requested quadrature scheme.");
53 }
54 return out;
55 }
56
57 /************************************************************************************/
58
59 /* get a quadrature scheme with numQuadNodes quadrature nodes for the tri */
60 /* as a squeezed scheme on a quad [0,1]^2 */
61
62 void Quad_getNodesTri(int numQuadNodes,double* quadNodes,double* quadWeights) {
63 int i;
64 double Q1,Q2,a,b,c,d,e,f,g,u,v,w;
65 #define DIM 2
66
67 /* the easy cases: */
68
69 if (numQuadNodes==1) {
70 QUADNODES(0,0)=1./3.;
71 QUADNODES(1,0)=1./3.;
72 QUADWEIGHTS(0)=1./2.;
73 } else if (numQuadNodes==3){
74 QUADNODES(0,0)=1./2.;
75 QUADNODES(1,0)=0.;
76 QUADWEIGHTS(0)=1./6.;
77 QUADNODES(0,1)=0.;
78 QUADNODES(1,1)=1./2.;
79 QUADWEIGHTS(1)=1./6.;
80 QUADNODES(0,2)=1./2.;
81 QUADNODES(1,2)=1./2.;
82 QUADWEIGHTS(2)=1./6.;
83 } else if (numQuadNodes==4){
84 QUADNODES(0,0)=1./3.;
85 QUADNODES(1,0)=1./3.;
86 QUADWEIGHTS(0)=-27./96.;
87 QUADNODES(0,1)=0.2;
88 QUADNODES(1,1)=0.2;
89 QUADWEIGHTS(1)=25./96.;
90 QUADNODES(0,2)=0.6;
91 QUADNODES(1,2)=0.2;
92 QUADWEIGHTS(2)=25./96.;
93 QUADNODES(0,3)=0.2;
94 QUADNODES(1,3)=0.6;
95 QUADWEIGHTS(3)=25./96.;
96 } else if (numQuadNodes==6){
97 QUADWEIGHTS(0) = 0.109951743655322/2.;
98 QUADWEIGHTS(1) = 0.109951743655322/2.;
99 QUADWEIGHTS(2) = 0.109951743655322/2.;
100 QUADWEIGHTS(3) = 0.223381589678011/2.;
101 QUADWEIGHTS(4) = 0.223381589678011/2.;
102 QUADWEIGHTS(5) = 0.223381589678011/2.;
103
104 QUADNODES(0,0) = 0.816847572980459;
105 QUADNODES(0,1) = 0.091576213509771;
106 QUADNODES(0,2) = 0.091576213509771;
107 QUADNODES(0,3) = 0.108103018168070;
108 QUADNODES(0,4) = 0.445948490915965;
109 QUADNODES(0,5) = 0.445948490915965;
110
111 QUADNODES(1,0) = 0.091576213509771;
112 QUADNODES(1,1) = 0.816847572980459;
113 QUADNODES(1,2) = 0.091576213509771;
114 QUADNODES(1,3) = 0.445948490915965;
115 QUADNODES(1,4) = 0.108103018168070;
116 QUADNODES(1,5) = 0.445948490915965;
117
118 } else if (numQuadNodes==7){
119 QUADNODES(0,0) = 0.33333333333333333;
120 QUADNODES(0,1) = 0.7974269853530872;
121 QUADNODES(0,2) = 0.10128650732345633;
122 QUADNODES(0,3) = 0.10128650732345633;
123 QUADNODES(0,4) = 0.059715871789769809;
124 QUADNODES(0,5) = 0.47014206410511505;
125 QUADNODES(0,6) = 0.47014206410511505;
126
127 QUADNODES(1,0) = 0.33333333333333333;
128 QUADNODES(1,1) = 0.10128650732345633;
129 QUADNODES(1,2) = 0.7974269853530872;
130 QUADNODES(1,3) = 0.10128650732345633;
131 QUADNODES(1,4) = 0.47014206410511505;
132 QUADNODES(1,5) = 0.059715871789769809;
133 QUADNODES(1,6) = 0.47014206410511505;
134
135 QUADWEIGHTS(0) = 0.225/2.;
136 QUADWEIGHTS(1) = 0.12593918054482717/2.;
137 QUADWEIGHTS(2) = 0.12593918054482717/2.;
138 QUADWEIGHTS(3) = 0.12593918054482717/2.;
139 QUADWEIGHTS(4) = 0.13239415278850616/2.;
140 QUADWEIGHTS(5) = 0.13239415278850616/2.;
141 QUADWEIGHTS(6) = 0.13239415278850616/2.;
142
143 } else if (numQuadNodes==12){
144 a = 0.873821971016996;
145 b = 0.063089014491502;
146 c = 0.501426509658179;
147 d = 0.249286745170910;
148 e = 0.636502499121399;
149 f = 0.310352451033785;
150 g = 0.053145049844816;
151
152 u = 0.050844906370207/2.;
153 v = 0.116786275726379/2.;
154 w = 0.082851075618374/2.;
155
156 QUADNODES(0,0) = a;
157 QUADNODES(0,1) = b;
158 QUADNODES(0,2) = b;
159 QUADNODES(0,3) = c;
160 QUADNODES(0,4) = d;
161 QUADNODES(0,5) = d;
162 QUADNODES(0,6) = e;
163 QUADNODES(0,7) = e;
164 QUADNODES(0,8) = f;
165 QUADNODES(0,9) = f;
166 QUADNODES(0,10) = g;
167 QUADNODES(0,11) = g;
168
169 QUADNODES(1,0) = b;
170 QUADNODES(1,1) = a;
171 QUADNODES(1,2) = b;
172 QUADNODES(1,3) = d;
173 QUADNODES(1,4) = c;
174 QUADNODES(1,5) = d;
175 QUADNODES(1,6) = f;
176 QUADNODES(1,7) = g;
177 QUADNODES(1,8) = e;
178 QUADNODES(1,9) = g;
179 QUADNODES(1,10) = e;
180 QUADNODES(1,11) = f;
181
182 QUADWEIGHTS(0)= u;
183 QUADWEIGHTS(1)= u;
184 QUADWEIGHTS(2)= u;
185 QUADWEIGHTS(3)= v;
186 QUADWEIGHTS(4)= v;
187 QUADWEIGHTS(5)= v;
188 QUADWEIGHTS(6)= w;
189 QUADWEIGHTS(7)= w;
190 QUADWEIGHTS(8)= w;
191 QUADWEIGHTS(9)= w;
192 QUADWEIGHTS(10)= w;
193 QUADWEIGHTS(11)= w;
194
195 } else if (numQuadNodes==13){
196 QUADWEIGHTS(0) =-0.149570044467670/2.;
197 QUADWEIGHTS(1) = 0.175615257433204/2.;
198 QUADWEIGHTS(2) = 0.175615257433204/2.;
199 QUADWEIGHTS(3) = 0.175615257433204/2.;
200 QUADWEIGHTS(4) = 0.053347235608839/2.;
201 QUADWEIGHTS(5) = 0.053347235608839/2.;
202 QUADWEIGHTS(6) = 0.053347235608839/2.;
203 QUADWEIGHTS(7) = 0.077113760890257/2.;
204 QUADWEIGHTS(8) = 0.077113760890257/2.;
205 QUADWEIGHTS(9) = 0.077113760890257/2.;
206 QUADWEIGHTS(10) = 0.077113760890257/2.;
207 QUADWEIGHTS(11) = 0.077113760890257/2.;
208 QUADWEIGHTS(12) = 0.077113760890257/2.;
209
210 QUADNODES(0,0) = 0.3333333333333333;
211 QUADNODES(0,1) = 0.479308067841923;
212 QUADNODES(0,2) = 0.260345966079038;
213 QUADNODES(0,3) = 0.260345966079038;
214 QUADNODES(0,4) = 0.869739794195568;
215 QUADNODES(0,5) = 0.065130102902216;
216 QUADNODES(0,6) = 0.065130102902216;
217 QUADNODES(0,7) = 0.638444188569809;
218 QUADNODES(0,8) = 0.638444188569809;
219 QUADNODES(0,9) = 0.048690315425316;
220 QUADNODES(0,10) = 0.048690315425316;
221 QUADNODES(0,11) = 0.312865496004875;
222 QUADNODES(0,12) = 0.312865496004875;
223
224 QUADNODES(1,0) = 0.3333333333333333;
225 QUADNODES(1,1) = 0.260345966079038;
226 QUADNODES(1,2) = 0.479308067841923;
227 QUADNODES(1,3) = 0.260345966079038;
228 QUADNODES(1,4) = 0.065130102902216;
229 QUADNODES(1,5) = 0.869739794195568;
230 QUADNODES(1,6) = 0.065130102902216;
231 QUADNODES(1,7) = 0.048690315425316;
232 QUADNODES(1,8) = 0.312865496004875;
233 QUADNODES(1,9) = 0.638444188569809;
234 QUADNODES(1,10) = 0.312865496004875;
235 QUADNODES(1,11) = 0.638444188569809;
236 QUADNODES(1,12) = 0.048690315425316;
237
238 } else if (numQuadNodes==16){
239 QUADWEIGHTS(0) = 0.07215780;
240 QUADWEIGHTS(1) = 0.04754582;
241 QUADWEIGHTS(2) = 0.04754582;
242 QUADWEIGHTS(3) = 0.04754582;
243 QUADWEIGHTS(4) = 0.01622925;
244 QUADWEIGHTS(5) = 0.01622925;
245 QUADWEIGHTS(6) = 0.01622925;
246 QUADWEIGHTS(7) = 0.05160869;
247 QUADWEIGHTS(8) = 0.05160869;
248 QUADWEIGHTS(9) = 0.05160869;
249 QUADWEIGHTS(10) = 0.01361516;
250 QUADWEIGHTS(11) = 0.01361516;
251 QUADWEIGHTS(12) = 0.01361516;
252 QUADWEIGHTS(13) = 0.01361516;
253 QUADWEIGHTS(14) = 0.01361516;
254 QUADWEIGHTS(15) = 0.01361516;
255
256 QUADNODES(0,0) = 0.3333333;
257 QUADNODES(0,1) = 0.08141482;
258 QUADNODES(0,2) = 0.4592926;
259 QUADNODES(0,3) = 0.4592926;
260 QUADNODES(0,4) = 0.8989055;
261 QUADNODES(0,5) = 0.05054723;
262 QUADNODES(0,6) = 0.05054723;
263 QUADNODES(0,7) = 0.6588614;
264 QUADNODES(0,8) = 0.1705693;
265 QUADNODES(0,9) = 0.1705693;
266 QUADNODES(0,10) = 0.008394777;
267 QUADNODES(0,11) = 0.008394777;
268 QUADNODES(0,12) = 0.7284924;
269 QUADNODES(0,13) = 0.7284924;
270 QUADNODES(0,14) = 0.2631128;
271 QUADNODES(0,15) = 0.2631128;
272
273 QUADNODES(1,0) = 0.3333333;
274 QUADNODES(1,1) = 0.4592926;
275 QUADNODES(1,2) = 0.08141482;
276 QUADNODES(1,3) = 0.4592926;
277 QUADNODES(1,4) = 0.05054723;
278 QUADNODES(1,5) = 0.8989055;
279 QUADNODES(1,6) = 0.05054723;
280 QUADNODES(1,7) = 0.1705693;
281 QUADNODES(1,8) = 0.6588614;
282 QUADNODES(1,9) = 0.1705693;
283 QUADNODES(1,10) = 0.7284924;
284 QUADNODES(1,11) = 0.2631128;
285 QUADNODES(1,12) = 0.008394777;
286 QUADNODES(1,13) = 0.2631128;
287 QUADNODES(1,14) = 0.008394777;
288 QUADNODES(1,15) = 0.7284924;
289
290 } else if (numQuadNodes==19){
291 QUADWEIGHTS(0) = 0.04856790;
292 QUADWEIGHTS(1) = 0.01566735;
293 QUADWEIGHTS(2) = 0.01566735;
294 QUADWEIGHTS(3) = 0.01566735;
295 QUADWEIGHTS(4) = 0.03891377;
296 QUADWEIGHTS(5) = 0.03891377;
297 QUADWEIGHTS(6) = 0.03891377;
298 QUADWEIGHTS(7) = 0.03982387;
299 QUADWEIGHTS(8) = 0.03982387;
300 QUADWEIGHTS(9) = 0.03982387;
301 QUADWEIGHTS(10) = 0.01278884;
302 QUADWEIGHTS(11) = 0.01278884;
303 QUADWEIGHTS(12) = 0.01278884;
304 QUADWEIGHTS(13) = 0.02164177;
305 QUADWEIGHTS(14) = 0.02164177;
