libMesh
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quadrature_gauss_1D.C
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1// The libMesh Finite Element Library.
2// Copyright (C) 2002-2026 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
3
4// This library is free software; you can redistribute it and/or
5// modify it under the terms of the GNU Lesser General Public
6// License as published by the Free Software Foundation; either
7// version 2.1 of the License, or (at your option) any later version.
8
9// This library is distributed in the hope that it will be useful,
10// but WITHOUT ANY WARRANTY; without even the implied warranty of
11// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
12// Lesser General Public License for more details.
13
14// You should have received a copy of the GNU Lesser General Public
15// License along with this library; if not, write to the Free Software
16// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
17
18
19
20// C++ includes
21
22// Local includes
23#include "libmesh/quadrature_gauss.h"
24
25namespace libMesh
26{
27
28
29
30void QGauss::init_1D()
31{
32 //----------------------------------------------------------------------
33 // 1D quadrature rules
34 switch(get_order())
35 {
36 case CONSTANT:
37 case FIRST:
38 {
39 _points.resize (1);
40 _weights.resize(1);
41
42 _points[0](0) = 0.;
43
44 _weights[0] = 2.;
45
46 return;
47 }
48 case SECOND:
49 case THIRD:
50 {
51 _points.resize (2);
52 _weights.resize(2);
53
54 _points[0](0) = -std::sqrt(Real(3))/3;
55 _points[1] = -_points[0];
56
57 _weights[0] = 1.;
58 _weights[1] = _weights[0];
59
60 return;
61 }
62 case FOURTH:
63 case FIFTH:
64 {
65 _points.resize (3);
66 _weights.resize(3);
67
68 _points[ 0](0) = -7.7459666924148337703585307995648e-01_R;
69 _points[ 1](0) = 0.;
70 _points[ 2] = -_points[0];
71
72 _weights[ 0] = Real(5)/9;
73 _weights[ 1] = Real(8)/9;
74 _weights[ 2] = _weights[0];
75
76 return;
77 }
78 case SIXTH:
79 case SEVENTH:
80 {
81 _points.resize (4);
82 _weights.resize(4);
83
84 _points[ 0](0) = -8.6113631159405257522394648889281e-01_R;
85 _points[ 1](0) = -3.3998104358485626480266575910324e-01_R;
86 _points[ 2] = -_points[1];
87 _points[ 3] = -_points[0];
88
89 _weights[ 0] = 3.4785484513745385737306394922200e-01_R;
90 _weights[ 1] = 6.5214515486254614262693605077800e-01_R;
91 _weights[ 2] = _weights[1];
92 _weights[ 3] = _weights[0];
93
94 return;
95 }
96 case EIGHTH:
97 case NINTH:
98 {
99 _points.resize (5);
100 _weights.resize(5);
101
102 _points[ 0](0) = -9.0617984593866399279762687829939e-01_R;
103 _points[ 1](0) = -5.3846931010568309103631442070021e-01_R;
104 _points[ 2](0) = 0.;
105 _points[ 3] = -_points[1];
106 _points[ 4] = -_points[0];
107
108 _weights[ 0] = 2.3692688505618908751426404071992e-01_R;
109 _weights[ 1] = 4.7862867049936646804129151483564e-01_R;
110 _weights[ 2] = 5.6888888888888888888888888888889e-01_R;
111 _weights[ 3] = _weights[1];
112 _weights[ 4] = _weights[0];
113
114 return;
115 }
116 case TENTH:
117 case ELEVENTH:
118 {
119 _points.resize (6);
120 _weights.resize(6);
121
122 _points[ 0](0) = -9.3246951420315202781230155449399e-01_R;
123 _points[ 1](0) = -6.6120938646626451366139959501991e-01_R;
124 _points[ 2](0) = -2.3861918608319690863050172168071e-01_R;
125 _points[ 3] = -_points[2];
126 _points[ 4] = -_points[1];
127 _points[ 5] = -_points[0];
128
129 _weights[ 0] = 1.7132449237917034504029614217273e-01_R;
130 _weights[ 1] = 3.6076157304813860756983351383772e-01_R;
131 _weights[ 2] = 4.6791393457269104738987034398955e-01_R;
132 _weights[ 3] = _weights[2];
133 _weights[ 4] = _weights[1];
134 _weights[ 5] = _weights[0];
135
136 return;
137 }
138 case TWELFTH:
139 case THIRTEENTH:
140 {
141 _points.resize (7);
142 _weights.resize(7);
143
144 _points[ 0](0) = -9.4910791234275852452618968404785e-01_R;
145 _points[ 1](0) = -7.4153118559939443986386477328079e-01_R;
146 _points[ 2](0) = -4.0584515137739716690660641207696e-01_R;
