libMesh
quadrature_gauss_1D.C
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1 // The libMesh Finite Element Library.
2 // Copyright (C) 2002-2017 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 
31  unsigned int p)
32 {
33  //----------------------------------------------------------------------
34  // 1D quadrature rules
35  switch(_order + 2*p)
36  {
37  case CONSTANT:
38  case FIRST:
39  {
40  _points.resize (1);
41  _weights.resize(1);
42 
43  _points[0](0) = 0.;
44 
45  _weights[0] = 2.;
46 
47  return;
48  }
49  case SECOND:
50  case THIRD:
51  {
52  _points.resize (2);
53  _weights.resize(2);
54 
55  _points[0](0) = -5.7735026918962576450914878050196e-01L; // -sqrt(3)/3
56  _points[1] = -_points[0];
57 
58  _weights[0] = 1.;
59  _weights[1] = _weights[0];
60 
61  return;
62  }
63  case FOURTH:
64  case FIFTH:
65  {
66  _points.resize (3);
67  _weights.resize(3);
68 
69  _points[ 0](0) = -7.7459666924148337703585307995648e-01L;
70  _points[ 1](0) = 0.;
71  _points[ 2] = -_points[0];
72 
73  _weights[ 0] = 5.5555555555555555555555555555556e-01L;
74  _weights[ 1] = 8.8888888888888888888888888888889e-01L;
75  _weights[ 2] = _weights[0];
76 
77  return;
78  }
79  case SIXTH:
80  case SEVENTH:
81  {
82  _points.resize (4);
83  _weights.resize(4);
84 
85  _points[ 0](0) = -8.6113631159405257522394648889281e-01L;
86  _points[ 1](0) = -3.3998104358485626480266575910324e-01L;
87  _points[ 2] = -_points[1];
88  _points[ 3] = -_points[0];
89 
90  _weights[ 0] = 3.4785484513745385737306394922200e-01L;
91  _weights[ 1] = 6.5214515486254614262693605077800e-01L;
92  _weights[ 2] = _weights[1];
93  _weights[ 3] = _weights[0];
94 
95  return;
96  }
97  case EIGHTH:
98  case NINTH:
99  {
100  _points.resize (5);
101  _weights.resize(5);
102 
103  _points[ 0](0) = -9.0617984593866399279762687829939e-01L;
104  _points[ 1](0) = -5.3846931010568309103631442070021e-01L;
105  _points[ 2](0) = 0.;
106  _points[ 3] = -_points[1];
107  _points[ 4] = -_points[0];
108 
109  _weights[ 0] = 2.3692688505618908751426404071992e-01L;
110  _weights[ 1] = 4.7862867049936646804129151483564e-01L;
111  _weights[ 2] = 5.6888888888888888888888888888889e-01L;
112  _weights[ 3] = _weights[1];
113  _weights[ 4] = _weights[0];
114 
115  return;
116  }
117  case TENTH:
118  case ELEVENTH:
119  {
120  _points.resize (6);
121  _weights.resize(6);
122 
123  _points[ 0](0) = -9.3246951420315202781230155449399e-01L;
124  _points[ 1](0) = -6.6120938646626451366139959501991e-01L;
125  _points[ 2](0) = -2.3861918608319690863050172168071e-01L;
126  _points[ 3] = -_points[2];
127  _points[ 4] = -_points[1];
128  _points[ 5] = -_points[0];
129 
130  _weights[ 0] = 1.7132449237917034504029614217273e-01L;
131  _weights[ 1] = 3.6076157304813860756983351383772e-01L;
132  _weights[ 2] = 4.6791393457269104738987034398955e-01L;
133  _weights[ 3] = _weights[2];
134  _weights[ 4] = _weights[1];
135  _weights[ 5] = _weights[0];
136 
137  return;
138  }
139  case TWELFTH:
140  case THIRTEENTH:
141  {
142  _points.resize (7);
143  _weights.resize(7);
144 
145  _points[ 0](0) = -9.4910791234275852452618968404785e-01L;
146  _points[ 1](0) = -7.4153118559939443986386477328079e-01L;
147  _points[ 2](0) = -4.0584515137739716690660641207696e-01L;
148  _points[ 3](0) = 0.;
149  _points[ 4] = -_points[2];
150  _points[ 5] = -_points[1];
151  _points[ 6] = -_points[0];
152 
153  _weights[ 0] = 1.2948496616886969327061143267908e-01L;
154  _weights[ 1] = 2.7970539148927666790146777142378e-01L;