306 QUADWEIGHTS(15) = 0.02164177;
307 QUADWEIGHTS(16) = 0.02164177;
308 QUADWEIGHTS(17) = 0.02164177;
309 QUADWEIGHTS(18) = 0.02164177;
310
311 QUADNODES(0,0) = 0.3333333;
312 QUADNODES(0,1) = 0.02063496;
313 QUADNODES(0,2) = 0.4896825;
314 QUADNODES(0,3) = 0.4896825;
315 QUADNODES(0,4) = 0.1258208;
316 QUADNODES(0,5) = 0.4370896;
317 QUADNODES(0,6) = 0.4370896;
318 QUADNODES(0,7) = 0.6235929;
319 QUADNODES(0,8) = 0.1882035;
320 QUADNODES(0,9) = 0.1882035;
321 QUADNODES(0,10) = 0.9105410;
322 QUADNODES(0,11) = 0.04472951;
323 QUADNODES(0,12) = 0.04472951;
324 QUADNODES(0,13) = 0.03683841;
325 QUADNODES(0,14) = 0.03683841;
326 QUADNODES(0,15) = 0.7411986;
327 QUADNODES(0,16) = 0.7411986;
328 QUADNODES(0,17) = 0.2219630;
329 QUADNODES(0,18) = 0.2219630;
330
331 QUADNODES(1,0) = 0.3333333;
332 QUADNODES(1,1) = 0.4896825;
333 QUADNODES(1,2) = 0.02063496;
334 QUADNODES(1,3) = 0.4896825;
335 QUADNODES(1,4) = 0.4370896;
336 QUADNODES(1,5) = 0.1258208;
337 QUADNODES(1,6) = 0.4370896;
338 QUADNODES(1,7) = 0.1882035;
339 QUADNODES(1,8) = 0.6235929;
340 QUADNODES(1,9) = 0.1882035;
341 QUADNODES(1,10) = 0.04472951;
342 QUADNODES(1,11) = 0.9105410;
343 QUADNODES(1,12) = 0.04472951;
344 QUADNODES(1,13) = 0.7411986;
345 QUADNODES(1,14) = 0.2219630;
346 QUADNODES(1,15) = 0.03683841;
347 QUADNODES(1,16) = 0.2219630;
348 QUADNODES(1,17) = 0.03683841;
349 QUADNODES(1,18) = 0.7411986;
350 } else {
351
352 /* get scheme on [0.1]^2 */
353 Quad_getNodesRec(numQuadNodes,quadNodes,quadWeights);
354 if (! Finley_noError()) return;
355
356 /* squeeze it: */
357
358 for (i=0;i<numQuadNodes;i++) {
359 Q1=QUADNODES(0,i);
360 Q2=QUADNODES(1,i);
361 QUADWEIGHTS(i)=QUADWEIGHTS(i)*(1.-(1./2.)*(Q1+Q2));
362 QUADNODES(0,i)=Q1*(1.-(1./2.)*Q2);
363 QUADNODES(1,i)=Q2*(1.-(1./2.)*Q1);
364 }
365 }
366 #undef DIM
367
368
369 }
370
371 /************************************************************************************/
372
373 /* get a quadrature scheme with numQuadNodes quadrature nodes for the tet */
374 /* as a squeezed scheme on a hex [0,1]^3 */
375
376 void Quad_getNodesTet(int numQuadNodes,double* quadNodes,double* quadWeights) {
377 int i;
378 double Q1,Q2,Q3,JA11,JA12,JA13,JA21,JA22,JA23,JA31,JA32,JA33,DET;
379 double a,b,c,d,e,f,g,h;
380 double alpha=0.58541019662496852;
381 double beta =0.1381966011250105;
382 #define DIM 3
383
384 /* the easy cases: */
385 if (numQuadNodes==1) {
386 QUADNODES(0,0)=0.25;
387 QUADNODES(1,0)=0.25;
388 QUADNODES(2,0)=0.25;
389 QUADWEIGHTS(0)=1./6.;
390 } else if (numQuadNodes==4){
391 QUADNODES(0,0)=beta;
392 QUADNODES(1,0)=beta;
393 QUADNODES(2,0)=beta;
394 QUADWEIGHTS(0)=1./24.;
395 QUADNODES(0,1)=alpha;
396 QUADNODES(1,1)=beta;
397 QUADNODES(2,1)=beta;
398 QUADWEIGHTS(1)=1./24.;
399 QUADNODES(0,2)=beta;
400 QUADNODES(1,2)=alpha;
401 QUADNODES(2,2)=beta;
402 QUADWEIGHTS(2)=1./24.;
403 QUADNODES(0,3)=beta;
404 QUADNODES(1,3)=beta;
405 QUADNODES(2,3)=alpha;
406 QUADWEIGHTS(3)=1./24.;
407 } else if (numQuadNodes==5){
408 QUADNODES(0,0)=1./4.;
409 QUADNODES(1,0)=1./4.;
410 QUADNODES(2,0)=1./4.;
411 QUADWEIGHTS(0)=-2./15.;
412 QUADNODES(0,1)=1./6.;
413 QUADNODES(1,1)=1./6.;
414 QUADNODES(2,1)=1./6.;
415 QUADWEIGHTS(1)=3./40.;
416 QUADNODES(0,2)=1./2.;
417 QUADNODES(1,2)=1./6.;
418 QUADNODES(2,2)=1./6.;
419 QUADWEIGHTS(2)=3./40.;
420 QUADNODES(0,3)=1./6.;
421 QUADNODES(1,3)=1./2.;
422 QUADNODES(2,3)=1./6.;
423 QUADWEIGHTS(3)=3./40.;
424 QUADNODES(0,4)=1./6.;
425 QUADNODES(1,4)=1./6.;
426 QUADNODES(2,4)=1./2.;
427 QUADWEIGHTS(4)=3./40.;
428
429 } else if (numQuadNodes==11){
430
431 a = 0.25;
432 b = 11.0/14.0;
433 c = 1.0/14.0;
434 d = 0.25 * (1.0 + sqrt ( 5.0 / 14.0 ) );
435 e = 0.25 * (1.0 - sqrt ( 5.0 / 14.0 ) );
436 f = -74.0 / 5625.0;
437 g = 343.0 / 45000.0;
438 h = 56.0 / 2250.0;
439
440 QUADWEIGHTS(401-401) = f;
441 QUADWEIGHTS(402-401) = g;
442 QUADWEIGHTS(403-401) = g;
443 QUADWEIGHTS(404-401) = g;
444 QUADWEIGHTS(405-401) = g;
445 QUADWEIGHTS(406-401) = h;
446 QUADWEIGHTS(407-401) = h;
447 QUADWEIGHTS(408-401) = h;
448 QUADWEIGHTS(409-401) = h;
449 QUADWEIGHTS(410-401) = h;
450 QUADWEIGHTS(411-401) = h;
451
452 QUADNODES(0,401-401) = a;
453 QUADNODES(0,402-401) = b;
454 QUADNODES(0,403-401) = c;
455 QUADNODES(0,404-401) = c;
456 QUADNODES(0,405-401) = c;
457 QUADNODES(0,406-401) = d;
458 QUADNODES(0,407-401) = d;
459 QUADNODES(0,408-401) = d;
460 QUADNODES(0,409-401) = e;
461 QUADNODES(0,410-401) = e;
462 QUADNODES(0,411-401) = e;
463
464 QUADNODES(1,401-401) = a;
465 QUADNODES(1,402-401) = c;
466 QUADNODES(1,403-401) = b;
467 QUADNODES(1,404-401) = c;
468 QUADNODES(1,405-401) = c;
469 QUADNODES(1,406-401) = d;
470 QUADNODES(1,407-401) = e;
471 QUADNODES(1,408-401) = e;
472 QUADNODES(1,409-401) = d;
473 QUADNODES(1,410-401) = d;
474 QUADNODES(1,411-401) = e;
475
476 QUADNODES(2,401-401) = a;
477 QUADNODES(2,402-401) = c;
478 QUADNODES(2,403-401) = c;
479 QUADNODES(2,404-401) = b;
480 QUADNODES(2,405-401) = c;
481 QUADNODES(2,406-401) = e;
482 QUADNODES(2,407-401) = d;
483 QUADNODES(2,408-401) = e;
484 QUADNODES(2,409-401) = d;
485 QUADNODES(2,410-401) = e;
486 QUADNODES(2,411-401) = d;
487
488 } else if (numQuadNodes==15){
489 QUADWEIGHTS(412-412) = 0.019753086419753086;
490 QUADWEIGHTS(413-412) = 0.01198951396316977;
491 QUADWEIGHTS(414-412) = 0.01198951396316977;
492 QUADWEIGHTS(415-412) = 0.01198951396316977;
493 QUADWEIGHTS(416-412) = 0.01198951396316977;
494 QUADWEIGHTS(417-412) = 0.011511367871045397;
495 QUADWEIGHTS(418-412) = 0.011511367871045397;
496 QUADWEIGHTS(419-412) = 0.011511367871045397;
497 QUADWEIGHTS(420-412) = 0.011511367871045397;
498 QUADWEIGHTS(421-412) = 0.0088183421516754845;
499 QUADWEIGHTS(422-412) = 0.0088183421516754845;
500 QUADWEIGHTS(423-412) = 0.0088183421516754845;
501 QUADWEIGHTS(424-412) = 0.0088183421516754845;
502 QUADWEIGHTS(425-412) = 0.0088183421516754845;
503 QUADWEIGHTS(426-412) = 0.0088183421516754845;
504
505 QUADNODES(0,412-412) = 0.2500000;
506 QUADNODES(0,413-412) = 0.091971078052723032;
507 QUADNODES(0,414-412) = 0.72408676584183096;
508 QUADNODES(0,415-412) = 0.091971078052723032;
509 QUADNODES(0,416-412) = 0.091971078052723032;
510 QUADNODES(0,417-412) = 0.31979362782962989;
511 QUADNODES(0,418-412) = 0.040619116511110234;
512 QUADNODES(0,419-412) = 0.31979362782962989;
513 QUADNODES(0,420-412) = 0.31979362782962989;
514 QUADNODES(0,421-412) = 0.056350832689629149;
515 QUADNODES(0,422-412) = 0.056350832689629149;
516 QUADNODES(0,423-412) = 0.056350832689629149;
517 QUADNODES(0,424-412) = 0.4436491673103708;
518 QUADNODES(0,425-412) = 0.4436491673103708;
519 QUADNODES(0,426-412) = 0.4436491673103708;
520
521 QUADNODES(1,412-412) = 0.2500000;
522 QUADNODES(1,413-412) = 0.091971078052723032;
523 QUADNODES(1,414-412) = 0.091971078052723032;
524 QUADNODES(1,415-412) = 0.72408676584183096;
525 QUADNODES(1,416-412) = 0.091971078052723032;
526 QUADNODES(1,417-412) = 0.31979362782962989;
527 QUADNODES(1,418-412) = 0.31979362782962989;
528 QUADNODES(1,419-412) = 0.040619116511110234;
529 QUADNODES(1,420-412) = 0.31979362782962989;
530 QUADNODES(1,421-412) = 0.056350832689629149;
531 QUADNODES(1,422-412) = 0.4436491673103708;
532 QUADNODES(1,423-412) = 0.4436491673103708;
533 QUADNODES(1,424-412) = 0.056350832689629149;
534 QUADNODES(1,425-412) = 0.056350832689629149;
535 QUADNODES(1,426-412) = 0.4436491673103708;
536
537 QUADNODES(2,412-412) = 0.2500000;
538 QUADNODES(2,413-412) = 0.091971078052723032;
539 QUADNODES(2,414-412) = 0.091971078052723032;
540 QUADNODES(2,415-412) = 0.091971078052723032;
541 QUADNODES(2,416-412) = 0.72408676584183096;
542 QUADNODES(2,417-412) = 0.31979362782962989;
543 QUADNODES(2,418-412) = 0.31979362782962989;
544 QUADNODES(2,419-412) = 0.31979362782962989;
545 QUADNODES(2,420-412) = 0.040619116511110234;
546 QUADNODES(2,421-412) = 0.4436491673103708;
547 QUADNODES(2,422-412) = 0.056350832689629149;
