libMesh
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quadrature_jacobi_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// Local includes
21#include "libmesh/quadrature_jacobi.h"
22
23namespace libMesh
24{
25
26void QJacobi::init_1D()
27{
28 //----------------------------------------------------------------------
29 // 1D quadrature rules
30 // Note that we need to check _alpha and _beta
31 // to determine which quadrature rule to implement.
32 // These rules have been pre-scaled based on their
33 // intended use. The weights of the (alpha=1,beta=0)
34 // rule sum to 0.5. The weights of the (alpha=2,beta=0)
35 // rule sum to 0.333333333333.
36
37 if ((_alpha == 1) && (_beta == 0))
38 {
39 switch(get_order())
40 {
41 case CONSTANT:
42 case FIRST:
43 {
44 _points.resize (1);
45 _weights.resize(1);
46
47 _points[0](0) = 1/Real(3);
48
49 _weights[0] = 0.5;
50
51 return;
52 }
53 case SECOND:
54 case THIRD:
55 {
56 _points.resize (2);
57 _weights.resize(2);
58
59 _points[ 0](0)=1.5505102572168219018027159252941e-01_R;
60 _points[ 1](0)=6.4494897427831780981972840747059e-01_R;
61
62 _weights[ 0]=3.1804138174397716939436900207516e-01_R;
63 _weights[ 1]=1.8195861825602283060563099792484e-01_R;
64
65 return;
66 }
67 case FOURTH:
68 case FIFTH:
69 {
70 _points.resize (3);
71 _weights.resize(3);
72
73 _points[ 0](0)=8.8587959512703947395546143769456e-02_R;
74 _points[ 1](0)=4.0946686444073471086492625206883e-01_R;
75 _points[ 2](0)=7.8765946176084705602524188987600e-01_R;
76
77 _weights[ 0]=2.0093191373895963077219813326460e-01_R;
78 _weights[ 1]=2.2924110635958624669392059455632e-01_R;
79 _weights[ 2]=6.9826979901454122533881272179077e-02_R;
80
81 return;
82 }
83 case SIXTH:
84 case SEVENTH:
85 {
86 _points.resize (4);
87 _weights.resize(4);
88
89 _points[ 0](0)=5.7104196114517682193121192554116e-02_R;
90 _points[ 1](0)=2.7684301363812382768004599768563e-01_R;
91 _points[ 2](0)=5.8359043236891682005669766866292e-01_R;
92 _points[ 3](0)=8.6024013565621944784791291887512e-01_R;
93
94 _weights[ 0]=1.3550691343148811620826417407794e-01_R;
95 _weights[ 1]=2.0346456801027136079140447593585e-01_R;
96 _weights[ 2]=1.2984754760823244082645620288963e-01_R;
97 _weights[ 3]=3.1180970950008082173875147096575e-02_R;
98
99 return;
100 }
101 case EIGHTH:
102 case NINTH:
103 {
104 _points.resize (5);
105 _weights.resize(5);
106
107 _points[ 0](0)=3.9809857051468742340806690093333e-02_R;
108 _points[ 1](0)=1.9801341787360817253579213679530e-01_R;
109 _points[ 2](0)=4.3797481024738614400501252000523e-01_R;
110 _points[ 3](0)=6.9546427335363609451461482372117e-01_R;
111 _points[ 4](0)=9.0146491420117357387650110211225e-01_R;
112
113 _weights[ 0]=9.6781590226651679274360971636151e-02_R;
114 _weights[ 1]=1.6717463809436956549167562309770e-01_R;
115 _weights[ 2]=1.4638698708466980869803786935596e-01_R;
116 _weights[ 3]=7.3908870072616670350633219341704e-02_R;
117 _weights[ 4]=1.5747914521692276185292316568488e-02_R;
118
119 return;
120 }
121 case TENTH:
122 case ELEVENTH:
123 {
124
125 _points.resize (6);
126 _weights.resize(6);
127
128 _points[ 0](0)=2.9316427159784891972050276913165e-02_R;