147 _points[ 3](0) = 0.;
148 _points[ 4] = -_points[2];
149 _points[ 5] = -_points[1];
150 _points[ 6] = -_points[0];
151
152 _weights[ 0] = 1.2948496616886969327061143267908e-01_R;
153 _weights[ 1] = 2.7970539148927666790146777142378e-01_R;
154 _weights[ 2] = 3.8183005050511894495036977548898e-01_R;
155 _weights[ 3] = 4.1795918367346938775510204081633e-01_R;
156 _weights[ 4] = _weights[2];
157 _weights[ 5] = _weights[1];
158 _weights[ 6] = _weights[0];
159
160 return;
161 }
162 case FOURTEENTH:
163 case FIFTEENTH:
164 {
165 _points.resize (8);
166 _weights.resize(8);
167
168 _points[ 0](0) = -9.6028985649753623168356086856947e-01_R;
169 _points[ 1](0) = -7.9666647741362673959155393647583e-01_R;
170 _points[ 2](0) = -5.2553240991632898581773904918925e-01_R;
171 _points[ 3](0) = -1.8343464249564980493947614236018e-01_R;
172 _points[ 4] = -_points[3];
173 _points[ 5] = -_points[2];
174 _points[ 6] = -_points[1];
175 _points[ 7] = -_points[0];
176
177 _weights[ 0] = 1.0122853629037625915253135430996e-01_R;
178 _weights[ 1] = 2.2238103445337447054435599442624e-01_R;
179 _weights[ 2] = 3.1370664587788728733796220198660e-01_R;
180 _weights[ 3] = 3.6268378337836198296515044927720e-01_R;
181 _weights[ 4] = _weights[3];
182 _weights[ 5] = _weights[2];
183 _weights[ 6] = _weights[1];
184 _weights[ 7] = _weights[0];
185
186 return;
187 }
188 case SIXTEENTH:
189 case SEVENTEENTH:
190 {
191 _points.resize (9);
192 _weights.resize(9);
193
194 _points[ 0](0) = -9.6816023950762608983557620290367e-01_R;
195 _points[ 1](0) = -8.3603110732663579429942978806973e-01_R;
196 _points[ 2](0) = -6.1337143270059039730870203934147e-01_R;
197 _points[ 3](0) = -3.2425342340380892903853801464334e-01_R;
198 _points[ 4](0) = 0.;
199 _points[ 5] = -_points[3];
200 _points[ 6] = -_points[2];
201 _points[ 7] = -_points[1];
202 _points[ 8] = -_points[0];
203
204 _weights[ 0] = 8.1274388361574411971892158110524e-02_R;
205 _weights[ 1] = 1.8064816069485740405847203124291e-01_R;
206 _weights[ 2] = 2.6061069640293546231874286941863e-01_R;
207 _weights[ 3] = 3.1234707704000284006863040658444e-01_R;
208 _weights[ 4] = 3.3023935500125976316452506928697e-01_R;
209 _weights[ 5] = _weights[3];
210 _weights[ 6] = _weights[2];
211 _weights[ 7] = _weights[1];
212 _weights[ 8] = _weights[0];
213
214 return;
215 }
216 case EIGHTTEENTH:
217 case NINETEENTH:
218 {
219 _points.resize (10);
220 _weights.resize(10);
221
222 _points[ 0](0) = -9.7390652851717172007796401208445e-01_R;
223 _points[ 1](0) = -8.6506336668898451073209668842349e-01_R;
224 _points[ 2](0) = -6.7940956829902440623432736511487e-01_R;
225 _points[ 3](0) = -4.3339539412924719079926594316578e-01_R;
226 _points[ 4](0) = -1.4887433898163121088482600112972e-01_R;
227 _points[ 5] = -_points[4];
228 _points[ 6] = -_points[3];
229 _points[ 7] = -_points[2];
230 _points[ 8] = -_points[1];
231 _points[ 9] = -_points[0];
232
233 _weights[ 0] = 6.6671344308688137593568809893332e-02_R;
234 _weights[ 1] = 1.4945134915058059314577633965770e-01_R;
235 _weights[ 2] = 2.1908636251598204399553493422816e-01_R;
236 _weights[ 3] = 2.6926671930999635509122692156947e-01_R;
237 _weights[ 4] = 2.9552422471475287017389299465134e-01_R;
238 _weights[ 5] = _weights[4];
239 _weights[ 6] = _weights[3];
240 _weights[ 7] = _weights[2];
241 _weights[ 8] = _weights[1];
242 _weights[ 9] = _weights[0];
243
244 return;
245 }
246
247 case TWENTIETH:
248 case TWENTYFIRST:
249 {
250 _points.resize (11);
251 _weights.resize(11);
252
253 _points[ 0](0) = -9.7822865814605699280393800112286e-01_R;
254 _points[ 1](0) = -8.8706259976809529907515776930393e-01_R;
255 _points[ 2](0) = -7.3015200557404932409341625203115e-01_R;
256 _points[ 3](0) = -5.1909612920681181592572566945861e-01_R;
257 _points[ 4](0) = -2.6954315595234497233153198540086e-01_R;
258 _points[ 5](0) = 0.;
259 _points[ 6] = -_points[4];
260 _points[ 7] = -_points[3];
261 _points[ 8] = -_points[2];
