libMesh
quadrature_gauss_1D.C
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1 // The libMesh Finite Element Library.
2 // Copyright (C) 2002-2025 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 
25 namespace libMesh
26 {
27 
28 
29 
30 void 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
The libMesh namespace provides an interface to certain functionality in the library.
libMesh::QBase::_points
std::vector< Point > _points
The locations of the quadrature points in reference element space.
Definition: quadrature.h:409
libMesh::QBase::_weights
std::vector< Real > _weights
The quadrature weights.
Definition: quadrature.h:415
libMesh::QBase::get_order
Order get_order() const
Definition: quadrature.h:249
libMesh::QBase::_order
Order _order
The polynomial order which the quadrature rule is capable of integrating exactly. ...
Definition: quadrature.h:385
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:144
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
Generated on Thu Oct 30 2025 20:01:54 for libMesh by   doxygen 1.8.14