129 _points[ 1](0)=1.4807859966848429184997685249598e-01_R;
130 _points[ 2](0)=3.3698469028115429909705297208078e-01_R;
131 _points[ 3](0)=5.5867151877155013208139334180552e-01_R;
132 _points[ 4](0)=7.6923386203005450091688336011565e-01_R;
133 _points[ 5](0)=9.2694567131974111485187396581968e-01_R;
134
135 _weights[ 0]=7.2310330725508683655454326124832e-02_R;
136 _weights[ 1]=1.3554249723151861684069039663805e-01_R;
137 _weights[ 2]=1.4079255378819892811907683907093e-01_R;
138 _weights[ 3]=9.8661150890655264120584510548360e-02_R;
139 _weights[ 4]=4.3955165550508975508176624305430e-02_R;
140 _weights[ 5]=8.7383018136095317560173033123989e-03_R;
141
142 return;
143 }
144 case TWELFTH:
145 case THIRTEENTH:
146 {
147 _points.resize (7);
148 _weights.resize(7);
149
150 _points[ 0](0)=2.2479386438712498108825499570845e-02_R;
151 _points[ 1](0)=1.1467905316090423190964023706751e-01_R;
152 _points[ 2](0)=2.6578982278458946847678939169339e-01_R;
153 _points[ 3](0)=4.5284637366944461699855144234765e-01_R;
154 _points[ 4](0)=6.4737528288683036262609222982876e-01_R;
155 _points[ 5](0)=8.1975930826310763501242005719082e-01_R;
156 _points[ 6](0)=9.4373743946307785353434780896769e-01_R;
157
158 _weights[ 0]=5.5967363423491051151562113429926e-02_R;
159 _weights[ 1]=1.1050925819087460242112073636961e-01_R;
160 _weights[ 2]=1.2739089729958832691873448577496e-01_R;
161 _weights[ 3]=1.0712506569587366999091225299986e-01_R;
162 _weights[ 4]=6.6384696465491469983647988763640e-02_R;
163 _weights[ 5]=2.7408356721873475444331048358226e-02_R;
164 _weights[ 6]=5.2143622028074040896913743037830e-03_R;
165
166 return;
167 }
168 case FOURTEENTH:
169 case FIFTEENTH:
170 {
171 _points.resize (8);
172 _weights.resize(8);
173
174 _points[ 0](0)=1.7779915147363451813205101037679e-02_R;
175 _points[ 1](0)=9.1323607899793956003741458074541e-02_R;
176 _points[ 2](0)=2.1430847939563075835754126758167e-01_R;
177 _points[ 3](0)=3.7193216458327230243085396048263e-01_R;
178 _points[ 4](0)=5.4518668480342664903227222995321e-01_R;
179 _points[ 5](0)=7.1317524285556948105131376025091e-01_R;
180 _points[ 6](0)=8.5563374295785442851478147977179e-01_R;
181 _points[ 7](0)=9.5536604471003014926687897814169e-01_R;
182
183 _weights[ 0]=4.4550804361555931326215619533963e-02_R;
184 _weights[ 1]=9.1119023636373626345722461782880e-02_R;
185 _weights[ 2]=1.1250579947088736617177209860428e-01_R;
186 _weights[ 3]=1.0604735943593001070453109641116e-01_R;
187 _weights[ 4]=7.9199599492319160120408189359892e-02_R;
188 _weights[ 5]=4.5439319504698898083055421095694e-02_R;
189 _weights[ 6]=1.7842902655986208393552797201042e-02_R;
190 _weights[ 7]=3.2951914422487988547423160110891e-03_R;
191
192 return;
193 }
194 case SIXTEENTH:
195 case SEVENTEENTH:
196 {
197 _points.resize (9);
198 _weights.resize(9);
199
200 _points[ 0](0)=1.4412409648876548632826740810813e-02_R;
201 _points[ 1](0)=7.4387389709196044635918185955999e-02_R;
202 _points[ 2](0)=1.7611665616299528186317574607257e-01_R;
203 _points[ 3](0)=3.0966757992763781705962046722948e-01_R;
204 _points[ 4](0)=4.6197040108101093488314310868056e-01_R;
205 _points[ 5](0)=6.1811723469529402463922975160350e-01_R;