155  _weights[ 2] = 3.8183005050511894495036977548898e-01L;
156  _weights[ 3] = 4.1795918367346938775510204081633e-01L;
157  _weights[ 4] = _weights[2];
158  _weights[ 5] = _weights[1];
159  _weights[ 6] = _weights[0];
160 
161  return;
162  }
163  case FOURTEENTH:
164  case FIFTEENTH:
165  {
166  _points.resize (8);
167  _weights.resize(8);
168 
169  _points[ 0](0) = -9.6028985649753623168356086856947e-01L;
170  _points[ 1](0) = -7.9666647741362673959155393647583e-01L;
171  _points[ 2](0) = -5.2553240991632898581773904918925e-01L;
172  _points[ 3](0) = -1.8343464249564980493947614236018e-01L;
173  _points[ 4] = -_points[3];
174  _points[ 5] = -_points[2];
175  _points[ 6] = -_points[1];
176  _points[ 7] = -_points[0];
177 
178  _weights[ 0] = 1.0122853629037625915253135430996e-01L;
179  _weights[ 1] = 2.2238103445337447054435599442624e-01L;
180  _weights[ 2] = 3.1370664587788728733796220198660e-01L;
181  _weights[ 3] = 3.6268378337836198296515044927720e-01L;
182  _weights[ 4] = _weights[3];
183  _weights[ 5] = _weights[2];
184  _weights[ 6] = _weights[1];
185  _weights[ 7] = _weights[0];
186 
187  return;
188  }
189  case SIXTEENTH:
190  case SEVENTEENTH:
191  {
192  _points.resize (9);
193  _weights.resize(9);
194 
195  _points[ 0](0) = -9.6816023950762608983557620290367e-01L;
196  _points[ 1](0) = -8.3603110732663579429942978806973e-01L;
197  _points[ 2](0) = -6.1337143270059039730870203934147e-01L;
198  _points[ 3](0) = -3.2425342340380892903853801464334e-01L;
199  _points[ 4](0) = 0.;
200  _points[ 5] = -_points[3];
201  _points[ 6] = -_points[2];
202  _points[ 7] = -_points[1];
203  _points[ 8] = -_points[0];
204 
205  _weights[ 0] = 8.1274388361574411971892158110524e-02L;
206  _weights[ 1] = 1.8064816069485740405847203124291e-01L;
207  _weights[ 2] = 2.6061069640293546231874286941863e-01L;
208  _weights[ 3] = 3.1234707704000284006863040658444e-01L;
209  _weights[ 4] = 3.3023935500125976316452506928697e-01L;
210  _weights[ 5] = _weights[3];
211  _weights[ 6] = _weights[2];
212  _weights[ 7] = _weights[1];
213  _weights[ 8] = _weights[0];
214 
215  return;
216  }
217  case EIGHTTEENTH:
218  case NINETEENTH:
219  {
220  _points.resize (10);
221  _weights.resize(10);
222 
223  _points[ 0](0) = -9.7390652851717172007796401208445e-01L;
224  _points[ 1](0) = -8.6506336668898451073209668842349e-01L;
225  _points[ 2](0) = -6.7940956829902440623432736511487e-01L;
226  _points[ 3](0) = -4.3339539412924719079926594316578e-01L;
227  _points[ 4](0) = -1.4887433898163121088482600112972e-01L;
228  _points[ 5] = -_points[4];
229  _points[ 6] = -_points[3];
230  _points[ 7] = -_points[2];
231  _points[ 8] = -_points[1];
232  _points[ 9] = -_points[0];
233 
234  _weights[ 0] = 6.6671344308688137593568809893332e-02L;
235  _weights[ 1] = 1.4945134915058059314577633965770e-01L;
236  _weights[ 2] = 2.1908636251598204399553493422816e-01L;
237  _weights[ 3] = 2.6926671930999635509122692156947e-01L;
238  _weights[ 4] = 2.9552422471475287017389299465134e-01L;
239  _weights[ 5] = _weights[4];
240  _weights[ 6] = _weights[3];
241  _weights[ 7] = _weights[2];
242  _weights[ 8] = _weights[1];
243  _weights[ 9] = _weights[0];
244 
245  return;
246  }
247 
248  case TWENTIETH:
249  case TWENTYFIRST:
250  {
251  _points.resize (11);
252  _weights.resize(11);
253 
254  _points[ 0](0) = -9.7822865814605699280393800112286e-01L;
255  _points[ 1](0) = -8.8706259976809529907515776930393e-01L;
256  _points[ 2](0) = -7.3015200557404932409341625203115e-01L;