548 QUADNODES(2,423-412) = 0.4436491673103708;
549 QUADNODES(2,424-412) = 0.056350832689629149;
550 QUADNODES(2,425-412) = 0.4436491673103708;
551 QUADNODES(2,426-412) = 0.056350832689629149;
552
553 } else if (numQuadNodes==24){
554 QUADWEIGHTS(427-427) = 0.006653792;
555 QUADWEIGHTS(428-427) = 0.006653792;
556 QUADWEIGHTS(429-427) = 0.006653792;
557 QUADWEIGHTS(430-427) = 0.006653792;
558 QUADWEIGHTS(431-427) = 0.001679535;
559 QUADWEIGHTS(432-427) = 0.001679535;
560 QUADWEIGHTS(433-427) = 0.001679535;
561 QUADWEIGHTS(434-427) = 0.001679535;
562 QUADWEIGHTS(435-427) = 0.009226197;
563 QUADWEIGHTS(436-427) = 0.009226197;
564 QUADWEIGHTS(437-427) = 0.009226197;
565 QUADWEIGHTS(438-427) = 0.009226197;
566 QUADWEIGHTS(439-427) = 0.008035714;
567 QUADWEIGHTS(440-427) = 0.008035714;
568 QUADWEIGHTS(441-427) = 0.008035714;
569 QUADWEIGHTS(442-427) = 0.008035714;
570 QUADWEIGHTS(443-427) = 0.008035714;
571 QUADWEIGHTS(444-427) = 0.008035714;
572 QUADWEIGHTS(445-427) = 0.008035714;
573 QUADWEIGHTS(446-427) = 0.008035714;
574 QUADWEIGHTS(447-427) = 0.008035714;
575 QUADWEIGHTS(448-427) = 0.008035714;
576 QUADWEIGHTS(449-427) = 0.008035714;
577 QUADWEIGHTS(450-427) = 0.008035714;
578
579 QUADNODES(0,427-427) = 0.3561914;
580 QUADNODES(0,428-427) = 0.2146029;
581 QUADNODES(0,429-427) = 0.2146029;
582 QUADNODES(0,430-427) = 0.2146029;
583 QUADNODES(0,431-427) = 0.8779781;
584 QUADNODES(0,432-427) = 0.04067396;
585 QUADNODES(0,433-427) = 0.04067396;
586 QUADNODES(0,434-427) = 0.04067396;
587 QUADNODES(0,435-427) = 0.03298633;
588 QUADNODES(0,436-427) = 0.3223379;
589 QUADNODES(0,437-427) = 0.3223379;
590 QUADNODES(0,438-427) = 0.3223379;
591 QUADNODES(0,439-427) = 0.6030057;
592 QUADNODES(0,440-427) = 0.6030057;
593 QUADNODES(0,441-427) = 0.6030057;
594 QUADNODES(0,442-427) = 0.2696723;
595 QUADNODES(0,443-427) = 0.2696723;
596 QUADNODES(0,444-427) = 0.2696723;
597 QUADNODES(0,445-427) = 0.06366100;
598 QUADNODES(0,446-427) = 0.06366100;
599 QUADNODES(0,447-427) = 0.06366100;
600 QUADNODES(0,448-427) = 0.06366100;
601 QUADNODES(0,449-427) = 0.06366100;
602 QUADNODES(0,450-427) = 0.06366100;
603
604 QUADNODES(1,427-427) = 0.2146029;
605 QUADNODES(1,428-427) = 0.3561914;
606 QUADNODES(1,429-427) = 0.2146029;
607 QUADNODES(1,430-427) = 0.2146029;
608 QUADNODES(1,431-427) = 0.04067396;
609 QUADNODES(1,432-427) = 0.8779781;
610 QUADNODES(1,433-427) = 0.04067396;
611 QUADNODES(1,434-427) = 0.04067396;
612 QUADNODES(1,435-427) = 0.3223379;
613 QUADNODES(1,436-427) = 0.03298633;
614 QUADNODES(1,437-427) = 0.3223379;
615 QUADNODES(1,438-427) = 0.3223379;
616 QUADNODES(1,439-427) = 0.2696723;
617 QUADNODES(1,440-427) = 0.06366100;
618 QUADNODES(1,441-427) = 0.06366100;
619 QUADNODES(1,442-427) = 0.6030057;
620 QUADNODES(1,443-427) = 0.06366100;
621 QUADNODES(1,444-427) = 0.06366100;
622 QUADNODES(1,445-427) = 0.6030057;
623 QUADNODES(1,446-427) = 0.6030057;
624 QUADNODES(1,447-427) = 0.2696723;
625 QUADNODES(1,448-427) = 0.2696723;
626 QUADNODES(1,449-427) = 0.06366100;
627 QUADNODES(1,450-427) = 0.06366100;
628
629 QUADNODES(2,427-427) = 0.2146029;
630 QUADNODES(2,428-427) = 0.2146029;
631 QUADNODES(2,429-427) = 0.3561914;
632 QUADNODES(2,430-427) = 0.2146029;
633 QUADNODES(2,431-427) = 0.04067396;
634 QUADNODES(2,432-427) = 0.04067396;
635 QUADNODES(2,433-427) = 0.8779781;
636 QUADNODES(2,434-427) = 0.04067396;
637 QUADNODES(2,435-427) = 0.3223379;
638 QUADNODES(2,436-427) = 0.3223379;
639 QUADNODES(2,437-427) = 0.03298633;
640 QUADNODES(2,438-427) = 0.3223379;
641 QUADNODES(2,439-427) = 0.06366100;
642 QUADNODES(2,440-427) = 0.2696723;
643 QUADNODES(2,441-427) = 0.06366100;
644 QUADNODES(2,442-427) = 0.06366100;
645 QUADNODES(2,443-427) = 0.6030057;
646 QUADNODES(2,444-427) = 0.06366100;
647 QUADNODES(2,445-427) = 0.2696723;
648 QUADNODES(2,446-427) = 0.06366100;
649 QUADNODES(2,447-427) = 0.6030057;
650 QUADNODES(2,448-427) = 0.06366100;
651 QUADNODES(2,449-427) = 0.6030057;
652 QUADNODES(2,450-427) = 0.2696723;
653
654 } else if (numQuadNodes==31){
655 QUADWEIGHTS(451-451) = 0.01826422;
656 QUADWEIGHTS(452-451) = 0.01059994;
657 QUADWEIGHTS(453-451) = 0.01059994;
658 QUADWEIGHTS(454-451) = 0.01059994;
659 QUADWEIGHTS(455-451) = 0.01059994;
660 QUADWEIGHTS(456-451) =-0.06251774;
661 QUADWEIGHTS(457-451) =-0.06251774;
662 QUADWEIGHTS(458-451) =-0.06251774;
663 QUADWEIGHTS(459-451) =-0.06251774;
664 QUADWEIGHTS(460-451) = 0.004891425;
665 QUADWEIGHTS(461-451) = 0.004891425;
666 QUADWEIGHTS(462-451) = 0.004891425;
667 QUADWEIGHTS(463-451) = 0.004891425;
668 QUADWEIGHTS(464-451) = 0.0009700176;
669 QUADWEIGHTS(465-451) = 0.0009700176;
670 QUADWEIGHTS(466-451) = 0.0009700176;
671 QUADWEIGHTS(467-451) = 0.0009700176;
672 QUADWEIGHTS(468-451) = 0.0009700176;
673 QUADWEIGHTS(469-451) = 0.0009700176;
674 QUADWEIGHTS(470-451) = 0.02755732;
675 QUADWEIGHTS(471-451) = 0.02755732;
676 QUADWEIGHTS(472-451) = 0.02755732;
677 QUADWEIGHTS(473-451) = 0.02755732;
678 QUADWEIGHTS(474-451) = 0.02755732;
679 QUADWEIGHTS(475-451) = 0.02755732;
680 QUADWEIGHTS(476-451) = 0.02755732;
681 QUADWEIGHTS(477-451) = 0.02755732;
682 QUADWEIGHTS(478-451) = 0.02755732;
683 QUADWEIGHTS(479-451) = 0.02755732;
684 QUADWEIGHTS(480-451) = 0.02755732;
685 QUADWEIGHTS(481-451) = 0.02755732;
686
687 QUADNODES(0,451-451) = 0.2500000;
688 QUADNODES(0,452-451) = 0.7653604;
689 QUADNODES(0,453-451) = 0.07821319;
690 QUADNODES(0,454-451) = 0.07821319;
691 QUADNODES(0,455-451) = 0.07821319;
692 QUADNODES(0,456-451) = 0.6344704;
693 QUADNODES(0,457-451) = 0.1218432;
694 QUADNODES(0,458-451) = 0.1218432;
695 QUADNODES(0,459-451) = 0.1218432;
696 QUADNODES(0,460-451) = 0.002382507;
697 QUADNODES(0,461-451) = 0.3325392;
698 QUADNODES(0,462-451) = 0.3325392;
699 QUADNODES(0,463-451) = 0.3325392;
700 QUADNODES(0,464-451) = 0.0000000;
701 QUADNODES(0,465-451) = 0.0000000;
702 QUADNODES(0,466-451) = 0.0000000;
703 QUADNODES(0,467-451) = 0.5000000;
704 QUADNODES(0,468-451) = 0.5000000;
705 QUADNODES(0,469-451) = 0.5000000;
706 QUADNODES(0,470-451) = 0.6000000;
707 QUADNODES(0,471-451) = 0.6000000;
708 QUADNODES(0,472-451) = 0.6000000;
709 QUADNODES(0,473-451) = 0.2000000;
710 QUADNODES(0,474-451) = 0.2000000;
711 QUADNODES(0,475-451) = 0.2000000;
712 QUADNODES(0,476-451) = 0.1000000;
713 QUADNODES(0,477-451) = 0.1000000;
714 QUADNODES(0,478-451) = 0.1000000;
715 QUADNODES(0,479-451) = 0.1000000;
716 QUADNODES(0,480-451) = 0.1000000;
717 QUADNODES(0,481-451) = 0.1000000;
718
719 QUADNODES(1,451-451) = 0.2500000;
720 QUADNODES(1,452-451) = 0.07821319;
721 QUADNODES(1,453-451) = 0.7653604;
722 QUADNODES(1,454-451) = 0.07821319;
723 QUADNODES(1,455-451) = 0.07821319;
724 QUADNODES(1,456-451) = 0.1218432;
725 QUADNODES(1,457-451) = 0.6344704;
726 QUADNODES(1,458-451) = 0.1218432;
727 QUADNODES(1,459-451) = 0.1218432;
728 QUADNODES(1,460-451) = 0.3325392;
729 QUADNODES(1,461-451) = 0.002382507;
730 QUADNODES(1,462-451) = 0.3325392;
731 QUADNODES(1,463-451) = 0.3325392;
732 QUADNODES(1,464-451) = 0.0000000;
733 QUADNODES(1,465-451) = 0.5000000;
734 QUADNODES(1,466-451) = 0.5000000;
735 QUADNODES(1,467-451) = 0.0000000;
736 QUADNODES(1,468-451) = 0.0000000;
737 QUADNODES(1,469-451) = 0.5000000;
738 QUADNODES(1,470-451) = 0.2000000;
739 QUADNODES(1,471-451) = 0.1000000;
740 QUADNODES(1,472-451) = 0.1000000;
741 QUADNODES(1,473-451) = 0.6000000;
742 QUADNODES(1,474-451) = 0.1000000;
743 QUADNODES(1,475-451) = 0.1000000;
744 QUADNODES(1,476-451) = 0.6000000;
745 QUADNODES(1,477-451) = 0.6000000;
746 QUADNODES(1,478-451) = 0.2000000;
747 QUADNODES(1,479-451) = 0.2000000;
748 QUADNODES(1,480-451) = 0.1000000;
749 QUADNODES(1,481-451) = 0.1000000;
750
751 QUADNODES(2,451-451) = 0.2500000;
752 QUADNODES(2,452-451) = 0.07821319;
753 QUADNODES(2,453-451) = 0.07821319;
754 QUADNODES(2,454-451) = 0.7653604;
755 QUADNODES(2,455-451) = 0.07821319;
756 QUADNODES(2,456-451) = 0.1218432;
757 QUADNODES(2,457-451) = 0.1218432;