262 _points[ 9] = -_points[1];
263 _points[10] = -_points[0];
264
265 _weights[ 0] = 5.5668567116173666482753720442549e-02_R;
266 _weights[ 1] = 1.2558036946490462463469429922394e-01_R;
267 _weights[ 2] = 1.8629021092773425142609764143166e-01_R;
268 _weights[ 3] = 2.3319376459199047991852370484318e-01_R;
269 _weights[ 4] = 2.6280454451024666218068886989051e-01_R;
270 _weights[ 5] = 2.7292508677790063071448352833634e-01_R;
271 _weights[ 6] = _weights[4];
272 _weights[ 7] = _weights[3];
273 _weights[ 8] = _weights[2];
274 _weights[ 9] = _weights[1];
275 _weights[10] = _weights[0];
276
277 return;
278 }
279
280 case TWENTYSECOND:
281 case TWENTYTHIRD:
282 {
283 _points.resize (12);
284 _weights.resize(12);
285
286 _points[ 0](0) = -9.8156063424671925069054909014928e-01_R;
287 _points[ 1](0) = -9.0411725637047485667846586611910e-01_R;
288 _points[ 2](0) = -7.6990267419430468703689383321282e-01_R;
289 _points[ 3](0) = -5.8731795428661744729670241894053e-01_R;
290 _points[ 4](0) = -3.6783149899818019375269153664372e-01_R;
291 _points[ 5](0) = -1.2523340851146891547244136946385e-01_R;
292 _points[ 6] = -_points[5];
293 _points[ 7] = -_points[4];
294 _points[ 8] = -_points[3];
295 _points[ 9] = -_points[2];
296 _points[10] = -_points[1];
297 _points[11] = -_points[0];
298
299 _weights[ 0] = 4.7175336386511827194615961485017e-02_R;
300 _weights[ 1] = 1.0693932599531843096025471819400e-01_R;
301 _weights[ 2] = 1.6007832854334622633465252954336e-01_R;
302 _weights[ 3] = 2.0316742672306592174906445580980e-01_R;
303 _weights[ 4] = 2.3349253653835480876084989892483e-01_R;
304 _weights[ 5] = 2.4914704581340278500056243604295e-01_R;
305 _weights[ 6] = _weights[5];
306 _weights[ 7] = _weights[4];
307 _weights[ 8] = _weights[3];
308 _weights[ 9] = _weights[2];
309 _weights[10] = _weights[1];
310 _weights[11] = _weights[0];
311
312 return;
313 }
314
315 case TWENTYFOURTH:
316 case TWENTYFIFTH:
317 {
318 _points.resize (13);
319 _weights.resize(13);
320
321 _points[ 0](0) = -9.8418305471858814947282944880711e-01_R;
322 _points[ 1](0) = -9.1759839922297796520654783650072e-01_R;
323 _points[ 2](0) = -8.0157809073330991279420648958286e-01_R;
324 _points[ 3](0) = -6.4234933944034022064398460699552e-01_R;
325 _points[ 4](0) = -4.4849275103644685287791285212764e-01_R;
326 _points[ 5](0) = -2.3045831595513479406552812109799e-01_R;
327 _points[ 6](0) = 0.;
328 _points[ 7] = -_points[5];
329 _points[ 8] = -_points[4];
330 _points[ 9] = -_points[3];
331 _points[10] = -_points[2];
332 _points[11] = -_points[1];
333 _points[12] = -_points[0];
334
335 _weights[ 0] = 4.0484004765315879520021592200986e-02_R;
336 _weights[ 1] = 9.2121499837728447914421775953797e-02_R;
337 _weights[ 2] = 1.3887351021978723846360177686887e-01_R;
338 _weights[ 3] = 1.7814598076194573828004669199610e-01_R;
339 _weights[ 4] = 2.0781604753688850231252321930605e-01_R;
340 _weights[ 5] = 2.2628318026289723841209018603978e-01_R;
341 _weights[ 6] = 2.3255155323087391019458951526884e-01_R;
342 _weights[ 7] = _weights[5];
343 _weights[ 8] = _weights[4];
344 _weights[ 9] = _weights[3];
345 _weights[10] = _weights[2];
346 _weights[11] = _weights[1];
347 _weights[12] = _weights[0];
348
349 return;
350 }
351
352 case TWENTYSIXTH:
353 case TWENTYSEVENTH:
354 {
355 _points.resize (14);
356 _weights.resize(14);
357
358 _points[ 0](0) = -9.8628380869681233884159726670405e-01_R;
359 _points[ 1](0) = -9.2843488366357351733639113937787e-01_R;
360 _points[ 2](0) = -8.2720131506976499318979474265039e-01_R;
361 _points[ 3](0) = -6.8729290481168547014801980301933e-01_R;
362 _points[ 4](0) = -5.1524863635815409196529071855119e-01_R;
363 _points[ 5](0) = -3.1911236892788976043567182416848e-01_R;
364 _points[ 6](0) = -1.0805494870734366206624465021983e-01_R;
365 _points[ 7] = -_points[6];
366 _points[ 8] = -_points[5];
367 _points[ 9] = -_points[4];
368 _points[10] = -_points[3];
369 _points[11] = -_points[2];
370 _points[12] = -_points[1];