257  _points[ 3](0) = -5.1909612920681181592572566945861e-01L;
258  _points[ 4](0) = -2.6954315595234497233153198540086e-01L;
259  _points[ 5](0) = 0.;
260  _points[ 6] = -_points[4];
261  _points[ 7] = -_points[3];
262  _points[ 8] = -_points[2];
263  _points[ 9] = -_points[1];
264  _points[10] = -_points[0];
265 
266  _weights[ 0] = 5.5668567116173666482753720442549e-02L;
267  _weights[ 1] = 1.2558036946490462463469429922394e-01L;
268  _weights[ 2] = 1.8629021092773425142609764143166e-01L;
269  _weights[ 3] = 2.3319376459199047991852370484318e-01L;
270  _weights[ 4] = 2.6280454451024666218068886989051e-01L;
271  _weights[ 5] = 2.7292508677790063071448352833634e-01L;
272  _weights[ 6] = _weights[4];
273  _weights[ 7] = _weights[3];
274  _weights[ 8] = _weights[2];
275  _weights[ 9] = _weights[1];
276  _weights[10] = _weights[0];
277 
278  return;
279  }
280 
281  case TWENTYSECOND:
282  case TWENTYTHIRD:
283  {
284  _points.resize (12);
285  _weights.resize(12);
286 
287  _points[ 0](0) = -9.8156063424671925069054909014928e-01L;
288  _points[ 1](0) = -9.0411725637047485667846586611910e-01L;
289  _points[ 2](0) = -7.6990267419430468703689383321282e-01L;
290  _points[ 3](0) = -5.8731795428661744729670241894053e-01L;
291  _points[ 4](0) = -3.6783149899818019375269153664372e-01L;
292  _points[ 5](0) = -1.2523340851146891547244136946385e-01L;
293  _points[ 6] = -_points[5];
294  _points[ 7] = -_points[4];
295  _points[ 8] = -_points[3];
296  _points[ 9] = -_points[2];
297  _points[10] = -_points[1];
298  _points[11] = -_points[0];
299 
300  _weights[ 0] = 4.7175336386511827194615961485017e-02L;
301  _weights[ 1] = 1.0693932599531843096025471819400e-01L;
302  _weights[ 2] = 1.6007832854334622633465252954336e-01L;
303  _weights[ 3] = 2.0316742672306592174906445580980e-01L;
304  _weights[ 4] = 2.3349253653835480876084989892483e-01L;
305  _weights[ 5] = 2.4914704581340278500056243604295e-01L;
306  _weights[ 6] = _weights[5];
307  _weights[ 7] = _weights[4];
308  _weights[ 8] = _weights[3];
309  _weights[ 9] = _weights[2];
310  _weights[10] = _weights[1];
311  _weights[11] = _weights[0];
312 
313  return;
314  }
315 
316  case TWENTYFOURTH:
317  case TWENTYFIFTH:
318  {
319  _points.resize (13);
320  _weights.resize(13);
321 
322  _points[ 0](0) = -9.8418305471858814947282944880711e-01L;
323  _points[ 1](0) = -9.1759839922297796520654783650072e-01L;
324  _points[ 2](0) = -8.0157809073330991279420648958286e-01L;
325  _points[ 3](0) = -6.4234933944034022064398460699552e-01L;
326  _points[ 4](0) = -4.4849275103644685287791285212764e-01L;
327  _points[ 5](0) = -2.3045831595513479406552812109799e-01L;
328  _points[ 6](0) = 0.;
329  _points[ 7] = -_points[5];
330  _points[ 8] = -_points[4];
331  _points[ 9] = -_points[3];
332  _points[10] = -_points[2];
333  _points[11] = -_points[1];
334  _points[12] = -_points[0];
335 
336  _weights[ 0] = 4.0484004765315879520021592200986e-02L;
337  _weights[ 1] = 9.2121499837728447914421775953797e-02L;
338  _weights[ 2] = 1.3887351021978723846360177686887e-01L;
339  _weights[ 3] = 1.7814598076194573828004669199610e-01L;
340  _weights[ 4] = 2.0781604753688850231252321930605e-01L;
341  _weights[ 5] = 2.2628318026289723841209018603978e-01L;
342  _weights[ 6] = 2.3255155323087391019458951526884e-01L;
343  _weights[ 7] = _weights[5];
344  _weights[ 8] = _weights[4];
345  _weights[ 9] = _weights[3];
346  _weights[10] = _weights[2];
347  _weights[11] = _weights[1];
