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

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Revision 2748 - (show annotations)
Tue Nov 17 07:32:59 2009 UTC (9 years, 9 months ago) by gross
File MIME type: text/plain
File size: 68021 byte(s)
Macro elements are implemented now. VTK writer for macro elements still needs testing.
1
2 /*******************************************************
3 *
4 * Copyright (c) 2003-2009 by University of Queensland
5 * Earth Systems Science Computational Center (ESSCC)
6 * http://www.uq.edu.au/esscc
7 *
8 * Primary Business: Queensland, Australia
9 * Licensed under the Open Software License version 3.0
10 * http://www.opensource.org/licenses/osl-3.0.php
11 *
12 *******************************************************/
13
14
15 /**************************************************************/
16
17 /* Finley: quadrature schemes */
18
19 /**************************************************************/
20
21 #include "Quadrature.h"
22
23
24 #define QUADNODES(_K_,_I_) quadNodes[INDEX2(_K_,_I_,DIM)]
25 #define QUADWEIGHTS(_I_) quadWeights[_I_]
26
27 /**************************************************************/
28
29 Finley_QuadInfo Finley_QuadInfoList[]={
30 {PointQuad, "Point", 0, 1, Finley_Quad_getNodesPoint, Finley_Quad_getNumNodesPoint, Finley_Quad_MacroPoint} ,
31 {LineQuad, "Line", 1, 2, Finley_Quad_getNodesLine, Finley_Quad_getNumNodesLine, Finley_Quad_MacroLine} ,
32 {TriQuad, "Tri", 2, 3, Finley_Quad_getNodesTri, Finley_Quad_getNumNodesTri, Finley_Quad_MacroTri},
33 {RecQuad, "Rec", 2, 4, Finley_Quad_getNodesRec, Finley_Quad_getNumNodesRec, Finley_Quad_MacroRec},
34 {TetQuad, "Tet", 3, 4, Finley_Quad_getNodesTet, Finley_Quad_getNumNodesTet, Finley_Quad_MacroTet},
35 {HexQuad, "Hex", 3, 8, Finley_Quad_getNodesHex, Finley_Quad_getNumNodesHex, Finley_Quad_MacroHex},
36 {NoQuad, "NoType", 0, 1, Finley_Quad_getNodesPoint, Finley_Quad_getNumNodesPoint, Finley_Quad_MacroPoint}
37 };
38
39 Finley_QuadInfo* Finley_QuadInfo_getInfo(Finley_QuadTypeId id)
40 {
41 int ptr=0;
42 Finley_QuadInfo* out=NULL;
43 while (Finley_QuadInfoList[ptr].TypeId!=NoQuad && out==NULL) {
44 if (Finley_QuadInfoList[ptr].TypeId==id) out=&(Finley_QuadInfoList[ptr]);
45 ptr++;
46 }
47 if (out==NULL) {
48 Finley_setError(VALUE_ERROR,"Finley_QuadInfo_getInfo: canot find requested quadrature scheme.");
49 }
50 return out;
51 }
52
53 /**************************************************************/
54
55 /* get a quadrature scheme with numQuadNodes quadrature nodes for the tri */
56 /* as a queezed scheme on a quad [0,1]^2 */
57
58 void Finley_Quad_getNodesTri(int numQuadNodes,double* quadNodes,double* quadWeights) {
59 int i;
60 double Q1,Q2,a,b,c,d,e,f,g,u,v,w;
61 #define DIM 2
62
63 /* the easy cases: */
64
65 if (numQuadNodes==1) {
66 QUADNODES(0,0)=1./3.;
67 QUADNODES(1,0)=1./3.;
68 QUADWEIGHTS(0)=1./2.;
69 } else if (numQuadNodes==3){
70 QUADNODES(0,0)=1./2.;
71 QUADNODES(1,0)=0.;
72 QUADWEIGHTS(0)=1./6.;
73 QUADNODES(0,1)=0.;
74 QUADNODES(1,1)=1./2.;
75 QUADWEIGHTS(1)=1./6.;
76 QUADNODES(0,2)=1./2.;
77 QUADNODES(1,2)=1./2.;
78 QUADWEIGHTS(2)=1./6.;
79 } else if (numQuadNodes==4){
80 QUADNODES(0,0)=1./3.;
81 QUADNODES(1,0)=1./3.;
82 QUADWEIGHTS(0)=-27./96.;
83 QUADNODES(0,1)=0.2;
84 QUADNODES(1,1)=0.2;
85 QUADWEIGHTS(1)=25./96.;
86 QUADNODES(0,2)=0.6;
87 QUADNODES(1,2)=0.2;
88 QUADWEIGHTS(2)=25./96.;
89 QUADNODES(0,3)=0.2;
90 QUADNODES(1,3)=0.6;
91 QUADWEIGHTS(3)=25./96.;
92 } else if (numQuadNodes==6){
93 QUADWEIGHTS(0) = 0.109951743655322/2.;
94 QUADWEIGHTS(1) = 0.109951743655322/2.;
95 QUADWEIGHTS(2) = 0.109951743655322/2.;
96 QUADWEIGHTS(3) = 0.223381589678011/2.;
97 QUADWEIGHTS(4) = 0.223381589678011/2.;
98 QUADWEIGHTS(5) = 0.223381589678011/2.;
99
100 QUADNODES(0,0) = 0.816847572980459;
101 QUADNODES(0,1) = 0.091576213509771;
102 QUADNODES(0,2) = 0.091576213509771;
103 QUADNODES(0,3) = 0.108103018168070;
104 QUADNODES(0,4) = 0.445948490915965;
105 QUADNODES(0,5) = 0.445948490915965;
106
107 QUADNODES(1,0) = 0.091576213509771;
108 QUADNODES(1,1) = 0.816847572980459;
109 QUADNODES(1,2) = 0.091576213509771;
110 QUADNODES(1,3) = 0.445948490915965;
111 QUADNODES(1,4) = 0.108103018168070;
112 QUADNODES(1,5) = 0.445948490915965;
113
114 } else if (numQuadNodes==7){
115 QUADNODES(0,0) = 0.33333333333333333;
116 QUADNODES(0,1) = 0.7974269853530872;
117 QUADNODES(0,2) = 0.10128650732345633;
118 QUADNODES(0,3) = 0.10128650732345633;
119 QUADNODES(0,4) = 0.059715871789769809;
120 QUADNODES(0,5) = 0.47014206410511505;
121 QUADNODES(0,6) = 0.47014206410511505;
122
123 QUADNODES(1,0) = 0.33333333333333333;
124 QUADNODES(1,1) = 0.10128650732345633;
125 QUADNODES(1,2) = 0.7974269853530872;
126 QUADNODES(1,3) = 0.10128650732345633;
127 QUADNODES(1,4) = 0.47014206410511505;
128 QUADNODES(1,5) = 0.059715871789769809;
129 QUADNODES(1,6) = 0.47014206410511505;
130
131 QUADWEIGHTS(0) = 0.225/2.;
132 QUADWEIGHTS(1) = 0.12593918054482717/2.;
133 QUADWEIGHTS(2) = 0.12593918054482717/2.;
134 QUADWEIGHTS(3) = 0.12593918054482717/2.;
135 QUADWEIGHTS(4) = 0.13239415278850616/2.;
136 QUADWEIGHTS(5) = 0.13239415278850616/2.;
137 QUADWEIGHTS(6) = 0.13239415278850616/2.;
138
139 } else if (numQuadNodes==12){
140 a = 0.873821971016996;
141 b = 0.063089014491502;
142 c = 0.501426509658179;
143 d = 0.249286745170910;
144 e = 0.636502499121399;
145 f = 0.310352451033785;
146 g = 0.053145049844816;
147
148 u = 0.050844906370207/2.;
149 v = 0.116786275726379/2.;
150 w = 0.082851075618374/2.;
151
152 QUADNODES(0,0) = a;
153 QUADNODES(0,1) = b;
154 QUADNODES(0,2) = b;
155 QUADNODES(0,3) = c;
156 QUADNODES(0,4) = d;
157 QUADNODES(0,5) = d;
158 QUADNODES(0,6) = e;
159 QUADNODES(0,7) = e;
160 QUADNODES(0,8) = f;
161 QUADNODES(0,9) = f;
162 QUADNODES(0,10) = g;
163 QUADNODES(0,11) = g;
164
165 QUADNODES(1,0) = b;
166 QUADNODES(1,1) = a;
167 QUADNODES(1,2) = b;
168 QUADNODES(1,3) = d;
169 QUADNODES(1,4) = c;
170 QUADNODES(1,5) = d;
171 QUADNODES(1,6) = f;
172 QUADNODES(1,7) = g;
173 QUADNODES(1,8) = e;
174 QUADNODES(1,9) = g;
175 QUADNODES(1,10) = e;
176 QUADNODES(1,11) = f;
177
178 QUADWEIGHTS(0)= u;
179 QUADWEIGHTS(1)= u;
180 QUADWEIGHTS(2)= u;
181 QUADWEIGHTS(3)= v;
182 QUADWEIGHTS(4)= v;
183 QUADWEIGHTS(5)= v;
184 QUADWEIGHTS(6)= w;
185 QUADWEIGHTS(7)= w;
186 QUADWEIGHTS(8)= w;
187 QUADWEIGHTS(9)= w;
188 QUADWEIGHTS(10)= w;
189 QUADWEIGHTS(11)= w;
190
191 } else if (numQuadNodes==13){
192 QUADWEIGHTS(0) =-0.149570044467670/2.;
193 QUADWEIGHTS(1) = 0.175615257433204/2.;
194 QUADWEIGHTS(2) = 0.175615257433204/2.;
195 QUADWEIGHTS(3) = 0.175615257433204/2.;
196 QUADWEIGHTS(4) = 0.053347235608839/2.;
197 QUADWEIGHTS(5) = 0.053347235608839/2.;
198 QUADWEIGHTS(6) = 0.053347235608839/2.;
199 QUADWEIGHTS(7) = 0.077113760890257/2.;
200 QUADWEIGHTS(8) = 0.077113760890257/2.;
201 QUADWEIGHTS(9) = 0.077113760890257/2.;
202 QUADWEIGHTS(10) = 0.077113760890257/2.;
203 QUADWEIGHTS(11) = 0.077113760890257/2.;
204 QUADWEIGHTS(12) = 0.077113760890257/2.;
205
206 QUADNODES(0,0) = 0.3333333333333333;
207 QUADNODES(0,1) = 0.479308067841923;
208 QUADNODES(0,2) = 0.260345966079038;
209 QUADNODES(0,3) = 0.260345966079038;
210 QUADNODES(0,4) = 0.869739794195568;
211 QUADNODES(0,5) = 0.065130102902216;
212 QUADNODES(0,6) = 0.065130102902216;
213 QUADNODES(0,7) = 0.638444188569809;
214 QUADNODES(0,8) = 0.638444188569809;
215 QUADNODES(0,9) = 0.048690315425316;
216 QUADNODES(0,10) = 0.048690315425316;
217 QUADNODES(0,11) = 0.312865496004875;
218 QUADNODES(0,12) = 0.312865496004875;
219
220 QUADNODES(1,0) = 0.3333333333333333;
221 QUADNODES(1,1) = 0.260345966079038;
222 QUADNODES(1,2) = 0.479308067841923;
223 QUADNODES(1,3) = 0.260345966079038;
224 QUADNODES(1,4) = 0.065130102902216;
225 QUADNODES(1,5) = 0.869739794195568;
226 QUADNODES(1,6) = 0.065130102902216;
227 QUADNODES(1,7) = 0.048690315425316;
228 QUADNODES(1,8) = 0.312865496004875;
229 QUADNODES(1,9) = 0.638444188569809;
230 QUADNODES(1,10) = 0.312865496004875;
231 QUADNODES(1,11) = 0.638444188569809;
232 QUADNODES(1,12) = 0.048690315425316;
233