206 _points[ 6](0)=7.6282301518503961468269330714673e-01_R;
207 _points[ 7](0)=8.8192102121000129980771488800526e-01_R;
208 _points[ 8](0)=9.6374218711679053905883569923192e-01_R;
209
210 _weights[ 0]=3.6278003523279871459649597941160e-02_R;
211 _weights[ 1]=7.6074255109308162580079303753964e-02_R;
212 _weights[ 2]=9.8533742172345705160173020369274e-02_R;
213 _weights[ 3]=1.0030880919336828965415022473259e-01_R;
214 _weights[ 4]=8.4358321844920349394250019958587e-02_R;
215 _weights[ 5]=5.8401195295165110565731522901640e-02_R;
216 _weights[ 6]=3.1804821491054001261690106935870e-02_R;
217 _weights[ 7]=1.2060004284785379051727152286900e-02_R;
218 _weights[ 8]=2.1808470857731308725490511200170e-03_R;
219
220 return;
221 }
222 case EIGHTTEENTH:
223 case NINETEENTH:
224 {
225 _points.resize (10);
226 _weights.resize(10);
227
228 _points[ 0](0)=1.1917613432415596909745586958986e-02_R;
229 _points[ 1](0)=6.1732071877148125522629367194250e-02_R;
230 _points[ 2](0)=1.4711144964307024042759943557982e-01_R;
231 _points[ 3](0)=2.6115967600845624026605165805485e-01_R;
232 _points[ 4](0)=3.9463984688578684296195210507761e-01_R;
233 _points[ 5](0)=5.3673876571566063287309517771189e-01_R;
234 _points[ 6](0)=6.7594446167666510735715050893476e-01_R;
235 _points[ 7](0)=8.0097892103689884513794630161724e-01_R;
236 _points[ 8](0)=9.0171098779014677034879897840977e-01_R;
237 _points[ 9](0)=9.6997096783851350295693564236559e-01_R;
238
239 _weights[ 0]=3.0099508024037023300654755523879e-02_R;
240 _weights[ 1]=6.4287154509082572874826538628865e-02_R;
241 _weights[ 2]=8.6211300289176036428333360711914e-02_R;
242 _weights[ 3]=9.2696893677723415844756991929711e-02_R;
243 _weights[ 4]=8.4557109690827332430645582165501e-02_R;
244 _weights[ 5]=6.6053075563350379166074502504878e-02_R;
245 _weights[ 6]=4.3401906407150625922456117586384e-02_R;
246 _weights[ 7]=2.2774591453263032586487649426060e-02_R;
247 _weights[ 8]=8.4193197829831874175163655187011e-03_R;
248 _weights[ 9]=1.4991406024063940282481360041064e-03_R;
249
250 return;
251 }
252 case TWENTIETH:
253 case TWENTYFIRST:
254 {
255 _points.resize (11);
256 _weights.resize(11);
257
258 _points[ 0](0)=1.0018280461680405843024729867805e-02_R;
259 _points[ 1](0)=5.2035451127180552583542695772964e-02_R;
260 _points[ 2](0)=1.2461922514444307373529958726391e-01_R;
261 _points[ 3](0)=2.2284060704383785550783145345736e-01_R;
262 _points[ 4](0)=3.4000815791466518823360523389702e-01_R;
263 _points[ 5](0)=4.6813761308958404208311038075775e-01_R;
264 _points[ 6](0)=5.9849727976713918322772071367304e-01_R;
265 _points[ 7](0)=7.2220328489096792556332130780461e-01_R;
266 _points[ 8](0)=8.3082489962281857403056654390566e-01_R;
267 _points[ 9](0)=9.1695838655259485329313462701803e-01_R;
268 _points[10](0)=9.7472637960247965024666881353837e-01_R;
269
270 _weights[ 0]=2.5367340688141426184944658517383e-02_R;
271 _weights[ 1]=5.4938091132871498258746681665651e-02_R;
272 _weights[ 2]=7.5620048057186998321377054841660e-02_R;
273 _weights[ 3]=8.4659422884017621219239388551910e-02_R;
274 _weights[ 4]=8.1879102988063470389586851943461e-02_R;