348  _weights[12] = _weights[0];
349 
350  return;
351  }
352 
353  case TWENTYSIXTH:
354  case TWENTYSEVENTH:
355  {
356  _points.resize (14);
357  _weights.resize(14);
358 
359  _points[ 0](0) = -9.8628380869681233884159726670405e-01L;
360  _points[ 1](0) = -9.2843488366357351733639113937787e-01L;
361  _points[ 2](0) = -8.2720131506976499318979474265039e-01L;
362  _points[ 3](0) = -6.8729290481168547014801980301933e-01L;
363  _points[ 4](0) = -5.1524863635815409196529071855119e-01L;
364  _points[ 5](0) = -3.1911236892788976043567182416848e-01L;
365  _points[ 6](0) = -1.0805494870734366206624465021983e-01L;
366  _points[ 7] = -_points[6];
367  _points[ 8] = -_points[5];
368  _points[ 9] = -_points[4];
369  _points[10] = -_points[3];
370  _points[11] = -_points[2];
371  _points[12] = -_points[1];
372  _points[13] = -_points[0];
373 
374  _weights[ 0] = 3.5119460331751863031832876138192e-02L;
375  _weights[ 1] = 8.0158087159760209805633277062854e-02L;
376  _weights[ 2] = 1.2151857068790318468941480907248e-01L;
377  _weights[ 3] = 1.5720316715819353456960193862384e-01L;
378  _weights[ 4] = 1.8553839747793781374171659012516e-01L;
379  _weights[ 5] = 2.0519846372129560396592406566122e-01L;
380  _weights[ 6] = 2.1526385346315779019587644331626e-01L;
381  _weights[ 7] = _weights[6];
382  _weights[ 8] = _weights[5];
383  _weights[ 9] = _weights[4];
384  _weights[10] = _weights[3];
385  _weights[11] = _weights[2];
386  _weights[12] = _weights[1];
387  _weights[13] = _weights[0];
388 
389  return;
390  }
391 
392  case TWENTYEIGHTH:
393  case TWENTYNINTH:
394  {
395  _points.resize (15);
396  _weights.resize(15);
397 
398  _points[ 0](0) = -9.8799251802048542848956571858661e-01L;
399  _points[ 1](0) = -9.3727339240070590430775894771021e-01L;
400  _points[ 2](0) = -8.4820658341042721620064832077422e-01L;
401  _points[ 3](0) = -7.2441773136017004741618605461394e-01L;
402  _points[ 4](0) = -5.7097217260853884753722673725391e-01L;
403  _points[ 5](0) = -3.9415134707756336989720737098105e-01L;
404  _points[ 6](0) = -2.0119409399743452230062830339460e-01L;
405  _points[ 7](0) = 0.;
406  _points[ 8] = -_points[6];
407  _points[ 9] = -_points[5];
408  _points[10] = -_points[4];
409  _points[11] = -_points[3];
410  _points[12] = -_points[2];
411  _points[13] = -_points[1];
412  _points[14] = -_points[0];
413 
414  _weights[ 0] = 3.0753241996117268354628393577204e-02L;
415  _weights[ 1] = 7.0366047488108124709267416450667e-02L;
416  _weights[ 2] = 1.0715922046717193501186954668587e-01L;
417  _weights[ 3] = 1.3957067792615431444780479451103e-01L;
418  _weights[ 4] = 1.6626920581699393355320086048121e-01L;
419  _weights[ 5] = 1.8616100001556221102680056186642e-01L;
420  _weights[ 6] = 1.9843148532711157645611832644384e-01L;
421  _weights[ 7] = 2.0257824192556127288062019996752e-01L;
422  _weights[ 8] = _weights[6];
423  _weights[ 9] = _weights[5];
424  _weights[10] = _weights[4];
425  _weights[11] = _weights[3];
426  _weights[12] = _weights[2];
427  _weights[13] = _weights[1];
428  _weights[14] = _weights[0];
429 
430  return;
431  }
432 
433  case THIRTIETH:
434  case THIRTYFIRST:
435  {
436  _points.resize (16);
437  _weights.resize(16);
438 
439  _points[ 0](0) = -9.8940093499164993259615417345033e-01L;
440  _points[ 1](0) = -9.4457502307323257607798841553461e-01L;
441  _points[ 2](0) = -8.6563120238783174388046789771239e-01L;
442  _points[ 3](0) = -7.5540440835500303389510119484744e-01L;
443  _points[ 4](0) = -6.1787624440264374844667176404879e-01L;