758 QUADNODES(2,458-451) = 0.6344704;
759 QUADNODES(2,459-451) = 0.1218432;
760 QUADNODES(2,460-451) = 0.3325392;
761 QUADNODES(2,461-451) = 0.3325392;
762 QUADNODES(2,462-451) = 0.002382507;
763 QUADNODES(2,463-451) = 0.3325392;
764 QUADNODES(2,464-451) = 0.5000000;
765 QUADNODES(2,465-451) = 0.0000000;
766 QUADNODES(2,466-451) = 0.5000000;
767 QUADNODES(2,467-451) = 0.0000000;
768 QUADNODES(2,468-451) = 0.5000000;
769 QUADNODES(2,469-451) = 0.0000000;
770 QUADNODES(2,470-451) = 0.1000000;
771 QUADNODES(2,471-451) = 0.2000000;
772 QUADNODES(2,472-451) = 0.1000000;
773 QUADNODES(2,473-451) = 0.1000000;
774 QUADNODES(2,474-451) = 0.6000000;
775 QUADNODES(2,475-451) = 0.1000000;
776 QUADNODES(2,476-451) = 0.2000000;
777 QUADNODES(2,477-451) = 0.1000000;
778 QUADNODES(2,478-451) = 0.6000000;
779 QUADNODES(2,479-451) = 0.1000000;
780 QUADNODES(2,480-451) = 0.6000000;
781 QUADNODES(2,481-451) = 0.2000000;
782
783 } else if (numQuadNodes==45){
784 QUADWEIGHTS(482-482) =-0.03932701;
785 QUADWEIGHTS(483-482) = 0.004081316;
786 QUADWEIGHTS(484-482) = 0.004081316;
787 QUADWEIGHTS(485-482) = 0.004081316;
788 QUADWEIGHTS(486-482) = 0.004081316;
789 QUADWEIGHTS(487-482) = 0.0006580868;
790 QUADWEIGHTS(488-482) = 0.0006580868;
791 QUADWEIGHTS(489-482) = 0.0006580868;
792 QUADWEIGHTS(490-482) = 0.0006580868;
793 QUADWEIGHTS(491-482) = 0.004384259;
794 QUADWEIGHTS(492-482) = 0.004384259;
795 QUADWEIGHTS(493-482) = 0.004384259;
796 QUADWEIGHTS(494-482) = 0.004384259;
797 QUADWEIGHTS(495-482) = 0.004384259;
798 QUADWEIGHTS(496-482) = 0.004384259;
799 QUADWEIGHTS(497-482) = 0.01383006;
800 QUADWEIGHTS(498-482) = 0.01383006;
801 QUADWEIGHTS(499-482) = 0.01383006;
802 QUADWEIGHTS(500-482) = 0.01383006;
803 QUADWEIGHTS(501-482) = 0.01383006;
804 QUADWEIGHTS(502-482) = 0.01383006;
805 QUADWEIGHTS(503-482) = 0.004240437;
806 QUADWEIGHTS(504-482) = 0.004240437;
807 QUADWEIGHTS(505-482) = 0.004240437;
808 QUADWEIGHTS(506-482) = 0.004240437;
809 QUADWEIGHTS(507-482) = 0.004240437;
810 QUADWEIGHTS(508-482) = 0.004240437;
811 QUADWEIGHTS(509-482) = 0.004240437;
812 QUADWEIGHTS(510-482) = 0.004240437;
813 QUADWEIGHTS(511-482) = 0.004240437;
814 QUADWEIGHTS(512-482) = 0.004240437;
815 QUADWEIGHTS(513-482) = 0.004240437;
816 QUADWEIGHTS(514-482) = 0.004240437;
817 QUADWEIGHTS(515-482) = 0.002238740;
818 QUADWEIGHTS(516-482) = 0.002238740;
819 QUADWEIGHTS(517-482) = 0.002238740;
820 QUADWEIGHTS(518-482) = 0.002238740;
821 QUADWEIGHTS(519-482) = 0.002238740;
822 QUADWEIGHTS(520-482) = 0.002238740;
823 QUADWEIGHTS(521-482) = 0.002238740;
824 QUADWEIGHTS(522-482) = 0.002238740;
825 QUADWEIGHTS(523-482) = 0.002238740;
826 QUADWEIGHTS(524-482) = 0.002238740;
827 QUADWEIGHTS(525-482) = 0.002238740;
828 QUADWEIGHTS(526-482) = 0.002238740;
829
830 QUADNODES(0,482-482) = 0.2500000;
831 QUADNODES(0,483-482) = 0.6175872;
832 QUADNODES(0,484-482) = 0.1274709;
833 QUADNODES(0,485-482) = 0.1274709;
834 QUADNODES(0,486-482) = 0.1274709;
835 QUADNODES(0,487-482) = 0.9037635;
836 QUADNODES(0,488-482) = 0.03207883;
837 QUADNODES(0,489-482) = 0.03207883;
838 QUADNODES(0,490-482) = 0.03207883;
839 QUADNODES(0,491-482) = 0.4502229;
840 QUADNODES(0,492-482) = 0.4502229;
841 QUADNODES(0,493-482) = 0.4502229;
842 QUADNODES(0,494-482) = 0.04977710;
843 QUADNODES(0,495-482) = 0.04977710;
844 QUADNODES(0,496-482) = 0.04977710;
845 QUADNODES(0,497-482) = 0.3162696;
846 QUADNODES(0,498-482) = 0.3162696;
847 QUADNODES(0,499-482) = 0.3162696;
848 QUADNODES(0,500-482) = 0.1837304;
849 QUADNODES(0,501-482) = 0.1837304;
850 QUADNODES(0,502-482) = 0.1837304;
851 QUADNODES(0,503-482) = 0.5132800;
852 QUADNODES(0,504-482) = 0.5132800;
853 QUADNODES(0,505-482) = 0.5132800;
854 QUADNODES(0,506-482) = 0.02291779;
855 QUADNODES(0,507-482) = 0.02291779;
856 QUADNODES(0,508-482) = 0.02291779;
857 QUADNODES(0,509-482) = 0.2319011;
858 QUADNODES(0,510-482) = 0.2319011;
859 QUADNODES(0,511-482) = 0.2319011;
860 QUADNODES(0,512-482) = 0.2319011;
861 QUADNODES(0,513-482) = 0.2319011;
862 QUADNODES(0,514-482) = 0.2319011;
863 QUADNODES(0,515-482) = 0.1937465;
864 QUADNODES(0,516-482) = 0.1937465;
865 QUADNODES(0,517-482) = 0.1937465;
866 QUADNODES(0,518-482) = 0.7303134;
867 QUADNODES(0,519-482) = 0.7303134;
868 QUADNODES(0,520-482) = 0.7303134;
869 QUADNODES(0,521-482) = 0.03797005;
870 QUADNODES(0,522-482) = 0.03797005;
871 QUADNODES(0,523-482) = 0.03797005;
872 QUADNODES(0,524-482) = 0.03797005;
873 QUADNODES(0,525-482) = 0.03797005;
874 QUADNODES(0,526-482) = 0.03797005;
875
876 QUADNODES(1,482-482) = 0.2500000;
877 QUADNODES(1,483-482) = 0.1274709;
878 QUADNODES(1,484-482) = 0.6175872;
879 QUADNODES(1,485-482) = 0.1274709;
880 QUADNODES(1,486-482) = 0.1274709;
881 QUADNODES(1,487-482) = 0.03207883;
882 QUADNODES(1,488-482) = 0.9037635;
883 QUADNODES(1,489-482) = 0.03207883;
884 QUADNODES(1,490-482) = 0.03207883;
885 QUADNODES(1,491-482) = 0.4502229;
886 QUADNODES(1,492-482) = 0.04977710;
887 QUADNODES(1,493-482) = 0.04977710;
888 QUADNODES(1,494-482) = 0.4502229;
889 QUADNODES(1,495-482) = 0.4502229;
890 QUADNODES(1,496-482) = 0.04977710;
891 QUADNODES(1,497-482) = 0.3162696;
892 QUADNODES(1,498-482) = 0.1837304;
893 QUADNODES(1,499-482) = 0.1837304;
894 QUADNODES(1,500-482) = 0.3162696;
895 QUADNODES(1,501-482) = 0.3162696;
896 QUADNODES(1,502-482) = 0.1837304;
897 QUADNODES(1,503-482) = 0.02291779;
898 QUADNODES(1,504-482) = 0.2319011;
899 QUADNODES(1,505-482) = 0.2319011;
900 QUADNODES(1,506-482) = 0.5132800;
901 QUADNODES(1,507-482) = 0.2319011;
902 QUADNODES(1,508-482) = 0.2319011;
903 QUADNODES(1,509-482) = 0.5132800;
904 QUADNODES(1,510-482) = 0.5132800;
905 QUADNODES(1,511-482) = 0.02291779;
906 QUADNODES(1,512-482) = 0.02291779;
907 QUADNODES(1,513-482) = 0.2319011;
908 QUADNODES(1,514-482) = 0.2319011;
909 QUADNODES(1,515-482) = 0.7303134;
910 QUADNODES(1,516-482) = 0.03797005;
911 QUADNODES(1,517-482) = 0.03797005;
912 QUADNODES(1,518-482) = 0.1937465;
913 QUADNODES(1,519-482) = 0.03797005;
914 QUADNODES(1,520-482) = 0.03797005;
915 QUADNODES(1,521-482) = 0.1937465;
916 QUADNODES(1,522-482) = 0.1937465;
917 QUADNODES(1,523-482) = 0.7303134;
918 QUADNODES(1,524-482) = 0.7303134;
919 QUADNODES(1,525-482) = 0.03797005;
920 QUADNODES(1,526-482) = 0.03797005;
921
922 QUADNODES(2,482-482) = 0.2500000;
923 QUADNODES(2,483-482) = 0.1274709;
924 QUADNODES(2,484-482) = 0.1274709;
925 QUADNODES(2,485-482) = 0.6175872;
926 QUADNODES(2,486-482) = 0.1274709;
927 QUADNODES(2,487-482) = 0.03207883;
928 QUADNODES(2,488-482) = 0.03207883;
929 QUADNODES(2,489-482) = 0.9037635;
930 QUADNODES(2,490-482) = 0.03207883;
931 QUADNODES(2,491-482) = 0.04977710;
932 QUADNODES(2,492-482) = 0.4502229;
933 QUADNODES(2,493-482) = 0.04977710;
934 QUADNODES(2,494-482) = 0.4502229;
935 QUADNODES(2,495-482) = 0.04977710;
936 QUADNODES(2,496-482) = 0.4502229;
937 QUADNODES(2,497-482) = 0.1837304;
938 QUADNODES(2,498-482) = 0.3162696;
939 QUADNODES(2,499-482) = 0.1837304;
940 QUADNODES(2,500-482) = 0.3162696;
941 QUADNODES(2,501-482) = 0.1837304;
942 QUADNODES(2,502-482) = 0.3162696;
943 QUADNODES(2,503-482) = 0.2319011;
944 QUADNODES(2,504-482) = 0.02291779;
945 QUADNODES(2,505-482) = 0.2319011;
946 QUADNODES(2,506-482) = 0.2319011;
947 QUADNODES(2,507-482) = 0.5132800;
948 QUADNODES(2,508-482) = 0.2319011;
949 QUADNODES(2,509-482) = 0.02291779;
950 QUADNODES(2,510-482) = 0.2319011;
951 QUADNODES(2,511-482) = 0.5132800;
952 QUADNODES(2,512-482) = 0.2319011;
953 QUADNODES(2,513-482) = 0.5132800;
954 QUADNODES(2,514-482) = 0.02291779;
955 QUADNODES(2,515-482) = 0.03797005;
956 QUADNODES(2,516-482) = 0.7303134;
957 QUADNODES(2,517-482) = 0.03797005;
958 QUADNODES(2,518-482) = 0.03797005;
959 QUADNODES(2,519-482) = 0.1937465;
960 QUADNODES(2,520-482) = 0.03797005;
961 QUADNODES(2,521-482) = 0.7303134;
962 QUADNODES(2,522-482) = 0.03797005;
963 QUADNODES(2,523-482) = 0.1937465;
964 QUADNODES(2,524-482) = 0.03797005;