371 _points[13] = -_points[0];
372
373 _weights[ 0] = 3.5119460331751863031832876138192e-02_R;
374 _weights[ 1] = 8.0158087159760209805633277062854e-02_R;
375 _weights[ 2] = 1.2151857068790318468941480907248e-01_R;
376 _weights[ 3] = 1.5720316715819353456960193862384e-01_R;
377 _weights[ 4] = 1.8553839747793781374171659012516e-01_R;
378 _weights[ 5] = 2.0519846372129560396592406566122e-01_R;
379 _weights[ 6] = 2.1526385346315779019587644331626e-01_R;
380 _weights[ 7] = _weights[6];
381 _weights[ 8] = _weights[5];
382 _weights[ 9] = _weights[4];
383 _weights[10] = _weights[3];
384 _weights[11] = _weights[2];
385 _weights[12] = _weights[1];
386 _weights[13] = _weights[0];
387
388 return;
389 }
390
391 case TWENTYEIGHTH:
392 case TWENTYNINTH:
393 {
394 _points.resize (15);
395 _weights.resize(15);
396
397 _points[ 0](0) = -9.8799251802048542848956571858661e-01_R;
398 _points[ 1](0) = -9.3727339240070590430775894771021e-01_R;
399 _points[ 2](0) = -8.4820658341042721620064832077422e-01_R;
400 _points[ 3](0) = -7.2441773136017004741618605461394e-01_R;
401 _points[ 4](0) = -5.7097217260853884753722673725391e-01_R;
402 _points[ 5](0) = -3.9415134707756336989720737098105e-01_R;
403 _points[ 6](0) = -2.0119409399743452230062830339460e-01_R;
404 _points[ 7](0) = 0.;
405 _points[ 8] = -_points[6];
406 _points[ 9] = -_points[5];
407 _points[10] = -_points[4];
408 _points[11] = -_points[3];
409 _points[12] = -_points[2];
410 _points[13] = -_points[1];
411 _points[14] = -_points[0];
412
413 _weights[ 0] = 3.0753241996117268354628393577204e-02_R;
414 _weights[ 1] = 7.0366047488108124709267416450667e-02_R;
415 _weights[ 2] = 1.0715922046717193501186954668587e-01_R;
416 _weights[ 3] = 1.3957067792615431444780479451103e-01_R;
417 _weights[ 4] = 1.6626920581699393355320086048121e-01_R;
418 _weights[ 5] = 1.8616100001556221102680056186642e-01_R;
419 _weights[ 6] = 1.9843148532711157645611832644384e-01_R;
420 _weights[ 7] = 2.0257824192556127288062019996752e-01_R;
421 _weights[ 8] = _weights[6];
422 _weights[ 9] = _weights[5];
423 _weights[10] = _weights[4];
424 _weights[11] = _weights[3];
425 _weights[12] = _weights[2];
426 _weights[13] = _weights[1];
427 _weights[14] = _weights[0];
428
429 return;
430 }
431
432 case THIRTIETH:
433 case THIRTYFIRST:
434 {
435 _points.resize (16);
436 _weights.resize(16);
437
438 _points[ 0](0) = -9.8940093499164993259615417345033e-01_R;
439 _points[ 1](0) = -9.4457502307323257607798841553461e-01_R;
440 _points[ 2](0) = -8.6563120238783174388046789771239e-01_R;
441 _points[ 3](0) = -7.5540440835500303389510119484744e-01_R;
442 _points[ 4](0) = -6.1787624440264374844667176404879e-01_R;
443 _points[ 5](0) = -4.5801677765722738634241944298358e-01_R;
444 _points[ 6](0) = -2.8160355077925891323046050146050e-01_R;
445 _points[ 7](0) = -9.5012509837637440185319335424958e-02_R;
446 _points[ 8] = -_points[7];
447 _points[ 9] = -_points[6];
448 _points[10] = -_points[5];
449 _points[11] = -_points[4];
450 _points[12] = -_points[3];
451 _points[13] = -_points[2];
452 _points[14] = -_points[1];
453 _points[15] = -_points[0];
454
455 _weights[ 0] = 2.7152459411754094851780572456018e-02_R;
456 _weights[ 1] = 6.2253523938647892862843836994378e-02_R;
457 _weights[ 2] = 9.5158511682492784809925107602246e-02_R;
458 _weights[ 3] = 1.2462897125553387205247628219202e-01_R;
459 _weights[ 4] = 1.4959598881657673208150173054748e-01_R;
460 _weights[ 5] = 1.6915651939500253818931207903033e-01_R;
461 _weights[ 6] = 1.8260341504492358886676366796922e-01_R;
462 _weights[ 7] = 1.8945061045506849628539672320828e-01_R;
463 _weights[ 8] = _weights[7];
464 _weights[ 9] = _weights[6];
465 _weights[10] = _weights[5];
466 _weights[11] = _weights[4];
467 _weights[12] = _weights[3];
468 _weights[13] = _weights[2];
469 _weights[14] = _weights[1];
470 _weights[15] = _weights[0];
471
472 return;
473 }
474
475 case THIRTYSECOND:
476 case THIRTYTHIRD:
477 {
478 _points.resize (17);
479 _weights.resize(17);
480