444  _points[ 5](0) = -4.5801677765722738634241944298358e-01L;
445  _points[ 6](0) = -2.8160355077925891323046050146050e-01L;
446  _points[ 7](0) = -9.5012509837637440185319335424958e-02L;
447  _points[ 8] = -_points[7];
448  _points[ 9] = -_points[6];
449  _points[10] = -_points[5];
450  _points[11] = -_points[4];
451  _points[12] = -_points[3];
452  _points[13] = -_points[2];
453  _points[14] = -_points[1];
454  _points[15] = -_points[0];
455 
456  _weights[ 0] = 2.7152459411754094851780572456018e-02L;
457  _weights[ 1] = 6.2253523938647892862843836994378e-02L;
458  _weights[ 2] = 9.5158511682492784809925107602246e-02L;
459  _weights[ 3] = 1.2462897125553387205247628219202e-01L;
460  _weights[ 4] = 1.4959598881657673208150173054748e-01L;
461  _weights[ 5] = 1.6915651939500253818931207903033e-01L;
462  _weights[ 6] = 1.8260341504492358886676366796922e-01L;
463  _weights[ 7] = 1.8945061045506849628539672320828e-01L;
464  _weights[ 8] = _weights[7];
465  _weights[ 9] = _weights[6];
466  _weights[10] = _weights[5];
467  _weights[11] = _weights[4];
468  _weights[12] = _weights[3];
469  _weights[13] = _weights[2];
470  _weights[14] = _weights[1];
471  _weights[15] = _weights[0];
472 
473  return;
474  }
475 
476  case THIRTYSECOND:
477  case THIRTYTHIRD:
478  {
479  _points.resize (17);
480  _weights.resize(17);
481 
482  _points[ 0](0) = -9.9057547531441733567543401994067e-01L;
483  _points[ 1](0) = -9.5067552176876776122271695789580e-01L;
484  _points[ 2](0) = -8.8023915372698590212295569448816e-01L;
485  _points[ 3](0) = -7.8151400389680140692523005552048e-01L;
486  _points[ 4](0) = -6.5767115921669076585030221664300e-01L;
487  _points[ 5](0) = -5.1269053708647696788624656862955e-01L;
488  _points[ 6](0) = -3.5123176345387631529718551709535e-01L;
489  _points[ 7](0) = -1.7848418149584785585067749365407e-01L;
490  _points[ 8](0) = 0.;
491  _points[ 9] = -_points[7];
492  _points[10] = -_points[6];
493  _points[11] = -_points[5];
494  _points[12] = -_points[4];
495  _points[13] = -_points[3];
496  _points[14] = -_points[2];
497  _points[15] = -_points[1];
498  _points[16] = -_points[0];
499 
500  _weights[ 0] = 2.4148302868547931960110026287565e-02L;
501  _weights[ 1] = 5.5459529373987201129440165358245e-02L;
502  _weights[ 2] = 8.5036148317179180883535370191062e-02L;
503  _weights[ 3] = 1.1188384719340397109478838562636e-01L;
504  _weights[ 4] = 1.3513636846852547328631998170235e-01L;
505  _weights[ 5] = 1.5404576107681028808143159480196e-01L;
506  _weights[ 6] = 1.6800410215645004450997066378832e-01L;
507  _weights[ 7] = 1.7656270536699264632527099011320e-01L;
508  _weights[ 8] = 1.7944647035620652545826564426189e-01L;
509  _weights[ 9] = _weights[7];
510  _weights[10] = _weights[6];
511  _weights[11] = _weights[5];
512  _weights[12] = _weights[4];
513  _weights[13] = _weights[3];
514  _weights[14] = _weights[2];
515  _weights[15] = _weights[1];
516  _weights[16] = _weights[0];
517 
518  return;
519  }
520 
521  case THIRTYFOURTH:
522  case THIRTYFIFTH:
523  {
524  _points.resize (18);
525  _weights.resize(18);
526 
527  _points[ 0](0) = -9.9156516842093094673001600470615e-01L;
528  _points[ 1](0) = -9.5582394957139775518119589292978e-01L;
529  _points[ 2](0) = -8.9260246649755573920606059112715e-01L;
530  _points[ 3](0) = -8.0370495897252311568241745501459e-01L;
531  _points[ 4](0) = -6.9168704306035320787489108128885e-01L;
532  _points[ 5](0) = -5.5977083107394753460787154852533e-01L;