965 QUADNODES(2,525-482) = 0.1937465;
966 QUADNODES(2,526-482) = 0.7303134;
967
968 } else {
969
970 /* get scheme on [0.1]^3 */
971
972 Quad_getNodesHex(numQuadNodes,quadNodes,quadWeights);
973 if (! Finley_noError()) return;
974
975 /* squeeze it: */
976 for (i=0;i<numQuadNodes;i++) {
977 Q1=QUADNODES(0,i);
978 Q2=QUADNODES(1,i);
979 Q3=QUADNODES(2,i);
980
981 JA11= (1./3.)*Q2*Q3-(1./2.)*(Q2+Q3) +1.;
982 JA12= (1./3.)*Q1*Q3-(1./2.)*Q1;
983 JA13= (1./3.)*Q1*Q2-(1./2.)*Q1;
984 JA21= (1./3.)*Q2*Q3-(1./2.)*Q2;
985 JA22= (1./3.)*Q1*Q3-(1./2.)*(Q1+Q3) +1.;
986 JA23= (1./3.)*Q1*Q2-(1./2.)*Q2;
987 JA31= (1./3.)*Q2*Q3-(1./2.)*Q3;
988 JA32= (1./3.)*Q1*Q3-(1./2.)*Q3;
989 JA33= (1./3.)*Q1*Q2-(1./2.)*(Q1+Q2) +1.;
990 DET=JA11*JA22*JA33+JA12*JA23*JA31+JA13*JA21*JA32-JA13*JA22*JA31-JA11*JA23*JA32-JA12*JA21*JA33;
991 quadWeights[i]=quadWeights[i]*ABS(DET);
992 QUADNODES(0,i)=Q1*((1./3.)*Q2*Q3-(1./2.)*(Q2+Q3)+1.);
993 QUADNODES(1,i)=Q2*((1./3.)*Q1*Q3-(1./2.)*(Q1+Q3)+1.);
994 QUADNODES(2,i)=Q3*((1./3.)*Q1*Q2-(1./2.)*(Q1+Q2)+1.);
995 }
996 }
997 #undef DIM
998 }
999
1000 /************************************************************************************/
1001
1002 /* get a quadrature scheme with numQuadNodes quadrature nodes for the quad [0.1]^2 */
1003 /* as a X-product of a 1D scheme. */
1004
1005 void Quad_getNodesRec(int numQuadNodes,double* quadNodes,double* quadWeights) {
1006 char error_msg[LenErrorMsg_MAX];
1007 int numQuadNodes1d,i,j,l;
1008 double *quadNodes1d=NULL,*quadWeights1d=NULL;
1009 bool_t set=FALSE;
1010 #define DIM 2
1011
1012 quadNodes1d=new double[numQuadNodes];
1013 quadWeights1d=new double[numQuadNodes];
1014 if (! ( Finley_checkPtr(quadNodes1d) || Finley_checkPtr(quadWeights1d) ) ) {
1015 /* find numQuadNodes1d with numQuadNodes1d**2==numQuadNodes: */
1016
1017 for (numQuadNodes1d=1;numQuadNodes1d<=MAX_numQuadNodesLine;numQuadNodes1d++) {
1018 if (numQuadNodes1d*numQuadNodes1d==numQuadNodes) {
1019
1020 /* get 1D scheme: */
1021
1022 Quad_getNodesLine(numQuadNodes1d,quadNodes1d,quadWeights1d);
1023
1024 /* make 2D scheme: */
1025
1026 if (Finley_noError()) {
1027 l=0;
1028 for (i=0;i<numQuadNodes1d;i++) {
1029 for (j=0;j<numQuadNodes1d;j++) {
1030 QUADNODES(0,l)=quadNodes1d[i];
1031 QUADNODES(1,l)=quadNodes1d[j];
1032 QUADWEIGHTS(l)=quadWeights1d[i]*quadWeights1d[j];
1033 l++;
1034 }
1035 }
1036 set=TRUE;
1037 break;
1038 }
1039 }
1040 }
1041 if (!set) {
1042 sprintf(error_msg,"Quad_getNodesRec: Illegal number of quadrature nodes %d on hexahedron.",numQuadNodes);
1043 Finley_setError(VALUE_ERROR,error_msg);
1044 }
1045 delete[] quadNodes1d;
1046 delete[] quadWeights1d;
1047 }
1048 #undef DIM
1049 }
1050
1051 /************************************************************************************/
1052
1053 /* get a quadrature scheme with numQuadNodes quadrature nodes for the hex [0.1]^3 */
1054 /* as a X-product of a 1D scheme. */
1055
1056 void Quad_getNodesHex(int numQuadNodes,double* quadNodes,double* quadWeights) {
1057 char error_msg[LenErrorMsg_MAX];
1058 int numQuadNodes1d,i,j,k,l;
1059 double *quadNodes1d=NULL,*quadWeights1d=NULL;
1060 bool_t set=FALSE;
1061 #define DIM 3
1062
1063 /* find numQuadNodes1d with numQuadNodes1d**3==numQuadNodes: */
1064
1065 quadNodes1d=new double[numQuadNodes];
1066 quadWeights1d=new double[numQuadNodes];
1067 if (! ( Finley_checkPtr(quadNodes1d) || Finley_checkPtr(quadWeights1d) ) ) {
1068 for (numQuadNodes1d=1;numQuadNodes1d<=MAX_numQuadNodesLine;numQuadNodes1d++) {
1069 if (numQuadNodes1d*numQuadNodes1d*numQuadNodes1d==numQuadNodes) {
1070
1071 /* get 1D scheme: */
1072
1073 Quad_getNodesLine(numQuadNodes1d,quadNodes1d,quadWeights1d);
1074
1075 /* make 3D scheme: */
1076
1077 if (Finley_noError()) {
1078 l=0;
1079 for (i=0;i<numQuadNodes1d;i++) {
1080 for (j=0;j<numQuadNodes1d;j++) {
1081 for (k=0;k<numQuadNodes1d;k++) {
1082 QUADNODES(0,l)=quadNodes1d[i];
1083 QUADNODES(1,l)=quadNodes1d[j];
1084 QUADNODES(2,l)=quadNodes1d[k];
1085 QUADWEIGHTS(l)=quadWeights1d[i]*quadWeights1d[j]*quadWeights1d[k];
1086 l++;
1087 }
1088 }
1089 }
1090 set=TRUE;
1091 break;
1092 }
1093 }
1094 }
1095 if (!set) {
1096 sprintf(error_msg,"Quad_getNodesHex: Illegal number of quadrature nodes %d on hexahedron.",numQuadNodes);
1097 Finley_setError(VALUE_ERROR,error_msg);
1098 }
1099 delete[] quadNodes1d;
1100 delete[] quadWeights1d;
1101 }
1102 #undef DIM
1103 }
1104
1105 /************************************************************************************/
1106
1107 /* get a quadrature scheme with numQuadNodes quadrature nodes for a point. As there */
1108 /* in no quadrature scheme for a point any value for numQuadNodes other than 0 throws */
1109 /* an error. */
1110
1111 void Quad_getNodesPoint(int numQuadNodes,double* quadNodes,double* quadWeights) {
1112 if (numQuadNodes>=0) {
1113 return;
1114 } else {
1115 Finley_setError(VALUE_ERROR,"Quad_getNodesPoint: Illegal number of quadrature nodes.");
1116 }
1117 }
1118
1119 /************************************************************************************/
1120
1121 /* get a quadrature scheme with numQuadNodes quadrature nodes on the line [0,1]: */
1122 /* The nodes and weights are set from a table. */
1123
1124 void Quad_getNodesLine(int numQuadNodes,double* quadNodes,double* quadWeights) {
1125 switch(numQuadNodes) {
1126 case 1:
1127 quadNodes[0]=0.5;
1128 quadWeights[0]=1.;
1129 break;
1130
1131 case 2:
1132 quadNodes[0]=(1.-.577350269189626)/2.;
1133 quadNodes[1]=(1.+.577350269189626)/2.;
1134 quadWeights[0]=.5;
1135 quadWeights[1]=.5;
1136 break;
1137
1138 case 3:
1139 quadNodes[0]=(1.-.774596669241483)/2.;
1140 quadNodes[1]=.5;
1141 quadNodes[2]=(1.+.774596669241483)/2.;
1142 quadWeights[0]=5./18.;
1143 quadWeights[1]=4./ 9.;
1144 quadWeights[2]=5./18.;
1145 break;
1146
1147 case 4:
1148 quadNodes[0]=(1.-.861136311594053)/2.;
1149 quadNodes[1]=(1.-.339981043584856)/2.;
1150 quadNodes[2]=(1.+.339981043584856)/2.;
1151 quadNodes[3]=(1.+.861136311594053)/2.;
1152 quadWeights[0]=.347854845137454/2.;
1153 quadWeights[1]=.652145154862546/2.;
1154 quadWeights[2]=.652145154862546/2.;
1155 quadWeights[3]=.347854845137454/2.;
1156 break;
1157
1158 case 5:
1159 quadNodes[0]=(1.-.906179845938664)/2.;
1160 quadNodes[1]=(1.-.538469310105683)/2.;
1161 quadNodes[2]= .5;
1162 quadNodes[3]=(1.+.538469310105683)/2.;
1163 quadNodes[4]=(1.+.906179845938664)/2.;
1164 quadWeights[0]=.236926885056189/2.;
1165 quadWeights[1]=.478628670499366/2.;
1166 quadWeights[2]=.568888888888889/2.;
1167 quadWeights[3]=.478628670499366/2.;
1168 quadWeights[4]=.236926885056189/2.;
1169 break;
1170
1171 case 6:
1172 quadNodes[0]=(1.-.932469514203152)/2.;
1173 quadNodes[1]=(1.-.661209386466265)/2.;
1174 quadNodes[2]=(1.-.238619186083197)/2.;
1175 quadNodes[3]=(1.+.238619186083197)/2.;
1176 quadNodes[4]=(1.+.661209386466265)/2.;
1177 quadNodes[5]=(1.+.932469514203152)/2.;
1178 quadWeights[0]=.171324492379170/2.;
1179 quadWeights[1]=.360761573048139/2.;
1180 quadWeights[2]=.467913934572691/2.;
1181 quadWeights[3]=.467913934572691/2.;
1182 quadWeights[4]=.360761573048139/2.;
1183 quadWeights[5]=.171324492379170/2.;
1184 break;
1185
1186 case 7:
1187 quadNodes[0]=(1.-.949107912342759)/2.;
1188 quadNodes[1]=(1.-.741531185599394)/2.;
1189 quadNodes[2]=(1.-.405845151377397)/2.;
1190 quadNodes[3]=0.5;
1191 quadNodes[4]=(1.+.405845151377397)/2.;
1192 quadNodes[5]=(1.+.741531185599394)/2.;
1193 quadNodes[6]=(1.+.949107912342759)/2.;
1194 quadWeights[0]= .129484966168870/2.;
1195 quadWeights[1]= .279705391489277/2.;
1196 quadWeights[2]= .381830050505119/2.;
1197 quadWeights[3]= .417959183673469/2.;
1198 quadWeights[4]= .381830050505119/2.;
1199 quadWeights[5]= .279705391489277/2.;
1200 quadWeights[6]= .129484966168870/2.;
1201 break;
1202
1203 case 8:
1204 quadNodes[0]=(1.-.960289856497536)/2.;
1205 quadNodes[1]=(1.-.796666477413627)/2.;
1206 quadNodes[2]=(1.-.525532409916329)/2.;