234 } else if (numQuadNodes==16){
235 QUADWEIGHTS(0) = 0.07215780;
236 QUADWEIGHTS(1) = 0.04754582;
237 QUADWEIGHTS(2) = 0.04754582;
238 QUADWEIGHTS(3) = 0.04754582;
239 QUADWEIGHTS(4) = 0.01622925;
240 QUADWEIGHTS(5) = 0.01622925;
241 QUADWEIGHTS(6) = 0.01622925;
242 QUADWEIGHTS(7) = 0.05160869;
243 QUADWEIGHTS(8) = 0.05160869;
244 QUADWEIGHTS(9) = 0.05160869;
245 QUADWEIGHTS(10) = 0.01361516;
246 QUADWEIGHTS(11) = 0.01361516;
247 QUADWEIGHTS(12) = 0.01361516;
248 QUADWEIGHTS(13) = 0.01361516;
249 QUADWEIGHTS(14) = 0.01361516;
250 QUADWEIGHTS(15) = 0.01361516;
251
252 QUADNODES(0,0) = 0.3333333;
253 QUADNODES(0,1) = 0.08141482;
254 QUADNODES(0,2) = 0.4592926;
255 QUADNODES(0,3) = 0.4592926;
256 QUADNODES(0,4) = 0.8989055;
257 QUADNODES(0,5) = 0.05054723;
258 QUADNODES(0,6) = 0.05054723;
259 QUADNODES(0,7) = 0.6588614;
260 QUADNODES(0,8) = 0.1705693;
261 QUADNODES(0,9) = 0.1705693;
262 QUADNODES(0,10) = 0.008394777;
263 QUADNODES(0,11) = 0.008394777;
264 QUADNODES(0,12) = 0.7284924;
265 QUADNODES(0,13) = 0.7284924;
266 QUADNODES(0,14) = 0.2631128;
267 QUADNODES(0,15) = 0.2631128;
268
269 QUADNODES(1,0) = 0.3333333;
270 QUADNODES(1,1) = 0.4592926;
271 QUADNODES(1,2) = 0.08141482;
272 QUADNODES(1,3) = 0.4592926;
273 QUADNODES(1,4) = 0.05054723;
274 QUADNODES(1,5) = 0.8989055;
275 QUADNODES(1,6) = 0.05054723;
276 QUADNODES(1,7) = 0.1705693;
277 QUADNODES(1,8) = 0.6588614;
278 QUADNODES(1,9) = 0.1705693;
279 QUADNODES(1,10) = 0.7284924;
280 QUADNODES(1,11) = 0.2631128;
281 QUADNODES(1,12) = 0.008394777;
282 QUADNODES(1,13) = 0.2631128;
283 QUADNODES(1,14) = 0.008394777;
284 QUADNODES(1,15) = 0.7284924;
285
286 } else if (numQuadNodes==19){
287 QUADWEIGHTS(0) = 0.04856790;
288 QUADWEIGHTS(1) = 0.01566735;
289 QUADWEIGHTS(2) = 0.01566735;
290 QUADWEIGHTS(3) = 0.01566735;
291 QUADWEIGHTS(4) = 0.03891377;
292 QUADWEIGHTS(5) = 0.03891377;
293 QUADWEIGHTS(6) = 0.03891377;
294 QUADWEIGHTS(7) = 0.03982387;
295 QUADWEIGHTS(8) = 0.03982387;
296 QUADWEIGHTS(9) = 0.03982387;
297 QUADWEIGHTS(10) = 0.01278884;
298 QUADWEIGHTS(11) = 0.01278884;
299 QUADWEIGHTS(12) = 0.01278884;
300 QUADWEIGHTS(13) = 0.02164177;
301 QUADWEIGHTS(14) = 0.02164177;
302 QUADWEIGHTS(15) = 0.02164177;
303 QUADWEIGHTS(16) = 0.02164177;
304 QUADWEIGHTS(17) = 0.02164177;
305 QUADWEIGHTS(18) = 0.02164177;
306
307 QUADNODES(0,0) = 0.3333333;
308 QUADNODES(0,1) = 0.02063496;
309 QUADNODES(0,2) = 0.4896825;
310 QUADNODES(0,3) = 0.4896825;
311 QUADNODES(0,4) = 0.1258208;
312 QUADNODES(0,5) = 0.4370896;
313 QUADNODES(0,6) = 0.4370896;
314 QUADNODES(0,7) = 0.6235929;
315 QUADNODES(0,8) = 0.1882035;
316 QUADNODES(0,9) = 0.1882035;
317 QUADNODES(0,10) = 0.9105410;
318 QUADNODES(0,11) = 0.04472951;
319 QUADNODES(0,12) = 0.04472951;
320 QUADNODES(0,13) = 0.03683841;
321 QUADNODES(0,14) = 0.03683841;
322 QUADNODES(0,15) = 0.7411986;
323 QUADNODES(0,16) = 0.7411986;
324 QUADNODES(0,17) = 0.2219630;
325 QUADNODES(0,18) = 0.2219630;
326
327 QUADNODES(1,0) = 0.3333333;
328 QUADNODES(1,1) = 0.4896825;
329 QUADNODES(1,2) = 0.02063496;
330 QUADNODES(1,3) = 0.4896825;
331 QUADNODES(1,4) = 0.4370896;
332 QUADNODES(1,5) = 0.1258208;
333 QUADNODES(1,6) = 0.4370896;
334 QUADNODES(1,7) = 0.1882035;
335 QUADNODES(1,8) = 0.6235929;
336 QUADNODES(1,9) = 0.1882035;
337 QUADNODES(1,10) = 0.04472951;
338 QUADNODES(1,11) = 0.9105410;
339 QUADNODES(1,12) = 0.04472951;
340 QUADNODES(1,13) = 0.7411986;
341 QUADNODES(1,14) = 0.2219630;
342 QUADNODES(1,15) = 0.03683841;
343 QUADNODES(1,16) = 0.2219630;
344 QUADNODES(1,17) = 0.03683841;
345 QUADNODES(1,18) = 0.7411986;
346 } else {
347
348 /* get scheme on [0.1]^2 */
349 Finley_Quad_getNodesRec(numQuadNodes,quadNodes,quadWeights);
350 if (! Finley_noError()) return;
351
352 /* squeeze it: */
353
354 for (i=0;i<numQuadNodes;i++) {
355 Q1=QUADNODES(0,i);
356 Q2=QUADNODES(1,i);
357 QUADWEIGHTS(i)=QUADWEIGHTS(i)*(1.-(1./2.)*(Q1+Q2));
358 QUADNODES(0,i)=Q1*(1.-(1./2.)*Q2);
359 QUADNODES(1,i)=Q2*(1.-(1./2.)*Q1);
360 }
361 }
362 #undef DIM
363
364
365 }
366
367 /**************************************************************/
368
369 /* get a quadrature scheme with numQuadNodes quadrature nodes for the tet */
370 /* as a queezed scheme on a hex [0,1]^3 */
371
372 void Finley_Quad_getNodesTet(int numQuadNodes,double* quadNodes,double* quadWeights) {
373 int i;
374 double Q1,Q2,Q3,JA11,JA12,JA13,JA21,JA22,JA23,JA31,JA32,JA33,DET;
375 double a,b,c,d,e,f,g,h;
376 double alpha=0.58541019662496852;
377 double beta =0.1381966011250105;
378 #define DIM 3
379
380 /* the easy cases: */
381 if (numQuadNodes==1) {
382 QUADNODES(0,0)=0.25;
383 QUADNODES(1,0)=0.25;
384 QUADNODES(2,0)=0.25;
385 QUADWEIGHTS(0)=1./6.;
386 } else if (numQuadNodes==4){
387 QUADNODES(0,0)=beta;
388 QUADNODES(1,0)=beta;
389 QUADNODES(2,0)=beta;
390 QUADWEIGHTS(0)=1./24.;
391 QUADNODES(0,1)=alpha;
392 QUADNODES(1,1)=beta;
393 QUADNODES(2,1)=beta;
394 QUADWEIGHTS(1)=1./24.;
395 QUADNODES(0,2)=beta;
396 QUADNODES(1,2)=alpha;
397 QUADNODES(2,2)=beta;
398 QUADWEIGHTS(2)=1./24.;
399 QUADNODES(0,3)=beta;
400 QUADNODES(1,3)=beta;
401 QUADNODES(2,3)=alpha;
402 QUADWEIGHTS(3)=1./24.;
403 } else if (numQuadNodes==5){
404 QUADNODES(0,0)=1./4.;
405 QUADNODES(1,0)=1./4.;
406 QUADNODES(2,0)=1./4.;
407 QUADWEIGHTS(0)=-2./15.;
408 QUADNODES(0,1)=1./6.;
409 QUADNODES(1,1)=1./6.;
410 QUADNODES(2,1)=1./6.;
411 QUADWEIGHTS(1)=3./40.;
412 QUADNODES(0,2)=1./2.;
413 QUADNODES(1,2)=1./6.;
414 QUADNODES(2,2)=1./6.;
415 QUADWEIGHTS(2)=3./40.;
416 QUADNODES(0,3)=1./6.;
417 QUADNODES(1,3)=1./2.;
418 QUADNODES(2,3)=1./6.;
419 QUADWEIGHTS(3)=3./40.;
420 QUADNODES(0,4)=1./6.;
421 QUADNODES(1,4)=1./6.;
422 QUADNODES(2,4)=1./2.;
423 QUADWEIGHTS(4)=3./40.;
424
425 } else if (numQuadNodes==11){
426
427 a = 0.25;
428 b = 11.0/14.0;
429 c = 1.0/14.0;
430 d = 0.25 * (1.0 + sqrt ( 5.0 / 14.0 ) );
431 e = 0.25 * (1.0 - sqrt ( 5.0 / 14.0 ) );
432 f = -74.0 / 5625.0;
433 g = 343.0 / 45000.0;
434 h = 56.0 / 2250.0;
435
436 QUADWEIGHTS(401-401) = f;
437 QUADWEIGHTS(402-401) = g;
438 QUADWEIGHTS(403-401) = g;
439 QUADWEIGHTS(404-401) = g;
440 QUADWEIGHTS(405-401) = g;
441 QUADWEIGHTS(406-401) = h;
442 QUADWEIGHTS(407-401) = h;
443 QUADWEIGHTS(408-401) = h;
444 QUADWEIGHTS(409-401) = h;
445 QUADWEIGHTS(410-401) = h;
446 QUADWEIGHTS(411-401) = h;
447
448 QUADNODES(0,401-401) = a;
449 QUADNODES(0,402-401) = b;
450 QUADNODES(0,403-401) = c;
451 QUADNODES(0,404-401) = c;
452 QUADNODES(0,405-401) = c;
453 QUADNODES(0,406-401) = d;
454 QUADNODES(0,407-401) = d;
455 QUADNODES(0,408-401) = d;
456 QUADNODES(0,409-401) = e;
457 QUADNODES(0,410-401) = e;
458 QUADNODES(0,411-401) = e;
459
460 QUADNODES(1,401-401) = a;
461 QUADNODES(1,402-401) = c;
462 QUADNODES(1,403-401) = b;
463 QUADNODES(1,404-401) = c;
464 QUADNODES(1,405-401) = c;
465 QUADNODES(1,406-401) = d;
466 QUADNODES(1,407-401) = e;
467 QUADNODES(1,408-401) = e;
468 QUADNODES(1,409-401) = d;
469 QUADNODES(1,410-401) = d;
470 QUADNODES(1,411-401) = e;
471
472 QUADNODES(2,401-401) = a;
473 QUADNODES(2,402-401) = c;
474 QUADNODES(2,403-401) = c;
475 QUADNODES(2,404-401) = b;
476 QUADNODES(2,405-401) = c;
477 QUADNODES(2,406-401) = e;
478 QUADNODES(2,407-401) = d;
479 QUADNODES(2,408-401) = e;
480 QUADNODES(2,409-401) = d;
481 QUADNODES(2,410-401) = e;
482 QUADNODES(2,411-401) = d;
483
484 } else if (numQuadNodes==15){
485 QUADWEIGHTS(412-412) = 0.019753086419753086;
486 QUADWEIGHTS(413-412) = 0.01198951396316977;
487 QUADWEIGHTS(414-412) = 0.01198951396316977;
488 QUADWEIGHTS(415-412) = 0.01198951396316977;
489 QUADWEIGHTS(416-412) = 0.01198951396316977;
490 QUADWEIGHTS(417-412) = 0.011511367871045397;
491 QUADWEIGHTS(418-412) = 0.011511367871045397;
492 QUADWEIGHTS(419-412) = 0.011511367871045397;
493 QUADWEIGHTS(420-412) = 0.011511367871045397;
494 QUADWEIGHTS(421-412) = 0.0088183421516754845;
495 QUADWEIGHTS(422-412) = 0.0088183421516754845;
496 QUADWEIGHTS(423-412) = 0.0088183421516754845;
497 QUADWEIGHTS(424-412) = 0.0088183421516754845;
498 QUADWEIGHTS(425-412) = 0.0088183421516754845;
499 QUADWEIGHTS(426-412) = 0.0088183421516754845;
500