533  _points[ 6](0) = -4.1175116146284264603593179383305e-01L;
534  _points[ 7](0) = -2.5188622569150550958897285487791e-01L;
535  _points[ 8](0) = -8.4775013041735301242261852935784e-02L;
536  _points[ 9] = -_points[8];
537  _points[10] = -_points[7];
538  _points[11] = -_points[6];
539  _points[12] = -_points[5];
540  _points[13] = -_points[4];
541  _points[14] = -_points[3];
542  _points[15] = -_points[2];
543  _points[16] = -_points[1];
544  _points[17] = -_points[0];
545 
546  _weights[ 0] = 2.1616013526483310313342710266452e-02L;
547  _weights[ 1] = 4.9714548894969796453334946202639e-02L;
548  _weights[ 2] = 7.6425730254889056529129677616637e-02L;
549  _weights[ 3] = 1.0094204410628716556281398492483e-01L;
550  _weights[ 4] = 1.2255520671147846018451912680020e-01L;
551  _weights[ 5] = 1.4064291467065065120473130375195e-01L;
552  _weights[ 6] = 1.5468467512626524492541800383637e-01L;
553  _weights[ 7] = 1.6427648374583272298605377646593e-01L;
554  _weights[ 8] = 1.6914238296314359184065647013499e-01L;
555  _weights[ 9] = _weights[8];
556  _weights[10] = _weights[7];
557  _weights[11] = _weights[6];
558  _weights[12] = _weights[5];
559  _weights[13] = _weights[4];
560  _weights[14] = _weights[3];
561  _weights[15] = _weights[2];
562  _weights[16] = _weights[1];
563  _weights[17] = _weights[0];
564 
565  return;
566  }
567 
568  case THIRTYSIXTH:
569  case THIRTYSEVENTH:
570  {
571  _points.resize (19);
572  _weights.resize(19);
573 
574  _points[ 0](0) = -9.9240684384358440318901767025326e-01L;
575  _points[ 1](0) = -9.6020815213483003085277884068765e-01L;
576  _points[ 2](0) = -9.0315590361481790164266092853231e-01L;
577  _points[ 3](0) = -8.2271465653714282497892248671271e-01L;
578  _points[ 4](0) = -7.2096617733522937861709586082378e-01L;
579  _points[ 5](0) = -6.0054530466168102346963816494624e-01L;
580  _points[ 6](0) = -4.6457074137596094571726714810410e-01L;
581  _points[ 7](0) = -3.1656409996362983199011732884984e-01L;
582  _points[ 8](0) = -1.6035864564022537586809611574074e-01L;
583  _points[ 9](0) = 0.;
584  _points[10] = -_points[8];
585  _points[11] = -_points[7];
586  _points[12] = -_points[6];
587  _points[13] = -_points[5];
588  _points[14] = -_points[4];
589  _points[15] = -_points[3];
590  _points[16] = -_points[2];
591  _points[17] = -_points[1];
592  _points[18] = -_points[0];
593 
594  _weights[ 0] = 1.9461788229726477036312041464438e-02L;
595  _weights[ 1] = 4.4814226765699600332838157401994e-02L;
596  _weights[ 2] = 6.9044542737641226580708258006013e-02L;
597  _weights[ 3] = 9.1490021622449999464462094123840e-02L;
598  _weights[ 4] = 1.1156664554733399471602390168177e-01L;
599  _weights[ 5] = 1.2875396253933622767551578485688e-01L;
600  _weights[ 6] = 1.4260670217360661177574610944190e-01L;
601  _weights[ 7] = 1.5276604206585966677885540089766e-01L;
602  _weights[ 8] = 1.5896884339395434764995643946505e-01L;
603  _weights[ 9] = 1.6105444984878369597916362532092e-01L;
604  _weights[10] = _weights[8];
605  _weights[11] = _weights[7];
606  _weights[12] = _weights[6];
607  _weights[13] = _weights[5];
608  _weights[14] = _weights[4];
609  _weights[15] = _weights[3];
610  _weights[16] = _weights[2];
611  _weights[17] = _weights[1];
612  _weights[18] = _weights[0];
613 
614  return;
615  }
616 
617  case THIRTYEIGHTH:
618  case THIRTYNINTH:
619  {
620  _points.resize (20);
621  _weights.resize(20);
622 
623  _points[ 0](0) = -9.9312859918509492478612238847132e-01L;
624  _points[ 1](0) = -9.6397192727791379126766613119728e-01L;