481 _points[ 0](0) = -9.9057547531441733567543401994067e-01_R;
482 _points[ 1](0) = -9.5067552176876776122271695789580e-01_R;
483 _points[ 2](0) = -8.8023915372698590212295569448816e-01_R;
484 _points[ 3](0) = -7.8151400389680140692523005552048e-01_R;
485 _points[ 4](0) = -6.5767115921669076585030221664300e-01_R;
486 _points[ 5](0) = -5.1269053708647696788624656862955e-01_R;
487 _points[ 6](0) = -3.5123176345387631529718551709535e-01_R;
488 _points[ 7](0) = -1.7848418149584785585067749365407e-01_R;
489 _points[ 8](0) = 0.;
490 _points[ 9] = -_points[7];
491 _points[10] = -_points[6];
492 _points[11] = -_points[5];
493 _points[12] = -_points[4];
494 _points[13] = -_points[3];
495 _points[14] = -_points[2];
496 _points[15] = -_points[1];
497 _points[16] = -_points[0];
498
499 _weights[ 0] = 2.4148302868547931960110026287565e-02_R;
500 _weights[ 1] = 5.5459529373987201129440165358245e-02_R;
501 _weights[ 2] = 8.5036148317179180883535370191062e-02_R;
502 _weights[ 3] = 1.1188384719340397109478838562636e-01_R;
503 _weights[ 4] = 1.3513636846852547328631998170235e-01_R;
504 _weights[ 5] = 1.5404576107681028808143159480196e-01_R;
505 _weights[ 6] = 1.6800410215645004450997066378832e-01_R;
506 _weights[ 7] = 1.7656270536699264632527099011320e-01_R;
507 _weights[ 8] = 1.7944647035620652545826564426189e-01_R;
508 _weights[ 9] = _weights[7];
509 _weights[10] = _weights[6];
510 _weights[11] = _weights[5];
511 _weights[12] = _weights[4];
512 _weights[13] = _weights[3];
513 _weights[14] = _weights[2];
514 _weights[15] = _weights[1];
515 _weights[16] = _weights[0];
516
517 return;
518 }
519
520 case THIRTYFOURTH:
521 case THIRTYFIFTH:
522 {
523 _points.resize (18);
524 _weights.resize(18);
525
526 _points[ 0](0) = -9.9156516842093094673001600470615e-01_R;
527 _points[ 1](0) = -9.5582394957139775518119589292978e-01_R;
528 _points[ 2](0) = -8.9260246649755573920606059112715e-01_R;
529 _points[ 3](0) = -8.0370495897252311568241745501459e-01_R;
530 _points[ 4](0) = -6.9168704306035320787489108128885e-01_R;
531 _points[ 5](0) = -5.5977083107394753460787154852533e-01_R;
532 _points[ 6](0) = -4.1175116146284264603593179383305e-01_R;
533 _points[ 7](0) = -2.5188622569150550958897285487791e-01_R;
534 _points[ 8](0) = -8.4775013041735301242261852935784e-02_R;
535 _points[ 9] = -_points[8];
536 _points[10] = -_points[7];
537 _points[11] = -_points[6];
538 _points[12] = -_points[5];
539 _points[13] = -_points[4];
540 _points[14] = -_points[3];
541 _points[15] = -_points[2];
542 _points[16] = -_points[1];
543 _points[17] = -_points[0];
544
545 _weights[ 0] = 2.1616013526483310313342710266452e-02_R;
546 _weights[ 1] = 4.9714548894969796453334946202639e-02_R;
547 _weights[ 2] = 7.6425730254889056529129677616637e-02_R;
548 _weights[ 3] = 1.0094204410628716556281398492483e-01_R;
549 _weights[ 4] = 1.2255520671147846018451912680020e-01_R;
550 _weights[ 5] = 1.4064291467065065120473130375195e-01_R;
551 _weights[ 6] = 1.5468467512626524492541800383637e-01_R;
552 _weights[ 7] = 1.6427648374583272298605377646593e-01_R;
553 _weights[ 8] = 1.6914238296314359184065647013499e-01_R;
554 _weights[ 9] = _weights[8];
555 _weights[10] = _weights[7];
556 _weights[11] = _weights[6];
557 _weights[12] = _weights[5];
558 _weights[13] = _weights[4];
559 _weights[14] = _weights[3];
560 _weights[15] = _weights[2];
561 _weights[16] = _weights[1];
562 _weights[17] = _weights[0];
563
564 return;
565 }
566
567 case THIRTYSIXTH:
568 case THIRTYSEVENTH:
569 {
570 _points.resize (19);
571 _weights.resize(19);
572
573 _points[ 0](0) = -9.9240684384358440318901767025326e-01_R;
574 _points[ 1](0) = -9.6020815213483003085277884068765e-01_R;
575 _points[ 2](0) = -9.0315590361481790164266092853231e-01_R;
576 _points[ 3](0) = -8.2271465653714282497892248671271e-01_R;
577 _points[ 4](0) = -7.2096617733522937861709586082378e-01_R;
578 _points[ 5](0) = -6.0054530466168102346963816494624e-01_R;
579 _points[ 6](0) = -4.6457074137596094571726714810410e-01_R;