501 QUADNODES(0,412-412) = 0.2500000;
502 QUADNODES(0,413-412) = 0.091971078052723032;
503 QUADNODES(0,414-412) = 0.72408676584183096;
504 QUADNODES(0,415-412) = 0.091971078052723032;
505 QUADNODES(0,416-412) = 0.091971078052723032;
506 QUADNODES(0,417-412) = 0.31979362782962989;
507 QUADNODES(0,418-412) = 0.040619116511110234;
508 QUADNODES(0,419-412) = 0.31979362782962989;
509 QUADNODES(0,420-412) = 0.31979362782962989;
510 QUADNODES(0,421-412) = 0.056350832689629149;
511 QUADNODES(0,422-412) = 0.056350832689629149;
512 QUADNODES(0,423-412) = 0.056350832689629149;
513 QUADNODES(0,424-412) = 0.4436491673103708;
514 QUADNODES(0,425-412) = 0.4436491673103708;
515 QUADNODES(0,426-412) = 0.4436491673103708;
516
517 QUADNODES(1,412-412) = 0.2500000;
518 QUADNODES(1,413-412) = 0.091971078052723032;
519 QUADNODES(1,414-412) = 0.091971078052723032;
520 QUADNODES(1,415-412) = 0.72408676584183096;
521 QUADNODES(1,416-412) = 0.091971078052723032;
522 QUADNODES(1,417-412) = 0.31979362782962989;
523 QUADNODES(1,418-412) = 0.31979362782962989;
524 QUADNODES(1,419-412) = 0.040619116511110234;
525 QUADNODES(1,420-412) = 0.31979362782962989;
526 QUADNODES(1,421-412) = 0.056350832689629149;
527 QUADNODES(1,422-412) = 0.4436491673103708;
528 QUADNODES(1,423-412) = 0.4436491673103708;
529 QUADNODES(1,424-412) = 0.056350832689629149;
530 QUADNODES(1,425-412) = 0.056350832689629149;
531 QUADNODES(1,426-412) = 0.4436491673103708;
532
533 QUADNODES(2,412-412) = 0.2500000;
534 QUADNODES(2,413-412) = 0.091971078052723032;
535 QUADNODES(2,414-412) = 0.091971078052723032;
536 QUADNODES(2,415-412) = 0.091971078052723032;
537 QUADNODES(2,416-412) = 0.72408676584183096;
538 QUADNODES(2,417-412) = 0.31979362782962989;
539 QUADNODES(2,418-412) = 0.31979362782962989;
540 QUADNODES(2,419-412) = 0.31979362782962989;
541 QUADNODES(2,420-412) = 0.040619116511110234;
542 QUADNODES(2,421-412) = 0.4436491673103708;
543 QUADNODES(2,422-412) = 0.056350832689629149;
544 QUADNODES(2,423-412) = 0.4436491673103708;
545 QUADNODES(2,424-412) = 0.056350832689629149;
546 QUADNODES(2,425-412) = 0.4436491673103708;
547 QUADNODES(2,426-412) = 0.056350832689629149;
548
549 } else if (numQuadNodes==24){
550 QUADWEIGHTS(427-427) = 0.006653792;
551 QUADWEIGHTS(428-427) = 0.006653792;
552 QUADWEIGHTS(429-427) = 0.006653792;
553 QUADWEIGHTS(430-427) = 0.006653792;
554 QUADWEIGHTS(431-427) = 0.001679535;
555 QUADWEIGHTS(432-427) = 0.001679535;
556 QUADWEIGHTS(433-427) = 0.001679535;
557 QUADWEIGHTS(434-427) = 0.001679535;
558 QUADWEIGHTS(435-427) = 0.009226197;
559 QUADWEIGHTS(436-427) = 0.009226197;
560 QUADWEIGHTS(437-427) = 0.009226197;
561 QUADWEIGHTS(438-427) = 0.009226197;
562 QUADWEIGHTS(439-427) = 0.008035714;
563 QUADWEIGHTS(440-427) = 0.008035714;
564 QUADWEIGHTS(441-427) = 0.008035714;
565 QUADWEIGHTS(442-427) = 0.008035714;
566 QUADWEIGHTS(443-427) = 0.008035714;
567 QUADWEIGHTS(444-427) = 0.008035714;
568 QUADWEIGHTS(445-427) = 0.008035714;
569 QUADWEIGHTS(446-427) = 0.008035714;
570 QUADWEIGHTS(447-427) = 0.008035714;
571 QUADWEIGHTS(448-427) = 0.008035714;
572 QUADWEIGHTS(449-427) = 0.008035714;
573 QUADWEIGHTS(450-427) = 0.008035714;
574
575 QUADNODES(0,427-427) = 0.3561914;
576 QUADNODES(0,428-427) = 0.2146029;
577 QUADNODES(0,429-427) = 0.2146029;
578 QUADNODES(0,430-427) = 0.2146029;
579 QUADNODES(0,431-427) = 0.8779781;
580 QUADNODES(0,432-427) = 0.04067396;
581 QUADNODES(0,433-427) = 0.04067396;
582 QUADNODES(0,434-427) = 0.04067396;
583 QUADNODES(0,435-427) = 0.03298633;
584 QUADNODES(0,436-427) = 0.3223379;
585 QUADNODES(0,437-427) = 0.3223379;
586 QUADNODES(0,438-427) = 0.3223379;
587 QUADNODES(0,439-427) = 0.6030057;
588 QUADNODES(0,440-427) = 0.6030057;
589 QUADNODES(0,441-427) = 0.6030057;
590 QUADNODES(0,442-427) = 0.2696723;
591 QUADNODES(0,443-427) = 0.2696723;
592 QUADNODES(0,444-427) = 0.2696723;
593 QUADNODES(0,445-427) = 0.06366100;
594 QUADNODES(0,446-427) = 0.06366100;
595 QUADNODES(0,447-427) = 0.06366100;
596 QUADNODES(0,448-427) = 0.06366100;
597 QUADNODES(0,449-427) = 0.06366100;
598 QUADNODES(0,450-427) = 0.06366100;
599
600 QUADNODES(1,427-427) = 0.2146029;
601 QUADNODES(1,428-427) = 0.3561914;
602 QUADNODES(1,429-427) = 0.2146029;
603 QUADNODES(1,430-427) = 0.2146029;
604 QUADNODES(1,431-427) = 0.04067396;
605 QUADNODES(1,432-427) = 0.8779781;
606 QUADNODES(1,433-427) = 0.04067396;
607 QUADNODES(1,434-427) = 0.04067396;
608 QUADNODES(1,435-427) = 0.3223379;
609 QUADNODES(1,436-427) = 0.03298633;
610 QUADNODES(1,437-427) = 0.3223379;
611 QUADNODES(1,438-427) = 0.3223379;
612 QUADNODES(1,439-427) = 0.2696723;
613 QUADNODES(1,440-427) = 0.06366100;
614 QUADNODES(1,441-427) = 0.06366100;
615 QUADNODES(1,442-427) = 0.6030057;
616 QUADNODES(1,443-427) = 0.06366100;
617 QUADNODES(1,444-427) = 0.06366100;
618 QUADNODES(1,445-427) = 0.6030057;
619 QUADNODES(1,446-427) = 0.6030057;
620 QUADNODES(1,447-427) = 0.2696723;
621 QUADNODES(1,448-427) = 0.2696723;
622 QUADNODES(1,449-427) = 0.06366100;
623 QUADNODES(1,450-427) = 0.06366100;
624
625 QUADNODES(2,427-427) = 0.2146029;
626 QUADNODES(2,428-427) = 0.2146029;
627 QUADNODES(2,429-427) = 0.3561914;
628 QUADNODES(2,430-427) = 0.2146029;
629 QUADNODES(2,431-427) = 0.04067396;
630 QUADNODES(2,432-427) = 0.04067396;
631 QUADNODES(2,433-427) = 0.8779781;
632 QUADNODES(2,434-427) = 0.04067396;
633 QUADNODES(2,435-427) = 0.3223379;
634 QUADNODES(2,436-427) = 0.3223379;
635 QUADNODES(2,437-427) = 0.03298633;
636 QUADNODES(2,438-427) = 0.3223379;
637 QUADNODES(2,439-427) = 0.06366100;
638 QUADNODES(2,440-427) = 0.2696723;
639 QUADNODES(2,441-427) = 0.06366100;
640 QUADNODES(2,442-427) = 0.06366100;
641 QUADNODES(2,443-427) = 0.6030057;
642 QUADNODES(2,444-427) = 0.06366100;
643 QUADNODES(2,445-427) = 0.2696723;
644 QUADNODES(2,446-427) = 0.06366100;
645 QUADNODES(2,447-427) = 0.6030057;
646 QUADNODES(2,448-427) = 0.06366100;
647 QUADNODES(2,449-427) = 0.6030057;
648 QUADNODES(2,450-427) = 0.2696723;
649
650 } else if (numQuadNodes==31){
651 QUADWEIGHTS(451-451) = 0.01826422;
652 QUADWEIGHTS(452-451) = 0.01059994;
653 QUADWEIGHTS(453-451) = 0.01059994;
654 QUADWEIGHTS(454-451) = 0.01059994;
655 QUADWEIGHTS(455-451) = 0.01059994;
656 QUADWEIGHTS(456-451) =-0.06251774;
657 QUADWEIGHTS(457-451) =-0.06251774;
658 QUADWEIGHTS(458-451) =-0.06251774;
659 QUADWEIGHTS(459-451) =-0.06251774;
660 QUADWEIGHTS(460-451) = 0.004891425;
661 QUADWEIGHTS(461-451) = 0.004891425;
662 QUADWEIGHTS(462-451) = 0.004891425;
663 QUADWEIGHTS(463-451) = 0.004891425;
664 QUADWEIGHTS(464-451) = 0.0009700176;
665 QUADWEIGHTS(465-451) = 0.0009700176;
666 QUADWEIGHTS(466-451) = 0.0009700176;
667 QUADWEIGHTS(467-451) = 0.0009700176;
668 QUADWEIGHTS(468-451) = 0.0009700176;
669 QUADWEIGHTS(469-451) = 0.0009700176;
670 QUADWEIGHTS(470-451) = 0.02755732;
671 QUADWEIGHTS(471-451) = 0.02755732;
672 QUADWEIGHTS(472-451) = 0.02755732;
673 QUADWEIGHTS(473-451) = 0.02755732;
674 QUADWEIGHTS(474-451) = 0.02755732;
675 QUADWEIGHTS(475-451) = 0.02755732;
676 QUADWEIGHTS(476-451) = 0.02755732;
677 QUADWEIGHTS(477-451) = 0.02755732;
678 QUADWEIGHTS(478-451) = 0.02755732;
679 QUADWEIGHTS(479-451) = 0.02755732;
680 QUADWEIGHTS(480-451) = 0.02755732;
681 QUADWEIGHTS(481-451) = 0.02755732;
682
683 QUADNODES(0,451-451) = 0.2500000;
684 QUADNODES(0,452-451) = 0.7653604;
685 QUADNODES(0,453-451) = 0.07821319;
686 QUADNODES(0,454-451) = 0.07821319;
687 QUADNODES(0,455-451) = 0.07821319;
688 QUADNODES(0,456-451) = 0.6344704;
689 QUADNODES(0,457-451) = 0.1218432;
690 QUADNODES(0,458-451) = 0.1218432;
691 QUADNODES(0,459-451) = 0.1218432;
692 QUADNODES(0,460-451) = 0.002382507;
693 QUADNODES(0,461-451) = 0.3325392;
694 QUADNODES(0,462-451) = 0.3325392;
695 QUADNODES(0,463-451) = 0.3325392;
696 QUADNODES(0,464-451) = 0.0000000;
697 QUADNODES(0,465-451) = 0.0000000;
698 QUADNODES(0,466-451) = 0.0000000;
699 QUADNODES(0,467-451) = 0.5000000;
700 QUADNODES(0,468-451) = 0.5000000;
701 QUADNODES(0,469-451) = 0.5000000;
702 QUADNODES(0,470-451) = 0.6000000;
703 QUADNODES(0,471-451) = 0.6000000;
704 QUADNODES(0,472-451) = 0.6000000;