625  _points[ 2](0) = -9.1223442825132590586775244120330e-01L;
626  _points[ 3](0) = -8.3911697182221882339452906170152e-01L;
627  _points[ 4](0) = -7.4633190646015079261430507035564e-01L;
628  _points[ 5](0) = -6.3605368072651502545283669622629e-01L;
629  _points[ 6](0) = -5.1086700195082709800436405095525e-01L;
630  _points[ 7](0) = -3.7370608871541956067254817702493e-01L;
631  _points[ 8](0) = -2.2778585114164507808049619536857e-01L;
632  _points[ 9](0) = -7.6526521133497333754640409398838e-02L;
633  _points[10] = -_points[9];
634  _points[11] = -_points[8];
635  _points[12] = -_points[7];
636  _points[13] = -_points[6];
637  _points[14] = -_points[5];
638  _points[15] = -_points[4];
639  _points[16] = -_points[3];
640  _points[17] = -_points[2];
641  _points[18] = -_points[1];
642  _points[19] = -_points[0];
643 
644  _weights[ 0] = 1.7614007139152118311861962351853e-02L;
645  _weights[ 1] = 4.0601429800386941331039952274932e-02L;
646  _weights[ 2] = 6.2672048334109063569506535187042e-02L;
647  _weights[ 3] = 8.3276741576704748724758143222046e-02L;
648  _weights[ 4] = 1.0193011981724043503675013548035e-01L;
649  _weights[ 5] = 1.1819453196151841731237737771138e-01L;
650  _weights[ 6] = 1.3168863844917662689849449974816e-01L;
651  _weights[ 7] = 1.4209610931838205132929832506716e-01L;
652  _weights[ 8] = 1.4917298647260374678782873700197e-01L;
653  _weights[ 9] = 1.5275338713072585069808433195510e-01L;
654  _weights[10] = _weights[9];
655  _weights[11] = _weights[8];
656  _weights[12] = _weights[7];
657  _weights[13] = _weights[6];
658  _weights[14] = _weights[5];
659  _weights[15] = _weights[4];
660  _weights[16] = _weights[3];
661  _weights[17] = _weights[2];
662  _weights[18] = _weights[1];
663  _weights[19] = _weights[0];
664 
665  return;
666  }
667 
668  case FORTIETH:
669  case FORTYFIRST:
670  {
671  _points.resize (21);
672  _weights.resize(21);
673 
674  _points[ 0](0) = -9.9375217062038950026024203593794e-01L;
675  _points[ 1](0) = -9.6722683856630629431662221490770e-01L;
676  _points[ 2](0) = -9.2009933415040082879018713371497e-01L;
677  _points[ 3](0) = -8.5336336458331728364725063858757e-01L;
678  _points[ 4](0) = -7.6843996347567790861587785130623e-01L;
679  _points[ 5](0) = -6.6713880419741231930596666999034e-01L;
680  _points[ 6](0) = -5.5161883588721980705901879672431e-01L;
681  _points[ 7](0) = -4.2434212020743878357366888854379e-01L;
682  _points[ 8](0) = -2.8802131680240109660079251606460e-01L;
683  _points[ 9](0) = -1.4556185416089509093703098233869e-01L;
684  _points[10](0) = 0.;
685  _points[11] = -_points[9];
686  _points[12] = -_points[8];
687  _points[13] = -_points[7];
688  _points[14] = -_points[6];
689  _points[15] = -_points[5];
690  _points[16] = -_points[4];
691  _points[17] = -_points[3];
692  _points[18] = -_points[2];
693  _points[19] = -_points[1];
694  _points[20] = -_points[0];
695 
696  _weights[ 0] = 1.6017228257774333324224616858471e-02L;
697  _weights[ 1] = 3.6953789770852493799950668299330e-02L;
698  _weights[ 2] = 5.7134425426857208283635826472448e-02L;
699  _weights[ 3] = 7.6100113628379302017051653300183e-02L;
700  _weights[ 4] = 9.3444423456033861553289741113932e-02L;
701  _weights[ 5] = 1.0879729916714837766347457807011e-01L;
702  _weights[ 6] = 1.2183141605372853419536717712572e-01L;
703  _weights[ 7] = 1.3226893863333746178105257449678e-01L;
704  _weights[ 8] = 1.3988739479107315472213342386758e-01L;
705  _weights[ 9] = 1.4452440398997005906382716655375e-01L;