275 _weights[ 5]=6.9531875158183049799050889633934e-02_R;
276 _weights[ 6]=5.1591360672297580193086641744608e-02_R;
277 _weights[ 7]=3.2641546713833346017953865389764e-02_R;
278 _weights[ 8]=1.6663623451680692415747124573826e-02_R;
279 _weights[ 9]=6.0439209604797757927329621765769e-03_R;
280 _weights[10]=1.0636672932445414075338809612253e-03_R;
281
282 return;
283 }
284 case TWENTYSECOND:
285 case TWENTYTHIRD:
286 {
287 _points.resize (12);
288 _weights.resize(12);
289
290 _points[ 0](0)=8.5390549884274193686644608778398e-03_R;
291 _points[ 1](0)=4.4446463155407723025466798785553e-02_R;
292 _points[ 2](0)=1.0685449088347665763410677043250e-01_R;
293 _points[ 3](0)=1.9215105452985404099105725622861e-01_R;
294 _points[ 4](0)=2.9538088426258022162291683437601e-01_R;
295 _points[ 5](0)=4.1054508120145768248903435055933e-01_R;
296 _points[ 6](0)=5.3095084931281767062893024289682e-01_R;
297 _points[ 7](0)=6.4960065027725499276629172334298e-01_R;
298 _points[ 8](0)=7.5959888952522705374260257404342e-01_R;
299 _points[ 9](0)=8.5455254376493588079021191640562e-01_R;
300 _points[10](0)=9.2894210126441101784881015513432e-01_R;
301 _points[11](0)=9.7843793683414963909190691691700e-01_R;
302
303 _weights[ 0]=2.1664860886871767324583472077976e-02_R;
304 _weights[ 1]=4.7427851980377470134309182197087e-02_R;
305 _weights[ 2]=6.6606750626673198130834485351975e-02_R;
306 _weights[ 3]=7.6896602680041006281204469112373e-02_R;
307 _weights[ 4]=7.7696316815531026628765631099760e-02_R;
308 _weights[ 5]=7.0109339997630094495921805029671e-02_R;
309 _weights[ 6]=5.6613843713667631943701105156121e-02_R;
310 _weights[ 7]=4.0451653706913616760646424250646e-02_R;
311 _weights[ 8]=2.4876780409265432012508172290016e-02_R;
312 _weights[ 9]=1.2436009166422265607483293056674e-02_R;
313 _weights[10]=4.4448077956684623227961458658283e-03_R;
314 _weights[11]=7.7518222093802835724581451187414e-04_R;
315
316 return;
317 }
318
319 case TWENTYFOURTH:
320 case TWENTYFIFTH:
321 {
322 _points.resize (13);
323 _weights.resize(13);
324
325 _points[ 0](0)=7.3646510260893216506914984138223e-03_R;
326 _points[ 1](0)=3.8398138739678350376832524864142e-02_R;
327 _points[ 2](0)=9.2595224699002635282891375438616e-02_R;
328 _points[ 3](0)=1.6725101139155773149552247875936e-01_R;
329 _points[ 4](0)=2.5862354070576251658979073282269e-01_R;
330 _points[ 5](0)=3.6213139728223880040868129822732e-01_R;
331 _points[ 6](0)=4.7258438600411772517509464267860e-01_R;
332 _points[ 7](0)=5.8444396402134045550422084781091e-01_R;
333 _points[ 8](0)=6.9210100171960165689704195168767e-01_R;
334 _points[ 9](0)=7.9015702827343748555286333249938e-01_R;
335 _points[10](0)=8.7369482130668941936771456713174e-01_R;
336 _points[11](0)=9.3852445910073101239763338676530e-01_R;
337 _points[12](0)=9.8138963498901214856028062215971e-01_R;
338
339 _weights[ 0]=1.8714731585615175193374408664994e-02_R;
340 _weights[ 1]=4.1320289419839298476611706952624e-02_R;
341 _weights[ 2]=5.8953937956647082536161503261961e-02_R;
342 _weights[ 3]=6.9713468282144398251416629950427e-02_R;
343 _weights[ 4]=7.2849696515818223079384033843973e-02_R;
344 _weights[ 5]=6.8815529487565417217837889436694e-02_R;