580 _points[ 7](0) = -3.1656409996362983199011732884984e-01_R;
581 _points[ 8](0) = -1.6035864564022537586809611574074e-01_R;
582 _points[ 9](0) = 0.;
583 _points[10] = -_points[8];
584 _points[11] = -_points[7];
585 _points[12] = -_points[6];
586 _points[13] = -_points[5];
587 _points[14] = -_points[4];
588 _points[15] = -_points[3];
589 _points[16] = -_points[2];
590 _points[17] = -_points[1];
591 _points[18] = -_points[0];
592
593 _weights[ 0] = 1.9461788229726477036312041464438e-02_R;
594 _weights[ 1] = 4.4814226765699600332838157401994e-02_R;
595 _weights[ 2] = 6.9044542737641226580708258006013e-02_R;
596 _weights[ 3] = 9.1490021622449999464462094123840e-02_R;
597 _weights[ 4] = 1.1156664554733399471602390168177e-01_R;
598 _weights[ 5] = 1.2875396253933622767551578485688e-01_R;
599 _weights[ 6] = 1.4260670217360661177574610944190e-01_R;
600 _weights[ 7] = 1.5276604206585966677885540089766e-01_R;
601 _weights[ 8] = 1.5896884339395434764995643946505e-01_R;
602 _weights[ 9] = 1.6105444984878369597916362532092e-01_R;
603 _weights[10] = _weights[8];
604 _weights[11] = _weights[7];
605 _weights[12] = _weights[6];
606 _weights[13] = _weights[5];
607 _weights[14] = _weights[4];
608 _weights[15] = _weights[3];
609 _weights[16] = _weights[2];
610 _weights[17] = _weights[1];
611 _weights[18] = _weights[0];
612
613 return;
614 }
615
616 case THIRTYEIGHTH:
617 case THIRTYNINTH:
618 {
619 _points.resize (20);
620 _weights.resize(20);
621
622 _points[ 0](0) = -9.9312859918509492478612238847132e-01_R;
623 _points[ 1](0) = -9.6397192727791379126766613119728e-01_R;
624 _points[ 2](0) = -9.1223442825132590586775244120330e-01_R;
625 _points[ 3](0) = -8.3911697182221882339452906170152e-01_R;
626 _points[ 4](0) = -7.4633190646015079261430507035564e-01_R;
627 _points[ 5](0) = -6.3605368072651502545283669622629e-01_R;
628 _points[ 6](0) = -5.1086700195082709800436405095525e-01_R;
629 _points[ 7](0) = -3.7370608871541956067254817702493e-01_R;
630 _points[ 8](0) = -2.2778585114164507808049619536857e-01_R;
631 _points[ 9](0) = -7.6526521133497333754640409398838e-02_R;
632 _points[10] = -_points[9];
633 _points[11] = -_points[8];
634 _points[12] = -_points[7];
635 _points[13] = -_points[6];
636 _points[14] = -_points[5];
637 _points[15] = -_points[4];
638 _points[16] = -_points[3];
639 _points[17] = -_points[2];
640 _points[18] = -_points[1];
641 _points[19] = -_points[0];
642
643 _weights[ 0] = 1.7614007139152118311861962351853e-02_R;
644 _weights[ 1] = 4.0601429800386941331039952274932e-02_R;
645 _weights[ 2] = 6.2672048334109063569506535187042e-02_R;
646 _weights[ 3] = 8.3276741576704748724758143222046e-02_R;
647 _weights[ 4] = 1.0193011981724043503675013548035e-01_R;
648 _weights[ 5] = 1.1819453196151841731237737771138e-01_R;
649 _weights[ 6] = 1.3168863844917662689849449974816e-01_R;
650 _weights[ 7] = 1.4209610931838205132929832506716e-01_R;
651 _weights[ 8] = 1.4917298647260374678782873700197e-01_R;
652 _weights[ 9] = 1.5275338713072585069808433195510e-01_R;
653 _weights[10] = _weights[9];
654 _weights[11] = _weights[8];
655 _weights[12] = _weights[7];
656 _weights[13] = _weights[6];
657 _weights[14] = _weights[5];
658 _weights[15] = _weights[4];
659 _weights[16] = _weights[3];
660 _weights[17] = _weights[2];
661 _weights[18] = _weights[1];
662 _weights[19] = _weights[0];
663
664 return;
665 }
666
667 case FORTIETH:
668 case FORTYFIRST:
669 {
670 _points.resize (21);
671 _weights.resize(21);
672
673 _points[ 0](0) = -9.9375217062038950026024203593794e-01_R;
674 _points[ 1](0) = -9.6722683856630629431662221490770e-01_R;
675 _points[ 2](0) = -9.2009933415040082879018713371497e-01_R;
676 _points[ 3](0) = -8.5336336458331728364725063858757e-01_R;
677 _points[ 4](0) = -7.6843996347567790861587785130623e-01_R;
678 _points[ 5](0) = -6.6713880419741231930596666999034e-01_R;
679 _points[ 6](0) = -5.5161883588721980705901879672431e-01_R;