1207 quadNodes[3]=(1.-.183434642495650)/2.;
1208 quadNodes[4]=(1.+.183434642495650)/2.;
1209 quadNodes[5]=(1.+.525532409916329)/2.;
1210 quadNodes[6]=(1.+.796666477413627)/2.;
1211 quadNodes[7]=(1.+.960289856497536)/2.;
1212 quadWeights[0]= .101228536290376/2.;
1213 quadWeights[1]= .222381034453374/2.;
1214 quadWeights[2]= .313706645877887/2.;
1215 quadWeights[3]= .362683783378362/2.;
1216 quadWeights[4]= .362683783378362/2.;
1217 quadWeights[5]= .313706645877887/2.;
1218 quadWeights[6]= .222381034453374/2.;
1219 quadWeights[7]= .101228536290376/2.;
1220 break;
1221
1222 case 9:
1223 quadNodes[0]=(1.-.968160239507626)/2.;
1224 quadNodes[1]=(1.-.836031107326636)/2.;
1225 quadNodes[2]=(1.-.613371432700590)/2.;
1226 quadNodes[3]=(1.-.324253423403809)/2.;
1227 quadNodes[4]= .5;
1228 quadNodes[5]=(1.+.324253423403809)/2.;
1229 quadNodes[6]=(1.+.613371432700590)/2.;
1230 quadNodes[7]=(1.+.836031107326636)/2.;
1231 quadNodes[8]=(1.+.968160239507626)/2.;
1232 quadWeights[0]= .081274388361574/2.;
1233 quadWeights[1]= .180648160694857/2.;
1234 quadWeights[2]= .260610696402935/2.;
1235 quadWeights[3]= .312347077040003/2.;
1236 quadWeights[4]= .330239355001260/2.;
1237 quadWeights[5]= .312347077040003/2.;
1238 quadWeights[6]= .260610696402935/2.;
1239 quadWeights[7]= .180648160694857/2.;
1240 quadWeights[8]= .081274388361574/2.;
1241 break;
1242
1243 case 10:
1244 quadNodes[0]=(1.-.973906528517172)/2.;
1245 quadNodes[1]=(1.-.865063366688985)/2.;
1246 quadNodes[2]=(1.-.679409568299024)/2.;
1247 quadNodes[3]=(1.-.433395394129247)/2.;
1248 quadNodes[4]=(1.-.148874338981631)/2.;
1249 quadNodes[5]=(1.+.148874338981631)/2.;
1250 quadNodes[6]=(1.+.433395394129247)/2.;
1251 quadNodes[7]=(1.+.679409568299024)/2.;
1252 quadNodes[8]=(1.+.865063366688985)/2.;
1253 quadNodes[9]=(1.+.973906528517172)/2.;
1254 quadWeights[0]= .066671344308688/2.;
1255 quadWeights[1]= .149451349150581/2.;
1256 quadWeights[2]= .219086362515982/2.;
1257 quadWeights[3]= .269266719309996/2.;
1258 quadWeights[4]= .295524224714753/2.;
1259 quadWeights[5]= .295524224714753/2.;
1260 quadWeights[6]= .269266719309996/2.;
1261 quadWeights[7]= .219086362515982/2.;
1262 quadWeights[8]= .149451349150581/2.;
1263 quadWeights[9]= .066671344308688/2.;
1264 break;
1265
1266 default:
1267 Finley_setError(VALUE_ERROR,"Quad_getNodesLine: Negative integration order.");
1268 break;
1269 }
1270 }
1271
1272
1273 /************************************************************************************/
1274
1275 /* The following functions Quad_getNumNodes* return the number of quadrature points needed to */
1276 /* achieve a certain accuracy. Notice that for Tet and Tri the order is increased */
1277 /* to consider the accuracy reduction through the construction process. */
1278
1279
1280 int Quad_getNumNodesPoint(int order) {
1281 return 1;
1282 }
1283
1284 int Quad_getNumNodesLine(int order) {
1285 char error_msg[LenErrorMsg_MAX];
1286 if (order <0 ) {
1287 Finley_setError(VALUE_ERROR,"Quad_getNumNodesLine: Negative integration order.");
1288 return -1;
1289 } else {
1290 if (order > 2*MAX_numQuadNodesLine-1) {
1291 sprintf(error_msg,"Quad_getNumNodesLine: requested integration order %d on line is too large (>%d).",
1292 order,2*MAX_numQuadNodesLine-1);
1293 Finley_setError(VALUE_ERROR,error_msg);
1294 return -1;
1295 } else {
1296 Finley_resetError();
1297 return order/2+1;
1298 }
1299 }
1300 }
1301
1302 int Quad_getNumNodesTri(int order) {
1303 int numQuadNodesLine;
1304 if (order<=1) {
1305 return 1;
1306 } else if (order<=2){
1307 return 3;
1308 } else if (order<=3){
1309 return 4;
1310 } else if (order<=4){
1311 return 6;
1312 } else if (order<=5){
1313 return 7;
1314 } else if (order<=6){
1315 return 12;
1316 } else if (order<=7){
1317 return 13;
1318 } else if (order<=8){
1319 return 16;
1320 } else if (order<=9){
1321 return 19;
1322 } else {
1323 numQuadNodesLine=Quad_getNumNodesLine(order+1);
1324 if (Finley_noError()) {
1325 return numQuadNodesLine*numQuadNodesLine;
1326 } else {
1327 return -1;
1328 }
1329 }
1330 }
1331
1332 int Quad_getNumNodesRec(int order) {
1333 int numQuadNodesLine;
1334 numQuadNodesLine=Quad_getNumNodesLine(order);
1335 if (Finley_noError()) {
1336 return numQuadNodesLine*numQuadNodesLine;
1337 } else {
1338 return -1;
1339 }
1340 }
1341
1342 int Quad_getNumNodesTet(int order) {
1343 int numQuadNodesLine;
1344 if (order<=1) {
1345 return 1;
1346 } else if (order<=2){
1347 return 4;
1348 } else if (order<=3){
1349 return 5;
1350 } else if (order<=4){
1351 return 11;
1352 } else if (order<=5){
1353 return 15;
1354 } else if (order<=6){
1355 return 24;
1356 } else if (order<=7){
1357 return 31;
1358 } else if (order<=8){
1359 return 45;
1360 } else {
1361 numQuadNodesLine=Quad_getNumNodesLine(order+2);
1362 if (Finley_noError()) {
1363 return numQuadNodesLine*numQuadNodesLine*numQuadNodesLine;
1364 } else {
1365 return -1;
1366 }
1367 }
1368 }
1369
1370 int Quad_getNumNodesHex(int order) {
1371 int numQuadNodesLine;
1372 numQuadNodesLine=Quad_getNumNodesLine(order);
1373 if (Finley_noError()) {
1374 return numQuadNodesLine*numQuadNodesLine*numQuadNodesLine;
1375 } else {
1376 return -1;
1377 }
1378 }
1379 dim_t Quad_MacroPoint(dim_t numSubElements, int numQuadNodes, double* quadNodes, double* quadWeights, dim_t numF, double* dFdv,
1380 dim_t new_len, double* new_quadNodes, double* new_quadWeights, double* new_dFdv )
1381 {
1382 return 0;
1383
1384 }
1385 dim_t Quad_MacroLine(dim_t numSubElements, int numQuadNodes, double* quadNodes, double* quadWeights, dim_t numF, double* dFdv,
1386 dim_t new_len, double* new_quadNodes, double* new_quadWeights, double* new_dFdv )
1387 {
1388 #define DIM 1
1389 dim_t s,q,i;
1390 register double x0, w;
1391 const double f=1./((double)numSubElements);
1392
1393 if (new_len < numSubElements*numQuadNodes) {
1394 Finley_setError(MEMORY_ERROR,"Quad_MacroLine: array for new quadrature scheme is too small");
1395 }
1396 for (q=0; q<numQuadNodes; ++q) {
1397
1398 x0=quadNodes[INDEX2(0,q,DIM)];
1399 w=f*quadWeights[q];
1400
1401 for (s=0; s<numSubElements; ++s) {
1402 new_quadWeights[INDEX2(q,s, numQuadNodes)] =w;
1403 new_quadNodes[INDEX3(0,q,s, DIM,numQuadNodes)] =(x0+s)*f;
1404 for (i=0;i<numF;i++) new_dFdv[INDEX4(i,0,q,s, numF, DIM,numQuadNodes)] = dFdv[INDEX3(i,0,numF, q,DIM)]*f;
1405 }
1406
1407 }
1408 #undef DIM
1409 return numSubElements*numQuadNodes;
1410 }
1411 #define HALF 0.5
1412 #define TWO 2.
1413 dim_t Quad_MacroTri(dim_t numSubElements, int numQuadNodes, double* quadNodes, double* quadWeights, dim_t numF, double* dFdv,
1414 dim_t new_len, double* new_quadNodes, double* new_quadWeights, double* new_dFdv )
1415 {
1416
1417 #define DIM 2
1418 dim_t q,i;
1419 register double x0, x1, w, df0, df1;
1420
1421 if (new_len < numSubElements*numQuadNodes) {
1422 Finley_setError(MEMORY_ERROR,"Quad_MacroTri: array for new quadrature scheme is too small");
1423 return -1;
1424 }
1425 if (numSubElements==1) {
1426
1427 for (q=0; q<numQuadNodes; ++q) {
1428
1429 x0=quadNodes[INDEX2(0,q,DIM)];
1430 x1=quadNodes[INDEX2(1,q,DIM)];
1431 w=quadWeights[q];
1432
1433 new_quadWeights[INDEX2(q,0,numQuadNodes)] =w;
1434 new_quadNodes[INDEX3(0,q,0,DIM,numQuadNodes)] =x0;
1435 new_quadNodes[INDEX3(1,q,0,DIM,numQuadNodes)] =x1;
1436 for (i=0;i<numF;i++) {
1437 new_dFdv[INDEX4(i,0,q,0, numF,DIM,numQuadNodes)] = dFdv[INDEX3(i,0,q, numF, DIM)];
1438 new_dFdv[INDEX4(i,1,q,0, numF,DIM,numQuadNodes)] = dFdv[INDEX3(i,1,q, numF, DIM)];
1439 }
1440
1441 }
1442
1443 } else if (numSubElements==4) {
1444 const double f = 0.25;
1445 for (q=0; q<numQuadNodes; ++q) {
1446
1447 x0=quadNodes[INDEX2(0,q,DIM)];
1448 x1=quadNodes[INDEX2(1,q,DIM)];
1449 w=f*quadWeights[q];
1450
1451 new_quadWeights[INDEX2(q,0,numQuadNodes)] =w;
1452 new_quadNodes[INDEX3(0,q,0,DIM,numQuadNodes)] =HALF*x0;
1453 new_quadNodes[INDEX3(1,q,0,DIM,numQuadNodes)] =HALF*x1;