345 _weights[ 6]=5.9120481314092327419290155953032e-02_R;
346 _weights[ 7]=4.5995780676052393313259784530213e-02_R;
347 _weights[ 8]=3.1936787162203148842381371158461e-02_R;
348 _weights[ 9]=1.9213957164719820645895497863743e-02_R;
349 _weights[10]=9.4489244795927503661800865492413e-03_R;
350 _weights[11]=3.3383592507737718066104206420419e-03_R;
351 _weights[12]=5.7805670493619285159651119259460e-04_R;
352
353 return;
354 }
355
356 case TWENTYSIXTH:
357 case TWENTYSEVENTH:
358 {
359 _points.resize (14);
360 _weights.resize(14);
361
362 _points[ 0](0)=6.4167607928184568108204640945072e-03_R;
363 _points[ 1](0)=3.3501404532013140035963928570572e-02_R;
364 _points[ 2](0)=8.0985499681955184392451307739982e-02_R;
365 _points[ 3](0)=1.4680486768121372992366016526080e-01_R;
366 _points[ 4](0)=2.2808427064925799153464409861994e-01_R;
367 _points[ 5](0)=3.2127174398893617440234039741304e-01_R;
368 _points[ 6](0)=4.2229465730757025784040898751810e-01_R;
369 _points[ 7](0)=5.2673786133987303205372694481288e-01_R;
370 _points[ 8](0)=6.3003668837040395788448059413143e-01_R;
371 _points[ 9](0)=7.2767645288926468543602672799033e-01_R;
372 _points[10](0)=8.1538973944347464197307421861206e-01_R;
373 _points[11](0)=8.8934280881951553969087166094649e-01_R;
374 _points[12](0)=9.4630270006027538353340594342472e-01_R;
375 _points[13](0)=9.8377523409860023828122800914100e-01_R;
376
377 _weights[ 0]=1.6326754322596839819449429350767e-02_R;
378 _weights[ 1]=3.6296078055443693187652118821852e-02_R;
379 _weights[ 2]=5.2445953501916745591081806162678e-02_R;
380 _weights[ 3]=6.3213025574329203442529115357932e-02_R;
381 _weights[ 4]=6.7831659604182837102347339834146e-02_R;
382 _weights[ 5]=6.6392350626085425132821358651277e-02_R;
383 _weights[ 6]=5.9785559022531584222614059168587e-02_R;
384 _weights[ 7]=4.9519454523203004580936179335753e-02_R;
385 _weights[ 8]=3.7443096458985826655938301826886e-02_R;
386 _weights[ 9]=2.5423465407148762115069898757459e-02_R;
387 _weights[10]=1.5032303743928643503408714751315e-02_R;
388 _weights[11]=7.2964841332126214434099222674776e-03_R;
389 _weights[12]=2.5541013176876539479794996099427e-03_R;
390 _weights[13]=4.3971370874715925476225610392609e-04_R;
391
392 return;
393 }
394
395 case TWENTYEIGHTH:
396 case TWENTYNINTH:
397 {
398 _points.resize (15);
399 _weights.resize(15);
400
401 _points[ 0](0)=5.6406889725117097575064665794442e-03_R;
402 _points[ 1](0)=2.9482298647942486631640984718004e-02_R;
403 _points[ 2](0)=7.1412953115158840054783901746735e-02_R;
404 _points[ 3](0)=1.2983102555359105597125453809429e-01_R;
405 _points[ 4](0)=2.0249275505010404756821998832023e-01_R;
406 _points[ 5](0)=2.8660608625752705998402604548440e-01_R;
407 _points[ 6](0)=3.7893868864697803810652900914277e-01_R;
408 _points[ 7](0)=4.7594230846323486057258899201585e-01_R;
409 _points[ 8](0)=5.7388916090668588067145385523753e-01_R;
410 _points[ 9](0)=6.6901519502995987653869563905314e-01_R;
411 _points[10](0)=7.5766473903134271199707427774029e-01_R;
412 _points[11](0)=8.3643096060561012397555908565418e-01_R;
413 _points[12](0)=9.0228670067937802663123850466201e-01_R;