680 _points[ 7](0) = -4.2434212020743878357366888854379e-01_R;
681 _points[ 8](0) = -2.8802131680240109660079251606460e-01_R;
682 _points[ 9](0) = -1.4556185416089509093703098233869e-01_R;
683 _points[10](0) = 0.;
684 _points[11] = -_points[9];
685 _points[12] = -_points[8];
686 _points[13] = -_points[7];
687 _points[14] = -_points[6];
688 _points[15] = -_points[5];
689 _points[16] = -_points[4];
690 _points[17] = -_points[3];
691 _points[18] = -_points[2];
692 _points[19] = -_points[1];
693 _points[20] = -_points[0];
694
695 _weights[ 0] = 1.6017228257774333324224616858471e-02_R;
696 _weights[ 1] = 3.6953789770852493799950668299330e-02_R;
697 _weights[ 2] = 5.7134425426857208283635826472448e-02_R;
698 _weights[ 3] = 7.6100113628379302017051653300183e-02_R;
699 _weights[ 4] = 9.3444423456033861553289741113932e-02_R;
700 _weights[ 5] = 1.0879729916714837766347457807011e-01_R;
701 _weights[ 6] = 1.2183141605372853419536717712572e-01_R;
702 _weights[ 7] = 1.3226893863333746178105257449678e-01_R;
703 _weights[ 8] = 1.3988739479107315472213342386758e-01_R;
704 _weights[ 9] = 1.4452440398997005906382716655375e-01_R;
705 _weights[10] = 1.4608113364969042719198514768337e-01_R;
706 _weights[11] = _weights[9];
707 _weights[12] = _weights[8];
708 _weights[13] = _weights[7];
709 _weights[14] = _weights[6];
710 _weights[15] = _weights[5];
711 _weights[16] = _weights[4];
712 _weights[17] = _weights[3];
713 _weights[18] = _weights[2];
714 _weights[19] = _weights[1];
715 _weights[20] = _weights[0];
716
717 return;
718 }
719
720 case FORTYSECOND:
721 case FORTYTHIRD:
722 {
723 _points.resize (22);
724 _weights.resize(22);
725
726 _points[ 0](0) = -9.9429458548239929207303142116130e-01_R;
727 _points[ 1](0) = -9.7006049783542872712395098676527e-01_R;
728 _points[ 2](0) = -9.2695677218717400052069293925905e-01_R;
729 _points[ 3](0) = -8.6581257772030013653642563701938e-01_R;
730 _points[ 4](0) = -7.8781680597920816200427795540835e-01_R;
731 _points[ 5](0) = -6.9448726318668278005068983576226e-01_R;
732 _points[ 6](0) = -5.8764040350691159295887692763865e-01_R;
733 _points[ 7](0) = -4.6935583798675702640633071096641e-01_R;
734 _points[ 8](0) = -3.4193582089208422515814742042738e-01_R;
735 _points[ 9](0) = -2.0786042668822128547884653391955e-01_R;
736 _points[10](0) = -6.9739273319722221213841796118628e-02_R;
737 _points[11] = -_points[10];
738 _points[12] = -_points[9];
739 _points[13] = -_points[8];
740 _points[14] = -_points[7];
741 _points[15] = -_points[6];
742 _points[16] = -_points[5];
743 _points[17] = -_points[4];
744 _points[18] = -_points[3];
745 _points[19] = -_points[2];
746 _points[20] = -_points[1];
747 _points[21] = -_points[0];
748
749 _weights[ 0] = 1.4627995298272200684991098047185e-02_R;
750 _weights[ 1] = 3.3774901584814154793302246865913e-02_R;
751 _weights[ 2] = 5.2293335152683285940312051273211e-02_R;
752 _weights[ 3] = 6.9796468424520488094961418930218e-02_R;
753 _weights[ 4] = 8.5941606217067727414443681372703e-02_R;
754 _weights[ 5] = 1.0041414444288096493207883783054e-01_R;
755 _weights[ 6] = 1.1293229608053921839340060742175e-01_R;
756 _weights[ 7] = 1.2325237681051242428556098615481e-01_R;
757 _weights[ 8] = 1.3117350478706237073296499253031e-01_R;
758 _weights[ 9] = 1.3654149834601517135257383123152e-01_R;
759 _weights[10] = 1.3925187285563199337541024834181e-01_R;
760 _weights[11] = _weights[10];
761 _weights[12] = _weights[9];
762 _weights[13] = _weights[8];
763 _weights[14] = _weights[7];
764 _weights[15] = _weights[6];
765 _weights[16] = _weights[5];
766 _weights[17] = _weights[4];
767 _weights[18] = _weights[3];
768 _weights[19] = _weights[2];
769 _weights[20] = _weights[1];
770 _weights[21] = _weights[0];
771
772 return;
773 }
774
775
776 default:
777 libmesh_error_msg("Quadrature rule " << _order << " not supported!");
778 }
779}
780
781} // namespace libMesh
libMesh::QBase::_points
std::vector< Point > _points
The locations of the quadrature points in reference element space.