705 QUADNODES(0,473-451) = 0.2000000;
706 QUADNODES(0,474-451) = 0.2000000;
707 QUADNODES(0,475-451) = 0.2000000;
708 QUADNODES(0,476-451) = 0.1000000;
709 QUADNODES(0,477-451) = 0.1000000;
710 QUADNODES(0,478-451) = 0.1000000;
711 QUADNODES(0,479-451) = 0.1000000;
712 QUADNODES(0,480-451) = 0.1000000;
713 QUADNODES(0,481-451) = 0.1000000;
714
715 QUADNODES(1,451-451) = 0.2500000;
716 QUADNODES(1,452-451) = 0.07821319;
717 QUADNODES(1,453-451) = 0.7653604;
718 QUADNODES(1,454-451) = 0.07821319;
719 QUADNODES(1,455-451) = 0.07821319;
720 QUADNODES(1,456-451) = 0.1218432;
721 QUADNODES(1,457-451) = 0.6344704;
722 QUADNODES(1,458-451) = 0.1218432;
723 QUADNODES(1,459-451) = 0.1218432;
724 QUADNODES(1,460-451) = 0.3325392;
725 QUADNODES(1,461-451) = 0.002382507;
726 QUADNODES(1,462-451) = 0.3325392;
727 QUADNODES(1,463-451) = 0.3325392;
728 QUADNODES(1,464-451) = 0.0000000;
729 QUADNODES(1,465-451) = 0.5000000;
730 QUADNODES(1,466-451) = 0.5000000;
731 QUADNODES(1,467-451) = 0.0000000;
732 QUADNODES(1,468-451) = 0.0000000;
733 QUADNODES(1,469-451) = 0.5000000;
734 QUADNODES(1,470-451) = 0.2000000;
735 QUADNODES(1,471-451) = 0.1000000;
736 QUADNODES(1,472-451) = 0.1000000;
737 QUADNODES(1,473-451) = 0.6000000;
738 QUADNODES(1,474-451) = 0.1000000;
739 QUADNODES(1,475-451) = 0.1000000;
740 QUADNODES(1,476-451) = 0.6000000;
741 QUADNODES(1,477-451) = 0.6000000;
742 QUADNODES(1,478-451) = 0.2000000;
743 QUADNODES(1,479-451) = 0.2000000;
744 QUADNODES(1,480-451) = 0.1000000;
745 QUADNODES(1,481-451) = 0.1000000;
746
747 QUADNODES(2,451-451) = 0.2500000;
748 QUADNODES(2,452-451) = 0.07821319;
749 QUADNODES(2,453-451) = 0.07821319;
750 QUADNODES(2,454-451) = 0.7653604;
751 QUADNODES(2,455-451) = 0.07821319;
752 QUADNODES(2,456-451) = 0.1218432;
753 QUADNODES(2,457-451) = 0.1218432;
754 QUADNODES(2,458-451) = 0.6344704;
755 QUADNODES(2,459-451) = 0.1218432;
756 QUADNODES(2,460-451) = 0.3325392;
757 QUADNODES(2,461-451) = 0.3325392;
758 QUADNODES(2,462-451) = 0.002382507;
759 QUADNODES(2,463-451) = 0.3325392;
760 QUADNODES(2,464-451) = 0.5000000;
761 QUADNODES(2,465-451) = 0.0000000;
762 QUADNODES(2,466-451) = 0.5000000;
763 QUADNODES(2,467-451) = 0.0000000;
764 QUADNODES(2,468-451) = 0.5000000;
765 QUADNODES(2,469-451) = 0.0000000;
766 QUADNODES(2,470-451) = 0.1000000;
767 QUADNODES(2,471-451) = 0.2000000;
768 QUADNODES(2,472-451) = 0.1000000;
769 QUADNODES(2,473-451) = 0.1000000;
770 QUADNODES(2,474-451) = 0.6000000;
771 QUADNODES(2,475-451) = 0.1000000;
772 QUADNODES(2,476-451) = 0.2000000;
773 QUADNODES(2,477-451) = 0.1000000;
774 QUADNODES(2,478-451) = 0.6000000;
775 QUADNODES(2,479-451) = 0.1000000;
776 QUADNODES(2,480-451) = 0.6000000;
777 QUADNODES(2,481-451) = 0.2000000;
778
779 } else if (numQuadNodes==45){
780 QUADWEIGHTS(482-482) =-0.03932701;
781 QUADWEIGHTS(483-482) = 0.004081316;
782 QUADWEIGHTS(484-482) = 0.004081316;
783 QUADWEIGHTS(485-482) = 0.004081316;
784 QUADWEIGHTS(486-482) = 0.004081316;
785 QUADWEIGHTS(487-482) = 0.0006580868;
786 QUADWEIGHTS(488-482) = 0.0006580868;
787 QUADWEIGHTS(489-482) = 0.0006580868;
788 QUADWEIGHTS(490-482) = 0.0006580868;
789 QUADWEIGHTS(491-482) = 0.004384259;
790 QUADWEIGHTS(492-482) = 0.004384259;
791 QUADWEIGHTS(493-482) = 0.004384259;
792 QUADWEIGHTS(494-482) = 0.004384259;
793 QUADWEIGHTS(495-482) = 0.004384259;
794 QUADWEIGHTS(496-482) = 0.004384259;
795 QUADWEIGHTS(497-482) = 0.01383006;
796 QUADWEIGHTS(498-482) = 0.01383006;
797 QUADWEIGHTS(499-482) = 0.01383006;
798 QUADWEIGHTS(500-482) = 0.01383006;
799 QUADWEIGHTS(501-482) = 0.01383006;
800 QUADWEIGHTS(502-482) = 0.01383006;
801 QUADWEIGHTS(503-482) = 0.004240437;
802 QUADWEIGHTS(504-482) = 0.004240437;
803 QUADWEIGHTS(505-482) = 0.004240437;
804 QUADWEIGHTS(506-482) = 0.004240437;
805 QUADWEIGHTS(507-482) = 0.004240437;
806 QUADWEIGHTS(508-482) = 0.004240437;
807 QUADWEIGHTS(509-482) = 0.004240437;
808 QUADWEIGHTS(510-482) = 0.004240437;
809 QUADWEIGHTS(511-482) = 0.004240437;
810 QUADWEIGHTS(512-482) = 0.004240437;
811 QUADWEIGHTS(513-482) = 0.004240437;
812 QUADWEIGHTS(514-482) = 0.004240437;
813 QUADWEIGHTS(515-482) = 0.002238740;
814 QUADWEIGHTS(516-482) = 0.002238740;
815 QUADWEIGHTS(517-482) = 0.002238740;
816 QUADWEIGHTS(518-482) = 0.002238740;
817 QUADWEIGHTS(519-482) = 0.002238740;
818 QUADWEIGHTS(520-482) = 0.002238740;
819 QUADWEIGHTS(521-482) = 0.002238740;
820 QUADWEIGHTS(522-482) = 0.002238740;
821 QUADWEIGHTS(523-482) = 0.002238740;
822 QUADWEIGHTS(524-482) = 0.002238740;
823 QUADWEIGHTS(525-482) = 0.002238740;
824 QUADWEIGHTS(526-482) = 0.002238740;
825
826 QUADNODES(0,482-482) = 0.2500000;
827 QUADNODES(0,483-482) = 0.6175872;
828 QUADNODES(0,484-482) = 0.1274709;
829 QUADNODES(0,485-482) = 0.1274709;
830 QUADNODES(0,486-482) = 0.1274709;
831 QUADNODES(0,487-482) = 0.9037635;
832 QUADNODES(0,488-482) = 0.03207883;
833 QUADNODES(0,489-482) = 0.03207883;
834 QUADNODES(0,490-482) = 0.03207883;
835 QUADNODES(0,491-482) = 0.4502229;
836 QUADNODES(0,492-482) = 0.4502229;
837 QUADNODES(0,493-482) = 0.4502229;
838 QUADNODES(0,494-482) = 0.04977710;
839 QUADNODES(0,495-482) = 0.04977710;
840 QUADNODES(0,496-482) = 0.04977710;
841 QUADNODES(0,497-482) = 0.3162696;
842 QUADNODES(0,498-482) = 0.3162696;
843 QUADNODES(0,499-482) = 0.3162696;
844 QUADNODES(0,500-482) = 0.1837304;
845 QUADNODES(0,501-482) = 0.1837304;
846 QUADNODES(0,502-482) = 0.1837304;
847 QUADNODES(0,503-482) = 0.5132800;
848 QUADNODES(0,504-482) = 0.5132800;
849 QUADNODES(0,505-482) = 0.5132800;
850 QUADNODES(0,506-482) = 0.02291779;
851 QUADNODES(0,507-482) = 0.02291779;
852 QUADNODES(0,508-482) = 0.02291779;
853 QUADNODES(0,509-482) = 0.2319011;
854 QUADNODES(0,510-482) = 0.2319011;
855 QUADNODES(0,511-482) = 0.2319011;
856 QUADNODES(0,512-482) = 0.2319011;
857 QUADNODES(0,513-482) = 0.2319011;
858 QUADNODES(0,514-482) = 0.2319011;
859 QUADNODES(0,515-482) = 0.1937465;
860 QUADNODES(0,516-482) = 0.1937465;
861 QUADNODES(0,517-482) = 0.1937465;
862 QUADNODES(0,518-482) = 0.7303134;
863 QUADNODES(0,519-482) = 0.7303134;
864 QUADNODES(0,520-482) = 0.7303134;
865 QUADNODES(0,521-482) = 0.03797005;
866 QUADNODES(0,522-482) = 0.03797005;
867 QUADNODES(0,523-482) = 0.03797005;
868 QUADNODES(0,524-482) = 0.03797005;
869 QUADNODES(0,525-482) = 0.03797005;
870 QUADNODES(0,526-482) = 0.03797005;
871
872 QUADNODES(1,482-482) = 0.2500000;
873 QUADNODES(1,483-482) = 0.1274709;
874 QUADNODES(1,484-482) = 0.6175872;
875 QUADNODES(1,485-482) = 0.1274709;
876 QUADNODES(1,486-482) = 0.1274709;
877 QUADNODES(1,487-482) = 0.03207883;
878 QUADNODES(1,488-482) = 0.9037635;
879 QUADNODES(1,489-482) = 0.03207883;
880 QUADNODES(1,490-482) = 0.03207883;
881 QUADNODES(1,491-482) = 0.4502229;
882 QUADNODES(1,492-482) = 0.04977710;
883 QUADNODES(1,493-482) = 0.04977710;
884 QUADNODES(1,494-482) = 0.4502229;
885 QUADNODES(1,495-482) = 0.4502229;
886 QUADNODES(1,496-482) = 0.04977710;
887 QUADNODES(1,497-482) = 0.3162696;
888 QUADNODES(1,498-482) = 0.1837304;
889 QUADNODES(1,499-482) = 0.1837304;
890 QUADNODES(1,500-482) = 0.3162696;
891 QUADNODES(1,501-482) = 0.3162696;
892 QUADNODES(1,502-482) = 0.1837304;
893 QUADNODES(1,503-482) = 0.02291779;
894 QUADNODES(1,504-482) = 0.2319011;
895 QUADNODES(1,505-482) = 0.2319011;
896 QUADNODES(1,506-482) = 0.5132800;
897 QUADNODES(1,507-482) = 0.2319011;
898 QUADNODES(1,508-482) = 0.2319011;
899 QUADNODES(1,509-482) = 0.5132800;
900 QUADNODES(1,510-482) = 0.5132800;
901 QUADNODES(1,511-482) = 0.02291779;
902 QUADNODES(1,512-482) = 0.02291779;
903 QUADNODES(1,513-482) = 0.2319011;
904 QUADNODES(1,514-482) = 0.2319011;
905 QUADNODES(1,515-482) = 0.7303134;
906 QUADNODES(1,516-482) = 0.03797005;
907 QUADNODES(1,517-482) = 0.03797005;
908 QUADNODES(1,518-482) = 0.1937465;
909 QUADNODES(1,519-482) = 0.03797005;
910 QUADNODES(1,520-482) = 0.03797005;
911 QUADNODES(1,521-482) = 0.1937465;
912 QUADNODES(1,522-482) = 0.1937465;
913 QUADNODES(1,523-482) = 0.7303134;
914 QUADNODES(1,524-482) = 0.7303134;
915 QUADNODES(1,525-482) = 0.03797005;
916 QUADNODES(1,526-482) = 0.03797005;
917