1454
1455 new_quadWeights[INDEX2(q,1,numQuadNodes)] =w;
1456 new_quadNodes[INDEX3(0,q,1,DIM,numQuadNodes)] =HALF*x0;
1457 new_quadNodes[INDEX3(1,q,1,DIM,numQuadNodes)] =HALF*(x1+1);
1458
1459 new_quadWeights[INDEX2(q,2,numQuadNodes)] =w;
1460 new_quadNodes[INDEX3(0,q,2,DIM,numQuadNodes)] =HALF*(x0+1);
1461 new_quadNodes[INDEX3(1,q,2,DIM,numQuadNodes)] =HALF*x1;
1462
1463 new_quadWeights[INDEX2(q,3,numQuadNodes)] =w;
1464 new_quadNodes[INDEX3(0,q,3,DIM,numQuadNodes)] =HALF*(1-x0);
1465 new_quadNodes[INDEX3(1,q,3,DIM,numQuadNodes)] =HALF*(1-x1);
1466
1467 for (i=0;i<numF;i++) {
1468 df0=dFdv[INDEX3(i,0,q, numF, DIM)]*TWO;
1469 df1=dFdv[INDEX3(i,1,q, numF, DIM)]*TWO;
1470
1471 new_dFdv[INDEX4(i,0,q,0, numF,DIM,numQuadNodes)] = df0;
1472 new_dFdv[INDEX4(i,1,q,0, numF,DIM,numQuadNodes)] = df1;
1473
1474 new_dFdv[INDEX4(i,0,q,1, numF,DIM,numQuadNodes)] = df0;
1475 new_dFdv[INDEX4(i,1,q,1, numF,DIM,numQuadNodes)] = df1;
1476
1477 new_dFdv[INDEX4(i,0,q,2, numF,DIM,numQuadNodes)] = df0;
1478 new_dFdv[INDEX4(i,1,q,2, numF,DIM,numQuadNodes)] = df1;
1479
1480 new_dFdv[INDEX4(i,0,q,3, numF,DIM,numQuadNodes)] = -df0;
1481 new_dFdv[INDEX4(i,1,q,3, numF,DIM,numQuadNodes)] = -df1;
1482 }
1483
1484
1485 }
1486 } else {
1487 Finley_setError(MEMORY_ERROR,"Quad_MacroTri: unable to create quadrature scheme for macro element.");
1488 return -1;
1489 }
1490 #undef DIM
1491 return numSubElements*numQuadNodes;
1492 }
1493
1494 dim_t Quad_MacroRec(dim_t numSubElements, int numQuadNodes, double* quadNodes, double* quadWeights, dim_t numF, double* dFdv,
1495 dim_t new_len, double* new_quadNodes, double* new_quadWeights, double* new_dFdv )
1496 {
1497
1498 #define DIM 2
1499 dim_t q,i;
1500 register double x0, x1, w, df0, df1;
1501
1502 if (new_len < numSubElements*numQuadNodes) {
1503 Finley_setError(MEMORY_ERROR,"Quad_MacroRec: array for new quadrature scheme is too small");
1504 return -1;
1505 }
1506 if (numSubElements==1) {
1507
1508 for (q=0; q<numQuadNodes; ++q) {
1509
1510 x0=quadNodes[INDEX2(0,q,DIM)];
1511 x1=quadNodes[INDEX2(1,q,DIM)];
1512 w=quadWeights[q];
1513
1514 new_quadWeights[INDEX2(q,0,numQuadNodes)] =w;
1515 new_quadNodes[INDEX3(0,q,0,DIM,numQuadNodes)] =x0;
1516 new_quadNodes[INDEX3(1,q,0,DIM,numQuadNodes)] =x1;
1517 for (i=0;i<numF;i++) {
1518 new_dFdv[INDEX4(i,0,q,0, numF, DIM,numQuadNodes)] = dFdv[INDEX3(i,0, q,numF, DIM)];
1519 new_dFdv[INDEX4(i,1,q,0, numF, DIM,numQuadNodes)] = dFdv[INDEX3(i,1, q,numF, DIM)];
1520 }
1521
1522 }
1523
1524 } else if (numSubElements==4) {
1525 const double f = 0.25;
1526 for (q=0; q<numQuadNodes; ++q) {
1527
1528 x0=quadNodes[INDEX2(0,q,DIM)];
1529 x1=quadNodes[INDEX2(1,q,DIM)];
1530 w=f*quadWeights[q];
1531
1532 new_quadWeights[INDEX2(q,0,numQuadNodes)] =w;
1533 new_quadNodes[INDEX3(0,q,0,DIM,numQuadNodes)] =HALF*x0;
1534 new_quadNodes[INDEX3(1,q,0,DIM,numQuadNodes)] =HALF*x1;
1535
1536 new_quadWeights[INDEX2(q,1,numQuadNodes)] =w;
1537 new_quadNodes[INDEX3(0,q,1,DIM,numQuadNodes)] =HALF*x0;
1538 new_quadNodes[INDEX3(1,q,1,DIM,numQuadNodes)] =HALF*(x1+1);
1539
1540 new_quadWeights[INDEX2(q,2,numQuadNodes)] =w;
1541 new_quadNodes[INDEX3(0,q,2,DIM,numQuadNodes)] =HALF*(x0+1);
1542 new_quadNodes[INDEX3(1,q,2,DIM,numQuadNodes)] =HALF*x1;
1543
1544 new_quadWeights[INDEX2(q,3,numQuadNodes)] =w;
1545 new_quadNodes[INDEX3(0,q,3,DIM,numQuadNodes)] =HALF*(x0+1);
1546 new_quadNodes[INDEX3(1,q,3,DIM,numQuadNodes)] =HALF*(x1+1);
1547
1548 for (i=0;i<numF;i++) {
1549 df0=dFdv[INDEX3(i,0,q, numF, DIM)]*TWO;
1550 df1=dFdv[INDEX3(i,1,q, numF, DIM)]*TWO;
1551
1552 new_dFdv[INDEX4(i,0,q,0, numF,DIM,numQuadNodes)] = df0;
1553 new_dFdv[INDEX4(i,1,q,0, numF,DIM,numQuadNodes)] = df1;
1554
1555 new_dFdv[INDEX4(i,0,q,1, numF,DIM,numQuadNodes)] = df0;
1556 new_dFdv[INDEX4(i,1,q,1, numF,DIM,numQuadNodes)] = df1;
1557
1558 new_dFdv[INDEX4(i,0,q,2, numF,DIM,numQuadNodes)] = df0;
1559 new_dFdv[INDEX4(i,1,q,2, numF,DIM,numQuadNodes)] = df1;
1560
1561 new_dFdv[INDEX4(i,0,q,3, numF,DIM,numQuadNodes)] = df0;
1562 new_dFdv[INDEX4(i,1,q,3, numF,DIM,numQuadNodes)] = df1;
1563 }
1564
1565 }
1566 } else {
1567 Finley_setError(MEMORY_ERROR,"Quad_MacroRec: unable to create quadrature scheme for macro element.");
1568 return -1;
1569 }
1570 #undef DIM
1571 return numSubElements*numQuadNodes;
1572 }
1573
1574
1575 dim_t Quad_MacroTet(dim_t numSubElements, int numQuadNodes, double* quadNodes, double* quadWeights, dim_t numF, double* dFdv,
1576 dim_t new_len, double* new_quadNodes, double* new_quadWeights, double* new_dFdv )
1577 {
1578 #define DIM 3
1579 dim_t q, i;
1580 register double x0, x1, x2, w, df0, df1, df2;
1581
1582 if (new_len < numSubElements*numQuadNodes) {
1583 Finley_setError(MEMORY_ERROR,"Quad_MacroTet: array for new quadrature scheme is too small");
1584 return -1;
1585 }
1586 if (numSubElements==1) {
1587
1588 for (q=0; q<numQuadNodes; ++q) {
1589
1590 x0=quadNodes[INDEX2(0,q,DIM)];
1591 x1=quadNodes[INDEX2(1,q,DIM)];
1592 x2=quadNodes[INDEX2(2,q,DIM)];
1593 w=quadWeights[q];
1594
1595 new_quadWeights[INDEX2(q,0,numQuadNodes)] =w;
1596 new_quadNodes[INDEX3(0,q,0,DIM,numQuadNodes)] =x0;
1597 new_quadNodes[INDEX3(1,q,0,DIM,numQuadNodes)] =x1;
1598 new_quadNodes[INDEX3(2,q,0,DIM,numQuadNodes)] =x2;
1599
1600 for (i=0;i<numF;i++) {
1601 new_dFdv[INDEX4(i,0,q,0, numF, DIM,numQuadNodes)] = dFdv[INDEX3(i,0,q, numF, DIM)];
1602 new_dFdv[INDEX4(i,1,q,0, numF, DIM,numQuadNodes)] = dFdv[INDEX3(i,1,q, numF, DIM)];
1603 new_dFdv[INDEX4(i,2,q,0, numF, DIM,numQuadNodes)] = dFdv[INDEX3(i,2,q, numF, DIM)];
1604 }
1605 }
1606
1607 } else if (numSubElements==8) {
1608 const double f = 0.125;
1609 for (q=0; q<numQuadNodes; ++q) {
1610
1611 x0=quadNodes[INDEX2(0,q,DIM)];
1612 x1=quadNodes[INDEX2(1,q,DIM)];
1613 x2=quadNodes[INDEX2(2,q,DIM)];
1614 w=f*quadWeights[q];
1615
1616 new_quadWeights[INDEX2(q,0,numQuadNodes)] =w;
1617 new_quadNodes[INDEX3(0,q,0,DIM,numQuadNodes)] =HALF*x0;
1618 new_quadNodes[INDEX3(1,q,0,DIM,numQuadNodes)] =HALF*x1;
1619 new_quadNodes[INDEX3(2,q,0,DIM,numQuadNodes)] =HALF*x2;
1620
1621 new_quadWeights[INDEX2(q,1,numQuadNodes)] =w;
1622 new_quadNodes[INDEX3(0,q,1,DIM,numQuadNodes)] =HALF*(x0+1);
1623 new_quadNodes[INDEX3(1,q,1,DIM,numQuadNodes)] =HALF*x1;
1624 new_quadNodes[INDEX3(2,q,1,DIM,numQuadNodes)] =HALF*x2;
1625
1626 new_quadWeights[INDEX2(q,2,numQuadNodes)] =w;
1627 new_quadNodes[INDEX3(0,q,2,DIM,numQuadNodes)] =HALF*x0;
1628 new_quadNodes[INDEX3(1,q,2,DIM,numQuadNodes)] =HALF*(x1+1);
1629 new_quadNodes[INDEX3(2,q,2,DIM,numQuadNodes)] =HALF*x2;
1630
1631 new_quadWeights[INDEX2(q,3,numQuadNodes)] =w;
1632 new_quadNodes[INDEX3(0,q,3,DIM,numQuadNodes)] =HALF*x0;
1633 new_quadNodes[INDEX3(1,q,3,DIM,numQuadNodes)] =HALF*x1;
1634 new_quadNodes[INDEX3(2,q,3,DIM,numQuadNodes)] =HALF*(x2+1);
1635
1636 new_quadWeights[INDEX2(q,4,numQuadNodes)] =w;
1637 new_quadNodes[INDEX3(0,q,4,DIM,numQuadNodes)] =HALF*(1-x1);
1638 new_quadNodes[INDEX3(1,q,4,DIM,numQuadNodes)] =HALF*(x0+x1);
1639 new_quadNodes[INDEX3(2,q,4,DIM,numQuadNodes)] =HALF*x2;
1640
1641 new_quadWeights[INDEX2(q,5,numQuadNodes)] =w;
1642 new_quadNodes[INDEX3(0,q,5,DIM,numQuadNodes)] =HALF*(1-x0-x2);
1643 new_quadNodes[INDEX3(1,q,5,DIM,numQuadNodes)] =HALF*(1-x1);
1644 new_quadNodes[INDEX3(2,q,5,DIM,numQuadNodes)] =HALF*(x0+x1);
1645
1646 new_quadWeights[INDEX2(q,6,numQuadNodes)] =w;
1647 new_quadNodes[INDEX3(0,q,6,DIM,numQuadNodes)] =HALF*x2;
1648 new_quadNodes[INDEX3(1,q,6,DIM,numQuadNodes)] =HALF*(1-x0-x2);
1649 new_quadNodes[INDEX3(2,q,6,DIM,numQuadNodes)] =HALF*(1-x1);
1650
1651 new_quadWeights[INDEX2(q,7,numQuadNodes)] =w;
1652 new_quadNodes[INDEX3(0,q,7,DIM,numQuadNodes)] =HALF*(x0+x2);
1653 new_quadNodes[INDEX3(1,q,7,DIM,numQuadNodes)] =HALF*x1;
1654 new_quadNodes[INDEX3(2,q,7,DIM,numQuadNodes)] =HALF*(1-x0-x1);
1655
1656 for (i=0;i<numF;i++) {
1657 df0=dFdv[INDEX3(i,0,q, numF, DIM)]*TWO;
1658 df1=dFdv[INDEX3(i,1,q, numF, DIM)]*TWO;