Definition quadrature.h:409
libMesh::QBase::get_order
Order get_order() const
Definition quadrature.h:249
libMesh::QBase::_weights
std::vector< Real > _weights
The quadrature weights.
Definition quadrature.h:415
libMesh::QBase::_order
Order _order
The polynomial order which the quadrature rule is capable of integrating exactly.
Definition quadrature.h:385
libMesh::QGauss::init_1D
virtual void init_1D() override
Initializes the 1D quadrature rule by filling the points and weights vectors with the appropriate val...
Definition quadrature_gauss_1D.C:30
libMesh
The libMesh namespace provides an interface to certain functionality in the library.
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition libmesh_common.h:144
libMesh::TWENTYSECOND
@ TWENTYSECOND
Definition enum_order.h:64
libMesh::THIRTYFOURTH
@ THIRTYFOURTH
Definition enum_order.h:76
libMesh::TWENTYSIXTH
@ TWENTYSIXTH
Definition enum_order.h:68
libMesh::SEVENTEENTH
@ SEVENTEENTH
Definition enum_order.h:58
libMesh::FORTYFIRST
@ FORTYFIRST
Definition enum_order.h:83
libMesh::TWENTYFIRST
@ TWENTYFIRST
Definition enum_order.h:63
libMesh::FORTYSECOND
@ FORTYSECOND
Definition enum_order.h:84
libMesh::TWENTYEIGHTH
@ TWENTYEIGHTH
Definition enum_order.h:70
libMesh::THIRTYFIRST
@ THIRTYFIRST
Definition enum_order.h:73
libMesh::THIRTYSECOND
@ THIRTYSECOND
Definition enum_order.h:74
libMesh::SIXTEENTH
@ SIXTEENTH
Definition enum_order.h:57
libMesh::FORTYTHIRD
@ FORTYTHIRD
Definition enum_order.h:85
libMesh::THIRTYNINTH
@ THIRTYNINTH
Definition enum_order.h:81
libMesh::THIRTYSEVENTH
@ THIRTYSEVENTH
Definition enum_order.h:79
libMesh::THIRTYSIXTH
@ THIRTYSIXTH
Definition enum_order.h:78
libMesh::THIRTYEIGHTH
@ THIRTYEIGHTH
Definition enum_order.h:80
libMesh::TWENTYSEVENTH
@ TWENTYSEVENTH
Definition enum_order.h:69
libMesh::TWENTIETH
@ TWENTIETH
Definition enum_order.h:62
libMesh::TWENTYNINTH
@ TWENTYNINTH
Definition enum_order.h:71
libMesh::THIRTIETH
@ THIRTIETH
Definition enum_order.h:72
libMesh::TWENTYTHIRD
@ TWENTYTHIRD
Definition enum_order.h:65
libMesh::TWENTYFIFTH
@ TWENTYFIFTH
Definition enum_order.h:67
libMesh::FIFTEENTH
@ FIFTEENTH
Definition enum_order.h:56
libMesh::FOURTEENTH
@ FOURTEENTH
Definition enum_order.h:55
libMesh::THIRTYFIFTH
@ THIRTYFIFTH
Definition enum_order.h:77
libMesh::EIGHTTEENTH
@ EIGHTTEENTH
Definition enum_order.h:59
libMesh::TWENTYFOURTH
@ TWENTYFOURTH
Definition enum_order.h:66
libMesh::NINETEENTH
@ NINETEENTH
Definition enum_order.h:61
libMesh::THIRTYTHIRD
@ THIRTYTHIRD
Definition enum_order.h:75
libMesh::THIRTEENTH
@ THIRTEENTH
Definition enum_order.h:54
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