918 QUADNODES(2,482-482) = 0.2500000;
919 QUADNODES(2,483-482) = 0.1274709;
920 QUADNODES(2,484-482) = 0.1274709;
921 QUADNODES(2,485-482) = 0.6175872;
922 QUADNODES(2,486-482) = 0.1274709;
923 QUADNODES(2,487-482) = 0.03207883;
924 QUADNODES(2,488-482) = 0.03207883;
925 QUADNODES(2,489-482) = 0.9037635;
926 QUADNODES(2,490-482) = 0.03207883;
927 QUADNODES(2,491-482) = 0.04977710;
928 QUADNODES(2,492-482) = 0.4502229;
929 QUADNODES(2,493-482) = 0.04977710;
930 QUADNODES(2,494-482) = 0.4502229;
931 QUADNODES(2,495-482) = 0.04977710;
932 QUADNODES(2,496-482) = 0.4502229;
933 QUADNODES(2,497-482) = 0.1837304;
934 QUADNODES(2,498-482) = 0.3162696;
935 QUADNODES(2,499-482) = 0.1837304;
936 QUADNODES(2,500-482) = 0.3162696;
937 QUADNODES(2,501-482) = 0.1837304;
938 QUADNODES(2,502-482) = 0.3162696;
939 QUADNODES(2,503-482) = 0.2319011;
940 QUADNODES(2,504-482) = 0.02291779;
941 QUADNODES(2,505-482) = 0.2319011;
942 QUADNODES(2,506-482) = 0.2319011;
943 QUADNODES(2,507-482) = 0.5132800;
944 QUADNODES(2,508-482) = 0.2319011;
945 QUADNODES(2,509-482) = 0.02291779;
946 QUADNODES(2,510-482) = 0.2319011;
947 QUADNODES(2,511-482) = 0.5132800;
948 QUADNODES(2,512-482) = 0.2319011;
949 QUADNODES(2,513-482) = 0.5132800;
950 QUADNODES(2,514-482) = 0.02291779;
951 QUADNODES(2,515-482) = 0.03797005;
952 QUADNODES(2,516-482) = 0.7303134;
953 QUADNODES(2,517-482) = 0.03797005;
954 QUADNODES(2,518-482) = 0.03797005;
955 QUADNODES(2,519-482) = 0.1937465;
956 QUADNODES(2,520-482) = 0.03797005;
957 QUADNODES(2,521-482) = 0.7303134;
958 QUADNODES(2,522-482) = 0.03797005;
959 QUADNODES(2,523-482) = 0.1937465;
960 QUADNODES(2,524-482) = 0.03797005;
961 QUADNODES(2,525-482) = 0.1937465;
962 QUADNODES(2,526-482) = 0.7303134;
963
964 } else {
965
966 /* get scheme on [0.1]^3 */
967
968 Finley_Quad_getNodesHex(numQuadNodes,quadNodes,quadWeights);
969 if (! Finley_noError()) return;
970
971 /* squeeze it: */
972 for (i=0;i<numQuadNodes;i++) {
973 Q1=QUADNODES(0,i);
974 Q2=QUADNODES(1,i);
975 Q3=QUADNODES(2,i);
976
977 JA11= (1./3.)*Q2*Q3-(1./2.)*(Q2+Q3) +1.;
978 JA12= (1./3.)*Q1*Q3-(1./2.)*Q1;
979 JA13= (1./3.)*Q1*Q2-(1./2.)*Q1;
980 JA21= (1./3.)*Q2*Q3-(1./2.)*Q2;
981 JA22= (1./3.)*Q1*Q3-(1./2.)*(Q1+Q3) +1.;
982 JA23= (1./3.)*Q1*Q2-(1./2.)*Q2;
983 JA31= (1./3.)*Q2*Q3-(1./2.)*Q3;
984 JA32= (1./3.)*Q1*Q3-(1./2.)*Q3;
985 JA33= (1./3.)*Q1*Q2-(1./2.)*(Q1+Q2) +1.;
986 DET=JA11*JA22*JA33+JA12*JA23*JA31+JA13*JA21*JA32-JA13*JA22*JA31-JA11*JA23*JA32-JA12*JA21*JA33;
987 quadWeights[i]=quadWeights[i]*ABS(DET);
988 QUADNODES(0,i)=Q1*((1./3.)*Q2*Q3-(1./2.)*(Q2+Q3)+1.);
989 QUADNODES(1,i)=Q2*((1./3.)*Q1*Q3-(1./2.)*(Q1+Q3)+1.);
990 QUADNODES(2,i)=Q3*((1./3.)*Q1*Q2-(1./2.)*(Q1+Q2)+1.);
991 }
992 }
993 #undef DIM
994 }
995
996 /**************************************************************/
997
998 /* get a quadrature scheme with numQuadNodes quadrature nodes for the quad [0.1]^2 */
999 /* as a X-product of a 1D scheme. */
1000
1001 void Finley_Quad_getNodesRec(int numQuadNodes,double* quadNodes,double* quadWeights) {
1002 char error_msg[LenErrorMsg_MAX];
1003 int numQuadNodes1d,i,j,l;
1004 double *quadNodes1d=NULL,*quadWeights1d=NULL;
1005 bool_t set=FALSE;
1006 #define DIM 2
1007
1008 quadNodes1d=TMPMEMALLOC(numQuadNodes,double);
1009 quadWeights1d=TMPMEMALLOC(numQuadNodes,double);
1010 if (! ( Finley_checkPtr(quadNodes1d) || Finley_checkPtr(quadWeights1d) ) ) {
1011 /* find numQuadNodes1d with numQuadNodes1d**2==numQuadNodes: */
1012
1013 for (numQuadNodes1d=1;numQuadNodes1d<=MAX_numQuadNodesLine;numQuadNodes1d++) {
1014 if (numQuadNodes1d*numQuadNodes1d==numQuadNodes) {
1015
1016 /* get 1D scheme: */
1017
1018 Finley_Quad_getNodesLine(numQuadNodes1d,quadNodes1d,quadWeights1d);
1019
1020 /* make 2D scheme: */
1021
1022 if (Finley_noError()) {
1023 l=0;
1024 for (i=0;i<numQuadNodes1d;i++) {
1025 for (j=0;j<numQuadNodes1d;j++) {
1026 QUADNODES(0,l)=quadNodes1d[i];
1027 QUADNODES(1,l)=quadNodes1d[j];
1028 QUADWEIGHTS(l)=quadWeights1d[i]*quadWeights1d[j];
1029 l++;
1030 }
1031 }
1032 set=TRUE;
1033 break;
1034 }
1035 }
1036 }
1037 if (!set) {
1038 sprintf(error_msg,"Finley_Quad_getNodesRec: Illegal number of quadrature nodes %d on hexahedron.",numQuadNodes);
1039 Finley_setError(VALUE_ERROR,error_msg);
1040 }
1041 TMPMEMFREE(quadNodes1d);
1042 TMPMEMFREE(quadWeights1d);
1043 }
1044 #undef DIM
1045 }
1046
1047 /**************************************************************/
1048
1049 /* get a quadrature scheme with numQuadNodes quadrature nodes for the hex [0.1]^3 */
1050 /* as a X-product of a 1D scheme. */
1051
1052 void Finley_Quad_getNodesHex(int numQuadNodes,double* quadNodes,double* quadWeights) {
1053 char error_msg[LenErrorMsg_MAX];
1054 int numQuadNodes1d,i,j,k,l;
1055 double *quadNodes1d=NULL,*quadWeights1d=NULL;
1056 bool_t set=FALSE;
1057 #define DIM 3
1058
1059 /* find numQuadNodes1d with numQuadNodes1d**3==numQuadNodes: */
1060
1061 quadNodes1d=TMPMEMALLOC(numQuadNodes,double);
1062 quadWeights1d=TMPMEMALLOC(numQuadNodes,double);
1063 if (! ( Finley_checkPtr(quadNodes1d) || Finley_checkPtr(quadWeights1d) ) ) {
1064 for (numQuadNodes1d=1;numQuadNodes1d<=MAX_numQuadNodesLine;numQuadNodes1d++) {
1065 if (numQuadNodes1d*numQuadNodes1d*numQuadNodes1d==numQuadNodes) {
1066
1067 /* get 1D scheme: */
1068
1069 Finley_Quad_getNodesLine(numQuadNodes1d,quadNodes1d,quadWeights1d);
1070
1071 /* make 3D scheme: */
1072
1073 if (Finley_noError()) {
1074 l=0;
1075 for (i=0;i<numQuadNodes1d;i++) {
1076 for (j=0;j<numQuadNodes1d;j++) {
1077 for (k=0;k<numQuadNodes1d;k++) {
1078 QUADNODES(0,l)=quadNodes1d[i];
1079 QUADNODES(1,l)=quadNodes1d[j];
1080 QUADNODES(2,l)=quadNodes1d[k];
1081 QUADWEIGHTS(l)=quadWeights1d[i]*quadWeights1d[j]*quadWeights1d[k];
1082 l++;
1083 }
1084 }
1085 }
1086 set=TRUE;
1087 break;
1088 }
1089 }
1090 }
1091 if (!set) {
1092 sprintf(error_msg,"Finley_Quad_getNodesHex: Illegal number of quadrature nodes %d on hexahedron.",numQuadNodes);
1093 Finley_setError(VALUE_ERROR,error_msg);
1094 }
1095 TMPMEMFREE(quadNodes1d);
1096 TMPMEMFREE(quadWeights1d);
1097 }
1098 #undef DIM
1099 }
1100
1101 /**************************************************************/
1102
1103 /* get a quadrature scheme with numQuadNodes quadrature nodes for a point. As there */
1104 /* in no quadrature scheme for a point any value for numQuadNodes other than 0 throws */
1105 /* an error. */
1106
1107 void Finley_Quad_getNodesPoint(int numQuadNodes,double* quadNodes,double* quadWeights) {
1108 if (numQuadNodes==0) {
1109 return;
1110 } else {
1111 Finley_setError(VALUE_ERROR,"Finley_Quad_getNodesPoint: Illegal number of quadrature nodes.");
1112 }
1113 }
1114
1115 /**************************************************************/
1116
1117 /* get a quadrature scheme with numQuadNodes quadrature nodes on the line [0,1]: */
1118 /* The nodes and weights are set from a table. */
1119
1120 void Finley_Quad_getNodesLine(int numQuadNodes,double* quadNodes,double* quadWeights) {
1121 switch(numQuadNodes) {
1122 case 1:
1123 quadNodes[0]=0.5;
1124 quadWeights[0]=1.;
1125 break;
1126
1127 case 2:
1128 quadNodes[0]=(1.-.577350269189626)/2.;
1129 quadNodes[1]=(1.+.577350269189626)/2.;
1130 quadWeights[0]=.5;
1131 quadWeights[1]=.5;
1132 break;
1133
1134 case 3:
1135 quadNodes[0]=(1.-.774596669241483)/2.;
1136 quadNodes[1]=.5;
1137 quadNodes[2]=(1.+.774596669241483)/2.;
1138 quadWeights[0]=5./18.;
1139 quadWeights[1]=4./ 9.;
1140 quadWeights[2]=5./18.;
1141 break;
1142
1143 case 4:
1144 quadNodes[0]=(1.-.861136311594053)/2.;
1145 quadNodes[1]=(1.-.339981043584856)/2.;
1146 quadNodes[2]=(1.+.339981043584856)/2.;
1147 quadNodes[3]=(1.+.861136311594053)/2.;
1148 quadWeights[0]=.347854845137454/2.;
1149 quadWeights[1]=.652145154862546/2.;
1150 quadWeights[2]=.652145154862546/2.;
1151 quadWeights[3]=.347854845137454/2.;
1152 break;
1153
1154 case 5:
1155 quadNodes[0]=(1.-.906179845938664)/2.;
1156 quadNodes[1]=(1.-.538469310105683)/2.;
1157 quadNodes[2]= .5;
1158 quadNodes[3]=(1.+.538469310105683)/2.;
1159 quadNodes[4]=(1.+.906179845938664)/2.;