1659 df2=dFdv[INDEX3(i,2,q, numF, DIM)]*TWO;
1660
1661 new_dFdv[INDEX4(i,0,q,0, numF,DIM,numQuadNodes)] = df0;
1662 new_dFdv[INDEX4(i,1,q,0, numF,DIM,numQuadNodes)] = df1;
1663 new_dFdv[INDEX4(i,2,q,0, numF,DIM,numQuadNodes)] = df2;
1664
1665 new_dFdv[INDEX4(i,0,q,1, numF,DIM,numQuadNodes)] = df0;
1666 new_dFdv[INDEX4(i,1,q,1, numF,DIM,numQuadNodes)] = df1;
1667 new_dFdv[INDEX4(i,2,q,1, numF,DIM,numQuadNodes)] = df2;
1668
1669 new_dFdv[INDEX4(i,0,q,2, numF,DIM,numQuadNodes)] = df0;
1670 new_dFdv[INDEX4(i,1,q,2, numF,DIM,numQuadNodes)] = df1;
1671 new_dFdv[INDEX4(i,2,q,2, numF,DIM,numQuadNodes)] = df2;
1672
1673 new_dFdv[INDEX4(i,0,q,3, numF,DIM,numQuadNodes)] = df0;
1674 new_dFdv[INDEX4(i,1,q,3, numF,DIM,numQuadNodes)] = df1;
1675 new_dFdv[INDEX4(i,2,q,3, numF,DIM,numQuadNodes)] = df2;
1676
1677 new_dFdv[INDEX4(i,0,q,4, numF,DIM,numQuadNodes)] = df0-df1;
1678 new_dFdv[INDEX4(i,1,q,4, numF,DIM,numQuadNodes)] = df0;
1679 new_dFdv[INDEX4(i,2,q,4, numF,DIM,numQuadNodes)] = df2;
1680
1681 new_dFdv[INDEX4(i,0,q,5, numF,DIM,numQuadNodes)] = -df2;
1682 new_dFdv[INDEX4(i,1,q,5, numF,DIM,numQuadNodes)] = df0-df2-df1;
1683 new_dFdv[INDEX4(i,2,q,5, numF,DIM,numQuadNodes)] = df0-df2;
1684
1685 new_dFdv[INDEX4(i,0,q,6, numF,DIM,numQuadNodes)] = -df0+df2;
1686 new_dFdv[INDEX4(i,1,q,6, numF,DIM,numQuadNodes)] = -df0;
1687 new_dFdv[INDEX4(i,2,q,6, numF,DIM,numQuadNodes)] = -df1;
1688
1689 new_dFdv[INDEX4(i,0,q,7, numF,DIM,numQuadNodes)] = df2;
1690 new_dFdv[INDEX4(i,1,q,7, numF,DIM,numQuadNodes)] = -df0+df1+df2;
1691 new_dFdv[INDEX4(i,2,q,7, numF,DIM,numQuadNodes)] = -df0+df2;
1692 }
1693
1694 }
1695 } else {
1696 Finley_setError(MEMORY_ERROR,"Quad_MacroTet: unable to create quadrature scheme for macro element.");
1697 return -1;
1698 }
1699 #undef DIM
1700 return numSubElements*numQuadNodes;
1701 }
1702
1703
1704 dim_t Quad_MacroHex(dim_t numSubElements, int numQuadNodes, double* quadNodes, double* quadWeights, dim_t numF, double* dFdv,
1705 dim_t new_len, double* new_quadNodes, double* new_quadWeights , double* new_dFdv)
1706 {
1707
1708 #define DIM 3
1709 dim_t q, i;
1710 register double x0, x1, x2, w, df0, df1, df2;
1711
1712 if (new_len < numSubElements*numQuadNodes) {
1713 Finley_setError(MEMORY_ERROR,"Quad_MacroHex: array for new quadrature scheme is too small");
1714 return -1;
1715 }
1716 if (numSubElements==1) {
1717
1718 for (q=0; q<numQuadNodes; ++q) {
1719
1720 x0=quadNodes[INDEX2(0,q,DIM)];
1721 x1=quadNodes[INDEX2(1,q,DIM)];
1722 x2=quadNodes[INDEX2(2,q,DIM)];
1723 w=quadWeights[q];
1724
1725 new_quadWeights[INDEX2(q,0,numQuadNodes)] =w;
1726 new_quadNodes[INDEX3(0,q,0,DIM,numQuadNodes)] =x0;
1727 new_quadNodes[INDEX3(1,q,0,DIM,numQuadNodes)] =x1;
1728 new_quadNodes[INDEX3(2,q,0,DIM,numQuadNodes)] =x2;
1729
1730 for (i=0;i<numF;i++) {
1731 new_dFdv[INDEX4(i,0,q,0, numF, DIM,numQuadNodes)] = dFdv[INDEX3(i,0,q,numF, DIM)];
1732 new_dFdv[INDEX4(i,1,q,0, numF, DIM,numQuadNodes)] = dFdv[INDEX3(i,1,q,numF, DIM)];
1733 new_dFdv[INDEX4(i,2,q,0, numF, DIM,numQuadNodes)] = dFdv[INDEX3(i,2,q,numF, DIM)];
1734 }
1735 }
1736
1737 } else if (numSubElements==8) {
1738 const double f = 0.125;
1739 for (q=0; q<numQuadNodes; ++q) {
1740
1741 x0=quadNodes[INDEX2(0,q,DIM)];
1742 x1=quadNodes[INDEX2(1,q,DIM)];
1743 x2=quadNodes[INDEX2(2,q,DIM)];
1744 w=f*quadWeights[q];
1745
1746 new_quadWeights[INDEX2(q,0,numQuadNodes)] =w;
1747 new_quadNodes[INDEX3(0,q,0,DIM,numQuadNodes)] =HALF*x0;
1748 new_quadNodes[INDEX3(1,q,0,DIM,numQuadNodes)] =HALF*x1;
1749 new_quadNodes[INDEX3(2,q,0,DIM,numQuadNodes)] =HALF*x2;
1750
1751 new_quadWeights[INDEX2(q,1,numQuadNodes)] =w;
1752 new_quadNodes[INDEX3(0,q,1,DIM,numQuadNodes)] =HALF*(x0+1);
1753 new_quadNodes[INDEX3(1,q,1,DIM,numQuadNodes)] =HALF*x1;
1754 new_quadNodes[INDEX3(2,q,1,DIM,numQuadNodes)] =HALF*x2;
1755
1756 new_quadWeights[INDEX2(q,2,numQuadNodes)] =w;
1757 new_quadNodes[INDEX3(0,q,2,DIM,numQuadNodes)] =HALF*x0;
1758 new_quadNodes[INDEX3(1,q,2,DIM,numQuadNodes)] =HALF*(x1+1);
1759 new_quadNodes[INDEX3(2,q,2,DIM,numQuadNodes)] =HALF*x2;
1760
1761 new_quadWeights[INDEX2(q,3,numQuadNodes)] =w;
1762 new_quadNodes[INDEX3(0,q,3,DIM,numQuadNodes)] =HALF*(x0+1);
1763 new_quadNodes[INDEX3(1,q,3,DIM,numQuadNodes)] =HALF*(x1+1);
1764 new_quadNodes[INDEX3(2,q,3,DIM,numQuadNodes)] =HALF*x2;
1765
1766 new_quadWeights[INDEX2(q,4,numQuadNodes)] =w;
1767 new_quadNodes[INDEX3(0,q,4,DIM,numQuadNodes)] =HALF*x0;
1768 new_quadNodes[INDEX3(1,q,4,DIM,numQuadNodes)] =HALF*x1;
1769 new_quadNodes[INDEX3(2,q,4,DIM,numQuadNodes)] =HALF*(x2+1);
1770
1771 new_quadWeights[INDEX2(q,5,numQuadNodes)] =w;
1772 new_quadNodes[INDEX3(0,q,5,DIM,numQuadNodes)] =HALF*(x0+1);
1773 new_quadNodes[INDEX3(1,q,5,DIM,numQuadNodes)] =HALF*x1;
1774 new_quadNodes[INDEX3(2,q,5,DIM,numQuadNodes)] =HALF*(x2+1);
1775
1776 new_quadWeights[INDEX2(q,6,numQuadNodes)] =w;
1777 new_quadNodes[INDEX3(0,q,6,DIM,numQuadNodes)] =HALF*x0;
1778 new_quadNodes[INDEX3(1,q,6,DIM,numQuadNodes)] =HALF*(x1+1);
1779 new_quadNodes[INDEX3(2,q,6,DIM,numQuadNodes)] =HALF*(x2+1);
1780
1781 new_quadWeights[INDEX2(q,7,numQuadNodes)] =w;
1782 new_quadNodes[INDEX3(0,q,7,DIM,numQuadNodes)] =HALF*(x0+1);
1783 new_quadNodes[INDEX3(1,q,7,DIM,numQuadNodes)] =HALF*(x1+1);
1784 new_quadNodes[INDEX3(2,q,7,DIM,numQuadNodes)] =HALF*(x2+1);
1785
1786 for (i=0;i<numF;i++) {
1787 df0=dFdv[INDEX3(i,0,q, numF, DIM)]*TWO;
1788 df1=dFdv[INDEX3(i,1,q, numF, DIM)]*TWO;
1789 df2=dFdv[INDEX3(i,2,q, numF, DIM)]*TWO;
1790
1791 new_dFdv[INDEX4(i,0,q,0, numF,DIM,numQuadNodes)] = df0;
1792 new_dFdv[INDEX4(i,1,q,0, numF,DIM,numQuadNodes)] = df1;
1793 new_dFdv[INDEX4(i,2,q,0, numF,DIM,numQuadNodes)] = df2;
1794
1795 new_dFdv[INDEX4(i,0,q,1, numF,DIM,numQuadNodes)] = df0;
1796 new_dFdv[INDEX4(i,1,q,1, numF,DIM,numQuadNodes)] = df1;
1797 new_dFdv[INDEX4(i,2,q,1, numF,DIM,numQuadNodes)] = df2;
1798
1799 new_dFdv[INDEX4(i,0,q,2, numF,DIM,numQuadNodes)] = df0;
1800 new_dFdv[INDEX4(i,1,q,2, numF,DIM,numQuadNodes)] = df1;
1801 new_dFdv[INDEX4(i,2,q,2, numF,DIM,numQuadNodes)] = df2;
1802
1803 new_dFdv[INDEX4(i,0,q,3, numF,DIM,numQuadNodes)] = df0;
1804 new_dFdv[INDEX4(i,1,q,3, numF,DIM,numQuadNodes)] = df1;
1805 new_dFdv[INDEX4(i,2,q,3, numF,DIM,numQuadNodes)] = df2;
1806
1807 new_dFdv[INDEX4(i,0,q,4, numF,DIM,numQuadNodes)] = df0;
1808 new_dFdv[INDEX4(i,1,q,4, numF,DIM,numQuadNodes)] = df1;
1809 new_dFdv[INDEX4(i,2,q,4, numF,DIM,numQuadNodes)] = df2;
1810
1811 new_dFdv[INDEX4(i,0,q,5, numF,DIM,numQuadNodes)] = df0;
1812 new_dFdv[INDEX4(i,1,q,5, numF,DIM,numQuadNodes)] = df1;
1813 new_dFdv[INDEX4(i,2,q,5, numF,DIM,numQuadNodes)] = df2;
1814
1815 new_dFdv[INDEX4(i,0,q,6, numF,DIM,numQuadNodes)] = df0;
1816 new_dFdv[INDEX4(i,1,q,6, numF,DIM,numQuadNodes)] = df1;
1817 new_dFdv[INDEX4(i,2,q,6, numF,DIM,numQuadNodes)] = df2;
1818
1819 new_dFdv[INDEX4(i,0,q,7, numF,DIM,numQuadNodes)] = df0;
1820 new_dFdv[INDEX4(i,1,q,7, numF,DIM,numQuadNodes)] = df1;
1821 new_dFdv[INDEX4(i,2,q,7, numF,DIM,numQuadNodes)] = df2;
1822 }
1823
1824 }
1825 } else {
1826 Finley_setError(MEMORY_ERROR,"Quad_MacroHex: unable to create quadrature scheme for macro element.");
1827 return -1;
1828 }
1829 #undef DIM
1830 return numSubElements*numQuadNodes;
1831 }
1832
1833 } // namespace finley
1834

Properties

Name Value
svn:eol-style native
svn:keywords Author Date Id Revision
svn:mergeinfo /branches/lapack2681/finley/src/Quadrature.cpp:2682-2741 /branches/pasowrap/finley/src/Quadrature.cpp:3661-3674 /branches/py3_attempt2/finley/src/Quadrature.cpp:3871-3891 /branches/restext/finley/src/Quadrature.cpp:2610-2624 /branches/ripleygmg_from_3668/finley/src/Quadrature.cpp:3669-3791 /branches/stage3.0/finley/src/Quadrature.cpp:2569-2590 /branches/symbolic_from_3470/finley/src/Quadrature.cpp:3471-3974 /release/3.0/finley/src/Quadrature.cpp:2591-2601 /trunk/finley/src/Quadrature.cpp:4257-4344

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