706  _weights[10] = 1.4608113364969042719198514768337e-01L;
707  _weights[11] = _weights[9];
708  _weights[12] = _weights[8];
709  _weights[13] = _weights[7];
710  _weights[14] = _weights[6];
711  _weights[15] = _weights[5];
712  _weights[16] = _weights[4];
713  _weights[17] = _weights[3];
714  _weights[18] = _weights[2];
715  _weights[19] = _weights[1];
716  _weights[20] = _weights[0];
717 
718  return;
719  }
720 
721  case FORTYSECOND:
722  case FORTYTHIRD:
723  {
724  _points.resize (22);
725  _weights.resize(22);
726 
727  _points[ 0](0) = -9.9429458548239929207303142116130e-01L;
728  _points[ 1](0) = -9.7006049783542872712395098676527e-01L;
729  _points[ 2](0) = -9.2695677218717400052069293925905e-01L;
730  _points[ 3](0) = -8.6581257772030013653642563701938e-01L;
731  _points[ 4](0) = -7.8781680597920816200427795540835e-01L;
732  _points[ 5](0) = -6.9448726318668278005068983576226e-01L;
733  _points[ 6](0) = -5.8764040350691159295887692763865e-01L;
734  _points[ 7](0) = -4.6935583798675702640633071096641e-01L;
735  _points[ 8](0) = -3.4193582089208422515814742042738e-01L;
736  _points[ 9](0) = -2.0786042668822128547884653391955e-01L;
737  _points[10](0) = -6.9739273319722221213841796118628e-02L;
738  _points[11] = -_points[10];
739  _points[12] = -_points[9];
740  _points[13] = -_points[8];
741  _points[14] = -_points[7];
742  _points[15] = -_points[6];
743  _points[16] = -_points[5];
744  _points[17] = -_points[4];
745  _points[18] = -_points[3];
746  _points[19] = -_points[2];
747  _points[20] = -_points[1];
748  _points[21] = -_points[0];
749 
750  _weights[ 0] = 1.4627995298272200684991098047185e-02L;
751  _weights[ 1] = 3.3774901584814154793302246865913e-02L;
752  _weights[ 2] = 5.2293335152683285940312051273211e-02L;
753  _weights[ 3] = 6.9796468424520488094961418930218e-02L;
754  _weights[ 4] = 8.5941606217067727414443681372703e-02L;
755  _weights[ 5] = 1.0041414444288096493207883783054e-01L;
756  _weights[ 6] = 1.1293229608053921839340060742175e-01L;
757  _weights[ 7] = 1.2325237681051242428556098615481e-01L;
758  _weights[ 8] = 1.3117350478706237073296499253031e-01L;
759  _weights[ 9] = 1.3654149834601517135257383123152e-01L;
760  _weights[10] = 1.3925187285563199337541024834181e-01L;
761  _weights[11] = _weights[10];
762  _weights[12] = _weights[9];
763  _weights[13] = _weights[8];
764  _weights[14] = _weights[7];
765  _weights[15] = _weights[6];
766  _weights[16] = _weights[5];
767  _weights[17] = _weights[4];
768  _weights[18] = _weights[3];
769  _weights[19] = _weights[2];
770  _weights[20] = _weights[1];
771  _weights[21] = _weights[0];
772 
773  return;
774  }
775 
776 
777  default:
778  libmesh_error_msg("Quadrature rule " << _order << " not supported!");
779  }
780 }
781 
782 } // namespace libMesh
virtual void init_1D(const ElemType _type=INVALID_ELEM, unsigned int p_level=0) libmesh_override
Initializes the 1D quadrature rule by filling the points and weights vectors with the appropriate val...
ElemType
Defines an enum for geometric element types.
The libMesh namespace provides an interface to certain functionality in the library.
std::vector< Point > _points
The locations of the quadrature points in reference element space.
Definition: quadrature.h:335
std::vector< Real > _weights
The quadrature weights.
Definition: quadrature.h:341
const Order _order
The polynomial order which the quadrature rule is capable of integrating exactly. ...
Definition: quadrature.h:317