1160 quadWeights[0]=.236926885056189/2.;
1161 quadWeights[1]=.478628670499366/2.;
1162 quadWeights[2]=.568888888888889/2.;
1163 quadWeights[3]=.478628670499366/2.;
1164 quadWeights[4]=.236926885056189/2.;
1165 break;
1166
1167 case 6:
1168 quadNodes[0]=(1.-.932469514203152)/2.;
1169 quadNodes[1]=(1.-.661209386466265)/2.;
1170 quadNodes[2]=(1.-.238619186083197)/2.;
1171 quadNodes[3]=(1.+.238619186083197)/2.;
1172 quadNodes[4]=(1.+.661209386466265)/2.;
1173 quadNodes[5]=(1.+.932469514203152)/2.;
1174 quadWeights[0]=.171324492379170/2.;
1175 quadWeights[1]=.360761573048139/2.;
1176 quadWeights[2]=.467913934572691/2.;
1177 quadWeights[3]=.467913934572691/2.;
1178 quadWeights[4]=.360761573048139/2.;
1179 quadWeights[5]=.171324492379170/2.;
1180 break;
1181
1182 case 7:
1183 quadNodes[0]=(1.-.949107912342759)/2.;
1184 quadNodes[1]=(1.-.741531185599394)/2.;
1185 quadNodes[2]=(1.-.405845151377397)/2.;
1186 quadNodes[3]=0.5;
1187 quadNodes[4]=(1.+.405845151377397)/2.;
1188 quadNodes[5]=(1.+.741531185599394)/2.;
1189 quadNodes[6]=(1.+.949107912342759)/2.;
1190 quadWeights[0]= .129484966168870/2.;
1191 quadWeights[1]= .279705391489277/2.;
1192 quadWeights[2]= .381830050505119/2.;
1193 quadWeights[3]= .417959183673469/2.;
1194 quadWeights[4]= .381830050505119/2.;
1195 quadWeights[5]= .279705391489277/2.;
1196 quadWeights[6]= .129484966168870/2.;
1197 break;
1198
1199 case 8:
1200 quadNodes[0]=(1.-.960289856497536)/2.;
1201 quadNodes[1]=(1.-.796666477413627)/2.;
1202 quadNodes[2]=(1.-.525532409916329)/2.;
1203 quadNodes[3]=(1.-.183434642495650)/2.;
1204 quadNodes[4]=(1.+.183434642495650)/2.;
1205 quadNodes[5]=(1.+.525532409916329)/2.;
1206 quadNodes[6]=(1.+.796666477413627)/2.;
1207 quadNodes[7]=(1.+.960289856497536)/2.;
1208 quadWeights[0]= .101228536290376/2.;
1209 quadWeights[1]= .222381034453374/2.;
1210 quadWeights[2]= .313706645877887/2.;
1211 quadWeights[3]= .362683783378362/2.;
1212 quadWeights[4]= .362683783378362/2.;
1213 quadWeights[5]= .313706645877887/2.;
1214 quadWeights[6]= .222381034453374/2.;
1215 quadWeights[7]= .101228536290376/2.;
1216 break;
1217
1218 case 9:
1219 quadNodes[0]=(1.-.968160239507626)/2.;
1220 quadNodes[1]=(1.-.836031107326636)/2.;
1221 quadNodes[2]=(1.-.613371432700590)/2.;
1222 quadNodes[3]=(1.-.324253423403809)/2.;
1223 quadNodes[4]= .5;
1224 quadNodes[5]=(1.+.324253423403809)/2.;
1225 quadNodes[6]=(1.+.613371432700590)/2.;
1226 quadNodes[7]=(1.+.836031107326636)/2.;
1227 quadNodes[8]=(1.+.968160239507626)/2.;
1228 quadWeights[0]= .081274388361574/2.;
1229 quadWeights[1]= .180648160694857/2.;
1230 quadWeights[2]= .260610696402935/2.;
1231 quadWeights[3]= .312347077040003/2.;
1232 quadWeights[4]= .330239355001260/2.;
1233 quadWeights[5]= .312347077040003/2.;
1234 quadWeights[6]= .260610696402935/2.;
1235 quadWeights[7]= .180648160694857/2.;
1236 quadWeights[8]= .081274388361574/2.;
1237 break;
1238
1239 case 10:
1240 quadNodes[0]=(1.-.973906528517172)/2.;
1241 quadNodes[1]=(1.-.865063366688985)/2.;
1242 quadNodes[2]=(1.-.679409568299024)/2.;
1243 quadNodes[3]=(1.-.433395394129247)/2.;
1244 quadNodes[4]=(1.-.148874338981631)/2.;
1245 quadNodes[5]=(1.+.148874338981631)/2.;
1246 quadNodes[6]=(1.+.433395394129247)/2.;
1247 quadNodes[7]=(1.+.679409568299024)/2.;
1248 quadNodes[8]=(1.+.865063366688985)/2.;
1249 quadNodes[9]=(1.+.973906528517172)/2.;
1250 quadWeights[0]= .066671344308688/2.;
1251 quadWeights[1]= .149451349150581/2.;
1252 quadWeights[2]= .219086362515982/2.;
1253 quadWeights[3]= .269266719309996/2.;
1254 quadWeights[4]= .295524224714753/2.;
1255 quadWeights[5]= .295524224714753/2.;
1256 quadWeights[6]= .269266719309996/2.;
1257 quadWeights[7]= .219086362515982/2.;
1258 quadWeights[8]= .149451349150581/2.;
1259 quadWeights[9]= .066671344308688/2.;
1260 break;
1261
1262 default:
1263 Finley_setError(VALUE_ERROR,"Finley_Quad_getNodesLine: Negative intergration order.");
1264 break;
1265 }
1266 }
1267
1268
1269 /**************************************************************/
1270
1271 /* The following functions Finley_Quad_getNumNodes* return the nmber of quadrature points needed to */
1272 /* achieve a certain accuracy. Notice that for Tet and Tri the the order is increased */
1273 /* to consider the accuracy reduction through the construction process. */
1274
1275
1276 int Finley_Quad_getNumNodesPoint(int order) {
1277 return 0;
1278 }
1279
1280 int Finley_Quad_getNumNodesLine(int order) {
1281 char error_msg[LenErrorMsg_MAX];
1282 if (order <0 ) {
1283 Finley_setError(VALUE_ERROR,"Finley_Quad_getNumNodesPoint: Negative intergration order.");
1284 return -1;
1285 } else {
1286 if (order > 2*MAX_numQuadNodesLine-1) {
1287 sprintf(error_msg,"Finley_Quad_getNumNodesPoint: requested integration order %d on line is too large (>%d).",
1288 order,2*MAX_numQuadNodesLine-1);
1289 Finley_setError(VALUE_ERROR,error_msg);
1290 return -1;
1291 } else {
1292 Finley_resetError();
1293 return order/2+1;
1294 }
1295 }
1296 }
1297
1298 int Finley_Quad_getNumNodesTri(int order) {
1299 int numQuadNodesLine;
1300 if (order<=1) {
1301 return 1;
1302 } else if (order<=2){
1303 return 3;
1304 } else if (order<=3){
1305 return 4;
1306 } else if (order<=4){
1307 return 6;
1308 } else if (order<=5){
1309 return 7;
1310 } else if (order<=6){
1311 return 12;
1312 } else if (order<=7){
1313 return 13;
1314 } else if (order<=8){
1315 return 16;
1316 } else if (order<=9){
1317 return 19;
1318 } else {
1319 numQuadNodesLine=Finley_Quad_getNumNodesLine(order+1);
1320 if (Finley_noError()) {
1321 return numQuadNodesLine*numQuadNodesLine;
1322 } else {
1323 return -1;
1324 }
1325 }
1326 }
1327
1328 int Finley_Quad_getNumNodesRec(int order) {
1329 int numQuadNodesLine;
1330 numQuadNodesLine=Finley_Quad_getNumNodesLine(order);
1331 if (Finley_noError()) {
1332 return numQuadNodesLine*numQuadNodesLine;
1333 } else {
1334 return -1;
1335 }
1336 }
1337
1338 int Finley_Quad_getNumNodesTet(int order) {
1339 int numQuadNodesLine;
1340 if (order<=1) {
1341 return 1;
1342 } else if (order<=2){
1343 return 4;
1344 } else if (order<=3){
1345 return 5;
1346 } else if (order<=4){
1347 return 11;
1348 } else if (order<=5){
1349 return 15;
1350 } else if (order<=6){
1351 return 24;
1352 } else if (order<=7){
1353 return 31;
1354 } else if (order<=8){
1355 return 45;
1356 } else {
1357 numQuadNodesLine=Finley_Quad_getNumNodesLine(order+2);
1358 if (Finley_noError()) {
1359 return numQuadNodesLine*numQuadNodesLine*numQuadNodesLine;
1360 } else {
1361 return -1;
1362 }
1363 }
1364 }
1365
1366 int Finley_Quad_getNumNodesHex(int order) {
1367 int numQuadNodesLine;
1368 numQuadNodesLine=Finley_Quad_getNumNodesLine(order);
1369 if (Finley_noError()) {
1370 return numQuadNodesLine*numQuadNodesLine*numQuadNodesLine;
1371 } else {
1372 return -1;
1373 }
1374 }
1375 dim_t Finley_Quad_MacroPoint(dim_t numSubElements, int numQuadNodes, double* quadNodes, double* quadWeights, dim_t numF, double* dFdv,
1376 dim_t new_len, double* new_quadNodes, double* new_quadWeights, double* new_dFdv )
1377 {
1378 return 0;
1379
1380 }
1381 dim_t Finley_Quad_MacroLine(dim_t numSubElements, int numQuadNodes, double* quadNodes, double* quadWeights, dim_t numF, double* dFdv,
1382 dim_t new_len, double* new_quadNodes, double* new_quadWeights, double* new_dFdv )
1383 {
1384 #define DIM 1
1385 dim_t s,q,i;
1386 register double x0, w;
1387 const double f=1./((double)numSubElements);
1388
1389 if (new_len < numSubElements*numQuadNodes) {
1390 Finley_setError(MEMORY_ERROR,"Finley_Quad_MacroLine: array for new qurature scheme is too small");
1391 }
1392 for (q=0; q<numQuadNodes; ++q) {
1393
1394 x0=quadNodes[INDEX2(0,q,DIM)];
1395 w=f*quadWeights[q];
1396
1397 for (s=0; s<numSubElements; ++s) {
1398 new_quadWeights[INDEX2(q,s, numQuadNodes)] =w;
1399 new_quadNodes[INDEX3(0,q,s, DIM,numQuadNodes)] =(x0+s)*f;
1400 for (i=0;i<numF;i++) new_dFdv[INDEX4(i,0,q,s, numF, DIM,numQuadNodes)] = dFdv[INDEX3(i,0,numF, q,DIM)]*f;
1401 }
1402
1403 }
1404 #undef DIM
1405 return numSubElements*numQuadNodes;
1406 }
1407 #define HALF 0.5
1408 #define TWO 2.
1409 dim_t Finley_Quad_MacroTri(dim_t numSubElements, int numQuadNodes, double* quadNodes, double* quadWeights, dim_t numF, double* dFdv,
1410 dim_t new_len, double* new_quadNodes, double* new_quadWeights, double* new_dFdv )
1411 {
1412
1413 #define DIM 2
1414 dim_t q,i;
1415 register double x0, x1, w, df0, df1;
1416
1417 if (new_len < numSubElements*numQuadNodes) {
1418 Finley_setError(MEMORY_ERROR,"Finley_Quad_MacroTri: array for new qurature scheme is too small");
1419 return -1;
1420 }
1421 if (numSubElements==1) {
1422
1423 for (q=0; q<numQuadNodes; ++q) {
1424
1425 x0=quadNodes[INDEX2(0,q,DIM)];
1426 x1=quadNodes[INDEX2(1,q,DIM)];
1427 w=quadWeights[q];
1428
1429 new_quadWeights[INDEX2(q,0,numQuadNodes)] =w;
1430 new_quadNodes[INDEX3(0,q,0,DIM,numQuadNodes)] =x0;
1431 new_quadNodes[INDEX3(1,q,0,DIM,numQuadNodes)] =x1;
1432 for (i=0;i<numF;i++) {
1433 new_dFdv[INDEX4(i,0,q,0, numF,DIM,numQuadNodes)] = dFdv[INDEX3(i,0,q, numF, DIM)];
1434 new_dFdv[INDEX4(i,1,q,0, numF,DIM,numQuadNodes)] = dFdv[INDEX3(i,1,q, numF, DIM)];
1435 }
1436
1437 }
1438
1439 } else if (numSubElements==4) {
1440 const double f = 0.25;
1441 for (q=0; q<numQuadNodes; ++q) {
1442
1443 x0=quadNodes[INDEX2(0,q,DIM)];
1444 x1=quadNodes[INDEX2(1,q,DIM)];
1445 w=f*quadWeights[q];
1446
1447 new_quadWeights[INDEX2(q,0,numQuadNodes)] =w;
1448 new_quadNodes[INDEX3(0,q,0,DIM,numQuadNodes)] =HALF*x0;
1449 new_quadNodes[INDEX3(1,q,0,DIM,numQuadNodes)] =HALF*x1;
1450
1451 new_quadWeights[INDEX2(q,1,numQuadNodes)] =w;
1452 new_quadNodes[INDEX3(0,q,1,DIM,numQuadNodes)] =HALF*x0;
1453 new_quadNodes[INDEX3(1,q,1,DIM,numQuadNodes)] =HALF*(x1+1);
1454
1455 new_quadWeights[INDEX2(q,2,numQuadNodes)] =w;
1456 new_quadNodes[INDEX3(0,q,2,DIM,numQuadNodes)] =HALF*(x0+1);
1457 new_quadNodes[INDEX3(1,q,2,DIM,numQuadNodes)] =HALF*x1;
1458
1459 new_quadWeights[INDEX2(q,3,numQuadNodes)] =w;
1460 new_quadNodes[INDEX3(0,q,3,DIM,numQuadNodes)] =HALF*(1-x0);
1461 new_quadNodes[INDEX3(1,q,3,DIM,numQuadNodes)] =HALF*(1-x1);
1462
1463 for (i=0;i<numF;i++) {
1464 df0=dFdv[INDEX3(i,0,q, numF, DIM)]*TWO;
1465 df1=dFdv[INDEX3(i,1,q, numF, DIM)]*TWO;
1466
1467 new_dFdv[INDEX4(i,0,q,0, numF,DIM,numQuadNodes)] = df0;
1468 new_dFdv[INDEX4(i,1,q,0, numF,DIM,numQuadNodes)] = df1;
1469
1470 new_dFdv[INDEX4(i,0,q,1, numF,DIM,numQuadNodes)] = df0;
1471 new_dFdv[INDEX4(i,1,q,1, numF,DIM,numQuadNodes)] = df1;
1472
1473 new_dFdv[INDEX4(i,0,q,2, numF,DIM,numQuadNodes)] = df0;
1474 new_dFdv[INDEX4(i,1,q,2, numF,DIM,numQuadNodes)] = df1;
1475
1476 new_dFdv[INDEX4(i,0,q,3, numF,DIM,numQuadNodes)] = -df0;
1477 new_dFdv[INDEX4(i,1,q,3, numF,DIM,numQuadNodes)] = -df1;
1478 }
1479
1480
1481 }
1482 } else {
1483 Finley_setError(MEMORY_ERROR,"Finley_Quad_MacroTri: unable to create quadrature scheme for macro element.");
1484 return -1;
1485 }
1486 #undef DIM
1487 return numSubElements*numQuadNodes;
1488 }
1489
1490 dim_t Finley_Quad_MacroRec(dim_t numSubElements, int numQuadNodes, double* quadNodes, double* quadWeights, dim_t numF, double* dFdv,
1491 dim_t new_len, double* new_quadNodes, double* new_quadWeights, double* new_dFdv )
1492 {
1493
1494 #define DIM 2
1495 dim_t q,i;
1496 register double x0, x1, w, df0, df1;
1497
1498 if (new_len < numSubElements*numQuadNodes) {
1499 Finley_setError(MEMORY_ERROR,"Finley_Quad_MacroRec: array for new qurature scheme is too small");
1500 return -1;
1501 }
1502 if (numSubElements==1) {
1503
1504 for (q=0; q<numQuadNodes; ++q) {
1505
1506 x0=quadNodes[INDEX2(0,q,DIM)];
1507 x1=quadNodes[INDEX2(1,q,DIM)];
1508 w=quadWeights[q];
1509
1510 new_quadWeights[INDEX2(q,0,numQuadNodes)] =w;
1511 new_quadNodes[INDEX3(0,q,0,DIM,numQuadNodes)] =x0;
1512 new_quadNodes[INDEX3(1,q,0,DIM,numQuadNodes)] =x1;
1513 for (i=0;i<numF;i++) {
1514 new_dFdv[INDEX4(i,0,q,0, numF, DIM,numQuadNodes)] = dFdv[INDEX3(i,0, q,numF, DIM)];
1515 new_dFdv[INDEX4(i,1,q,0, numF, DIM,numQuadNodes)] = dFdv[INDEX3(i,1, q,numF, DIM)];
1516 }
1517
1518 }
1519
1520 } else if (numSubElements==4) {
1521 const double f = 0.25;
1522 for (q=0; q<numQuadNodes; ++q) {
1523
1524 x0=quadNodes[INDEX2(0,q,DIM)];
1525 x1=quadNodes[INDEX2(1,q,DIM)];
1526 w=f*quadWeights[q];
1527
1528 new_quadWeights[INDEX2(q,0,numQuadNodes)] =w;
1529 new_quadNodes[INDEX3(0,q,0,DIM,numQuadNodes)] =HALF*x0;
1530 new_quadNodes[INDEX3(1,q,0,DIM,numQuadNodes)] =HALF*x1;
1531
1532 new_quadWeights[INDEX2(q,1,numQuadNodes)] =w;
1533 new_quadNodes[INDEX3(0,q,1,DIM,numQuadNodes)] =HALF*x0;
1534 new_quadNodes[INDEX3(1,q,1,DIM,numQuadNodes)] =HALF*(x1+1);
1535
1536 new_quadWeights[INDEX2(q,2,numQuadNodes)] =w;
1537 new_quadNodes[INDEX3(0,q,2,DIM,numQuadNodes)] =HALF*(x0+1);
1538 new_quadNodes[INDEX3(1,q,2,DIM,numQuadNodes)] =HALF*x1;
1539
1540 new_quadWeights[INDEX2(q,3,numQuadNodes)] =w;
1541 new_quadNodes[INDEX3(0,q,3,DIM,numQuadNodes)] =HALF*(x0+1);
1542 new_quadNodes[INDEX3(1,q,3,DIM,numQuadNodes)] =HALF*(x1+1);
1543
1544 for (i=0;i<numF;i++) {
1545 df0=dFdv[INDEX3(i,0,q, numF, DIM)]*TWO;
1546 df1=dFdv[INDEX3(i,1,q, numF, DIM)]*TWO;
1547
1548 new_dFdv[INDEX4(i,0,q,0, numF,DIM,numQuadNodes)] = df0;
1549 new_dFdv[INDEX4(i,1,q,0, numF,DIM,numQuadNodes)] = df1;
1550
1551 new_dFdv[INDEX4(i,0,q,1, numF,DIM,numQuadNodes)] = df0;
1552 new_dFdv[INDEX4(i,1,q,1, numF,DIM,numQuadNodes)] = df1;
1553
1554 new_dFdv[INDEX4(i,0,q,2, numF,DIM,numQuadNodes)] = df0;
1555 new_dFdv[INDEX4(i,1,q,2, numF,DIM,numQuadNodes)] = df1;
1556
1557 new_dFdv[INDEX4(i,0,q,3, numF,DIM,numQuadNodes)] = df0;
1558 new_dFdv[INDEX4(i,1,q,3, numF,DIM,numQuadNodes)] = df1;
1559 }
1560
1561 }
1562 } else {
1563 Finley_setError(MEMORY_ERROR,"Finley_Quad_MacroRec: unable to create quadrature scheme for macro element.");
1564 return -1;
1565 }
1566 #undef DIM
1567 return numSubElements*numQuadNodes;
1568 }
1569
1570
1571 dim_t Finley_Quad_MacroTet(dim_t numSubElements, int numQuadNodes, double* quadNodes, double* quadWeights, dim_t numF, double* dFdv,
1572 dim_t new_len, double* new_quadNodes, double* new_quadWeights, double* new_dFdv )
1573 {
1574 #define DIM 3
1575 dim_t q, i;
1576 register double x0, x1, x2, w, df0, df1, df2;
1577
1578 if (new_len < numSubElements*numQuadNodes) {
1579 Finley_setError(MEMORY_ERROR,"Finley_Quad_MacroTet: array for new qurature scheme is too small");
1580 return -1;
1581 }
1582 if (numSubElements==1) {
1583
1584 for (q=0; q<numQuadNodes; ++q) {
1585
1586 x0=quadNodes[INDEX2(0,q,DIM)];
1587 x1=quadNodes[INDEX2(1,q,DIM)];
1588 x2=quadNodes[INDEX2(2,q,DIM)];
1589 w=quadWeights[q];
1590
1591 new_quadWeights[INDEX2(q,0,numQuadNodes)] =w;
1592 new_quadNodes[INDEX3(0,q,0,DIM,numQuadNodes)] =x0;
1593 new_quadNodes[INDEX3(1,q,0,DIM,numQuadNodes)] =x1;
1594 new_quadNodes[INDEX3(2,q,0,DIM,numQuadNodes)] =x2;
1595
1596 for (i=0;i<numF;i++) {
1597 new_dFdv[INDEX4(i,0,q,0, numF, DIM,numQuadNodes)] = dFdv[INDEX3(i,0,q, numF, DIM)];
1598 new_dFdv[INDEX4(i,1,q,0, numF, DIM,numQuadNodes)] = dFdv[INDEX3(i,1,q, numF, DIM)];
1599 new_dFdv[INDEX4(i,2,q,0, numF, DIM,numQuadNodes)] = dFdv[INDEX3(i,2,q, numF, DIM)];
1600 }
1601 }
1602
1603 } else if (numSubElements==8) {
1604 const double f = 0.125;
1605 for (q=0; q<numQuadNodes; ++q) {
1606
1607 x0=quadNodes[INDEX2(0,q,DIM)];
1608 x1=quadNodes[INDEX2(1,q,DIM)];
1609 x2=quadNodes[INDEX2(2,q,DIM)];
1610 w=f*quadWeights[q];
1611
1612 new_quadWeights[INDEX2(q,0,numQuadNodes)] =w;
1613 new_quadNodes[INDEX3(0,q,0,DIM,numQuadNodes)] =HALF*x0;
1614 new_quadNodes[INDEX3(1,q,0,DIM,numQuadNodes)] =HALF*x1;
1615 new_quadNodes[INDEX3(2,q,0,DIM,numQuadNodes)] =HALF*x2;
1616
1617 new_quadWeights[INDEX2(q,1,numQuadNodes)] =w;
1618 new_quadNodes[INDEX3(0,q,1,DIM,numQuadNodes)] =HALF*(x0+1);
1619 new_quadNodes[INDEX3(1,q,1,DIM,numQuadNodes)] =HALF*x1;
1620 new_quadNodes[INDEX3(2,q,1,DIM,numQuadNodes)] =HALF*x2;
1621
1622 new_quadWeights[INDEX2(q,2,numQuadNodes)] =w;
1623 new_quadNodes[INDEX3(0,q,2,DIM,numQuadNodes)] =HALF*x0;
1624 new_quadNodes[INDEX3(1,q,2,DIM,numQuadNodes)] =HALF*(x1+1);
1625 new_quadNodes[INDEX3(2,q,2,DIM,numQuadNodes)] =HALF*x2;
1626
1627 new_quadWeights[INDEX2(q,3,numQuadNodes)] =w;
1628 new_quadNodes[INDEX3(0,q,3,DIM,numQuadNodes)] =HALF*x0;
1629 new_quadNodes[INDEX3(1,q,3,DIM,numQuadNodes)] =HALF*x1;
1630 new_quadNodes[INDEX3(2,q,3,DIM,numQuadNodes)] =HALF*(x2+1);
1631
1632 new_quadWeights[INDEX2(q,4,numQuadNodes)] =w;
1633 new_quadNodes[INDEX3(0,q,4,DIM,numQuadNodes)] =HALF*(1-x1);
1634 new_quadNodes[INDEX3(1,q,4,DIM,numQuadNodes)] =HALF*(x0+x1);
1635 new_quadNodes[INDEX3(2,q,4,DIM,numQuadNodes)] =HALF*x2;
1636
1637 new_quadWeights[INDEX2(q,5,numQuadNodes)] =w;
1638 new_quadNodes[INDEX3(0,q,5,DIM,numQuadNodes)] =HALF*(1-x0-x2);
1639 new_quadNodes[INDEX3(1,q,5,DIM,numQuadNodes)] =HALF*(1-x1);
1640 new_quadNodes[INDEX3(2,q,5,DIM,numQuadNodes)] =HALF*(x0+x1);
1641
1642 new_quadWeights[INDEX2(q,6,numQuadNodes)] =w;
1643 new_quadNodes[INDEX3(0,q,6,DIM,numQuadNodes)] =HALF*x2;
1644 new_quadNodes[INDEX3(1,q,6,DIM,numQuadNodes)] =HALF*(1-x0-x2);
1645 new_quadNodes[INDEX3(2,q,6,DIM,numQuadNodes)] =HALF*(1-x1);
1646
1647 new_quadWeights[INDEX2(q,7,numQuadNodes)] =w;
1648 new_quadNodes[INDEX3(0,q,7,DIM,numQuadNodes)] =HALF*(x0+x2);
1649 new_quadNodes[INDEX3(1,q,7,DIM,numQuadNodes)] =HALF*x1;
1650 new_quadNodes[INDEX3(2,q,7,DIM,numQuadNodes)] =HALF*(1-x0-x1);
1651
1652 for (i=0;i<numF;i++) {
1653 df0=dFdv[INDEX3(i,0,q, numF, DIM)]*TWO;
1654 df1=dFdv[INDEX3(i,1,q, numF, DIM)]*TWO;
1655 df2=dFdv[INDEX3(i,2,q, numF, DIM)]*TWO;
1656
1657 new_dFdv[INDEX4(i,0,q,0, numF,DIM,numQuadNodes)] = df0;
1658 new_dFdv[INDEX4(i,1,q,0, numF,DIM,numQuadNodes)] = df1;
1659 new_dFdv[INDEX4(i,2,q,0, numF,DIM,numQuadNodes)] = df2;
1660
1661 new_dFdv[INDEX4(i,0,q,1, numF,DIM,numQuadNodes)] = df0;
1662 new_dFdv[INDEX4(i,1,q,1, numF,DIM,numQuadNodes)] = df1;
1663 new_dFdv[INDEX4(i,2,q,1, numF,DIM,numQuadNodes)] = df2;
1664
1665 new_dFdv[INDEX4(i,0,q,2, numF,DIM,numQuadNodes)] = df0;
1666 new_dFdv[INDEX4(i,1,q,2, numF,DIM,numQuadNodes)] = df1;
1667 new_dFdv[INDEX4(i,2,q,2, numF,DIM,numQuadNodes)] = df2;
1668
1669 new_dFdv[INDEX4(i,0,q,3, numF,DIM,numQuadNodes)] = df0;
1670 new_dFdv[INDEX4(i,1,q,3, numF,DIM,numQuadNodes)] = df1;
1671 new_dFdv[INDEX4(i,2,q,3, numF,DIM,numQuadNodes)] = df2;
1672
1673 new_dFdv[INDEX4(i,0,q,4, numF,DIM,numQuadNodes)] = df0-df1;
1674 new_dFdv[INDEX4(i,1,q,4, numF,DIM,numQuadNodes)] = df0;
1675 new_dFdv[INDEX4(i,2,q,4, numF,DIM,numQuadNodes)] = df2;
1676
1677 new_dFdv[INDEX4(i,0,q,5, numF,DIM,numQuadNodes)] = -df2;
1678 new_dFdv[INDEX4(i,1,q,5, numF,DIM,numQuadNodes)] = df0-df2-df1;
1679 new_dFdv[INDEX4(i,2,q,5, numF,DIM,numQuadNodes)] = df0-df2;
1680
1681 new_dFdv[INDEX4(i,0,q,6, numF,DIM,numQuadNodes)] = -df0+df2;
1682 new_dFdv[INDEX4(i,1,q,6, numF,DIM,numQuadNodes)] = -df0;
1683 new_dFdv[INDEX4(i,2,q,6, numF,DIM,numQuadNodes)] = -df1;
1684
1685 new_dFdv[INDEX4(i,0,q,7, numF,DIM,numQuadNodes)] = df2;
1686 new_dFdv[INDEX4(i,1,q,7, numF,DIM,numQuadNodes)] = -df0+df1+df2;
1687 new_dFdv[INDEX4(i,2,q,7, numF,DIM,numQuadNodes)] = -df0+df2;
1688 }
1689
1690 }
1691 } else {
1692 Finley_setError(MEMORY_ERROR,"Finley_Quad_MacroTet: unable to create quadrature scheme for macro element.");
1693 return -1;
1694 }
1695 #undef DIM
1696 return numSubElements*numQuadNodes;
1697 }
1698
1699
1700 dim_t Finley_Quad_MacroHex(dim_t numSubElements, int numQuadNodes, double* quadNodes, double* quadWeights, dim_t numF, double* dFdv,
1701 dim_t new_len, double* new_quadNodes, double* new_quadWeights , double* new_dFdv)
1702 {
1703
1704 #define DIM 3
1705 dim_t q, i;
1706 register double x0, x1, x2, w, df0, df1, df2;
1707
1708 if (new_len < numSubElements*numQuadNodes) {
1709 Finley_setError(MEMORY_ERROR,"Finley_Quad_MacroHex: array for new qurature scheme is too small");
1710 return -1;
1711 }
1712 if (numSubElements==1) {
1713
1714 for (q=0; q<numQuadNodes; ++q) {
1715
1716 x0=quadNodes[INDEX2(0,q,DIM)];
1717 x1=quadNodes[INDEX2(1,q,DIM)];
1718 x2=quadNodes[INDEX2(2,q,DIM)];
1719 w=quadWeights[q];
1720
1721 new_quadWeights[INDEX2(q,0,numQuadNodes)] =w;
1722 new_quadNodes[INDEX3(0,q,0,DIM,numQuadNodes)] =x0;
1723 new_quadNodes[INDEX3(1,q,0,DIM,numQuadNodes)] =x1;
1724 new_quadNodes[INDEX3(2,q,0,DIM,numQuadNodes)] =x2;
1725
1726 for (i=0;i<numF;i++) {
1727 new_dFdv[INDEX4(i,0,q,0, numF, DIM,numQuadNodes)] = dFdv[INDEX3(i,0,q,numF, DIM)];
1728 new_dFdv[INDEX4(i,1,q,0, numF, DIM,numQuadNodes)] = dFdv[INDEX3(i,1,q,numF, DIM)];
1729 new_dFdv[INDEX4(i,2,q,0, numF, DIM,numQuadNodes)] = dFdv[INDEX3(i,2,q,numF, DIM)];
1730 }
1731 }
1732
1733 } else if (numSubElements==8) {
1734 const double f = 0.125;
1735 for (q=0; q<numQuadNodes; ++q) {
1736
1737 x0=quadNodes[INDEX2(0,q,DIM)];
1738 x1=quadNodes[INDEX2(1,q,DIM)];
1739 x2=quadNodes[INDEX2(2,q,DIM)];
1740 w=f*quadWeights[q];
1741
1742 new_quadWeights[INDEX2(q,0,numQuadNodes)] =w;
1743 new_quadNodes[INDEX3(0,q,0,DIM,numQuadNodes)] =HALF*x0;
1744 new_quadNodes[INDEX3(1,q,0,DIM,numQuadNodes)] =HALF*x1;
1745 new_quadNodes[INDEX3(2,q,0,DIM,numQuadNodes)] =HALF*x2;
1746
1747 new_quadWeights[INDEX2(q,1,numQuadNodes)] =w;
1748 new_quadNodes[INDEX3(0,q,1,DIM,numQuadNodes)] =HALF*(x0+1);
1749 new_quadNodes[INDEX3(1,q,1,DIM,numQuadNodes)] =HALF*x1;
1750 new_quadNodes[INDEX3(2,q,1,DIM,numQuadNodes)] =HALF*x2;
1751
1752 new_quadWeights[INDEX2(q,2,numQuadNodes)] =w;
1753 new_quadNodes[INDEX3(0,q,2,DIM,numQuadNodes)] =HALF*x0;
1754 new_quadNodes[INDEX3(1,q,2,DIM,numQuadNodes)] =HALF*(x1+1);
1755 new_quadNodes[INDEX3(2,q,2,DIM,numQuadNodes)] =HALF*x2;
1756
1757 new_quadWeights[INDEX2(q,3,numQuadNodes)] =w;
1758 new_quadNodes[INDEX3(0,q,3,DIM,numQuadNodes)] =HALF*(x0+1);
1759 new_quadNodes[INDEX3(1,q,3,DIM,numQuadNodes)] =HALF*(x1+1);
1760 new_quadNodes[INDEX3(2,q,3,DIM,numQuadNodes)] =HALF*x2;
1761
1762 new_quadWeights[INDEX2(q,4,numQuadNodes)] =w;
1763 new_quadNodes[INDEX3(0,q,4,DIM,numQuadNodes)] =HALF*x0;
1764 new_quadNodes[INDEX3(1,q,4,DIM,numQuadNodes)] =HALF*x1;
1765 new_quadNodes[INDEX3(2,q,4,DIM,numQuadNodes)] =HALF*(x2+1);
1766
1767 new_quadWeights[INDEX2(q,5,numQuadNodes)] =w;
1768 new_quadNodes[INDEX3(0,q,5,DIM,numQuadNodes)] =HALF*(x0+1);
1769 new_quadNodes[INDEX3(1,q,5,DIM,numQuadNodes)] =HALF*x1;
1770 new_quadNodes[INDEX3(2,q,5,DIM,numQuadNodes)] =HALF*(x2+1);
1771
1772 new_quadWeights[INDEX2(q,6,numQuadNodes)] =w;
1773 new_quadNodes[INDEX3(0,q,6,DIM,numQuadNodes)] =HALF*x0;
1774 new_quadNodes[INDEX3(1,q,6,DIM,numQuadNodes)] =HALF*(x1+1);
1775 new_quadNodes[INDEX3(2,q,6,DIM,numQuadNodes)] =HALF*(x2+1);
1776
1777 new_quadWeights[INDEX2(q,7,numQuadNodes)] =w;
1778 new_quadNodes[INDEX3(0,q,7,DIM,numQuadNodes)] =HALF*(x0+1);
1779 new_quadNodes[INDEX3(1,q,7,DIM,numQuadNodes)] =HALF*(x1+1);
1780 new_quadNodes[INDEX3(2,q,7,DIM,numQuadNodes)] =HALF*(x2+1);
1781
1782 for (i=0;i<numF;i++) {
1783 df0=dFdv[INDEX3(i,0,q, numF, DIM)]*TWO;
1784 df1=dFdv[INDEX3(i,1,q, numF, DIM)]*TWO;
1785 df2=dFdv[INDEX3(i,2,q, numF, DIM)]*TWO;
1786
1787 new_dFdv[INDEX4(i,0,q,0, numF,DIM,numQuadNodes)] = df0;
1788 new_dFdv[INDEX4(i,1,q,0, numF,DIM,numQuadNodes)] = df1;
1789 new_dFdv[INDEX4(i,2,q,0, numF,DIM,numQuadNodes)] = df2;
1790
1791 new_dFdv[INDEX4(i,0,q,1, numF,DIM,numQuadNodes)] = df0;
1792 new_dFdv[INDEX4(i,1,q,1, numF,DIM,numQuadNodes)] = df1;
1793 new_dFdv[INDEX4(i,2,q,1, numF,DIM,numQuadNodes)] = df2;
1794
1795 new_dFdv[INDEX4(i,0,q,2, numF,DIM,numQuadNodes)] = df0;
1796 new_dFdv[INDEX4(i,1,q,2, numF,DIM,numQuadNodes)] = df1;
1797 new_dFdv[INDEX4(i,2,q,2, numF,DIM,numQuadNodes)] = df2;
1798
1799 new_dFdv[INDEX4(i,0,q,3, numF,DIM,numQuadNodes)] = df0;
1800 new_dFdv[INDEX4(i,1,q,3, numF,DIM,numQuadNodes)] = df1;
1801 new_dFdv[INDEX4(i,2,q,3, numF,DIM,numQuadNodes)] = df2;
1802
1803 new_dFdv[INDEX4(i,0,q,4, numF,DIM,numQuadNodes)] = df0;
1804 new_dFdv[INDEX4(i,1,q,4, numF,DIM,numQuadNodes)] = df1;
1805 new_dFdv[INDEX4(i,2,q,4, numF,DIM,numQuadNodes)] = df2;
1806
1807 new_dFdv[INDEX4(i,0,q,5, numF,DIM,numQuadNodes)] = df0;
1808 new_dFdv[INDEX4(i,1,q,5, numF,DIM,numQuadNodes)] = df1;
1809 new_dFdv[INDEX4(i,2,q,5, numF,DIM,numQuadNodes)] = df2;
1810
1811 new_dFdv[INDEX4(i,0,q,6, numF,DIM,numQuadNodes)] = df0;
1812 new_dFdv[INDEX4(i,1,q,6, numF,DIM,numQuadNodes)] = df1;
1813 new_dFdv[INDEX4(i,2,q,6, numF,DIM,numQuadNodes)] = df2;
1814
1815 new_dFdv[INDEX4(i,0,q,7, numF,DIM,numQuadNodes)] = df0;
1816 new_dFdv[INDEX4(i,1,q,7, numF,DIM,numQuadNodes)] = df1;
1817 new_dFdv[INDEX4(i,2,q,7, numF,DIM,numQuadNodes)] = df2;
1818 }
1819
1820 }
1821 } else {
1822 Finley_setError(MEMORY_ERROR,"Finley_Quad_MacroHex: unable to create quadrature scheme for macro element.");
1823 return -1;
1824 }
1825 #undef DIM
1826 return numSubElements*numQuadNodes;
1827 }

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