414 _points[13](0)=9.5270040990583331433804420752426e-01_R;
415 _points[14](0)=9.8573054526317422526590063305913e-01_R;
416
417 _weights[ 0]=1.4367069621712523019113300206269e-02_R;
418 _weights[ 1]=3.2119044874965915878547666076448e-02_R;
419 _weights[ 2]=4.6891639944059925679345570546797e-02_R;
420 _weights[ 3]=5.7398825506941289374618916116414e-02_R;
421 _weights[ 4]=6.2918106648596909592665349230551e-02_R;
422 _weights[ 5]=6.3343955161511392519350738069297e-02_R;
423 _weights[ 6]=5.9174192059712931565021168664588e-02_R;
424 _weights[ 7]=5.1412362311886468530400169371359e-02_R;
425 _weights[ 8]=4.1400735184422578228813150524935e-02_R;
426 _weights[ 9]=3.0609769586468540804291808789747e-02_R;
427 _weights[10]=2.0416309272619835691190995270654e-02_R;
428 _weights[11]=1.1904190355097578843030186960250e-02_R;
429 _weights[12]=5.7172223947211761716246502974268e-03_R;
430 _weights[13]=1.9862346931450380410338051145760e-03_R;
431 _weights[14]=3.4034238413789606095252476068833e-04_R;
432
433 return;
434 }
435
436
437 case THIRTIETH:
438 case THIRTYFIRST:
439 {
440 _points.resize (16);
441 _weights.resize(16);
442
443 _points[ 0](0)=4.9972996637719210426511496015207e-03_R;
444 _points[ 1](0)=2.6143513681394051978549323380543e-02_R;
445 _points[ 2](0)=6.3430945583836745492528222770701e-02_R;
446 _points[ 3](0)=1.1559843757981594017892362824740e-01_R;
447 _points[ 4](0)=1.8087055965788366624757339125570e-01_R;
448 _points[ 5](0)=2.5702480784517085992294423955927e-01_R;
449 _points[ 6](0)=3.4146792754782306862589929793869e-01_R;
450 _points[ 7](0)=4.3132434359562537508359226958274e-01_R;
451 _points[ 8](0)=5.2353411602516832051747016507566e-01_R;
452 _points[ 9](0)=6.1495715187648951748964083381908e-01_R;
453 _points[10](0)=7.0248013792504104445480697553762e-01_R;
454 _points[11](0)=7.8312255396486808385218178256205e-01_R;
455 _points[12](0)=8.5413814777521063366511368381932e-01_R;
456 _points[13](0)=9.1310837653714127462958554670327e-01_R;
457 _points[14](0)=9.5802441769047545454495934455429e-01_R;
458 _points[15](0)=9.8735302062604161803115590316790e-01_R;
459
460 _weights[ 0]=1.2739310657334184747549845879578e-02_R;
461 _weights[ 1]=2.8612452590143149357558068987418e-02_R;
462 _weights[ 2]=4.2129431157428284757515740541878e-02_R;
463 _weights[ 3]=5.2228594403959147363509678893029e-02_R;
464 _weights[ 4]=5.8254240209855835379301779422393e-02_R;
465 _weights[ 5]=6.0000854888113507055385942002166e-02_R;
466 _weights[ 6]=5.7718879609267823617681995467969e-02_R;
467 _weights[ 7]=5.2064137843806583754973352189273e-02_R;
468 _weights[ 8]=4.3997382189243923173481417304490e-02_R;
469 _weights[ 9]=3.4647816579285799103084877873731e-02_R;
470 _weights[10]=2.5159233106470040585653957496918e-02_R;
471 _weights[11]=1.6539584355635793501225242083105e-02_R;
472 _weights[12]=9.5341678846659366549669638207733e-03_R;
473 _weights[13]=4.5392323861386350682211111786128e-03_R;
474 _weights[14]=1.5671884735958197030724006964051e-03_R;
475 _weights[15]=2.6749366505553617681762616226073e-04_R;
476
477 return;
478 }
479
480
481 case THIRTYSECOND:
482 case THIRTYTHIRD:
483 {
484 _points.resize (17);
485 _weights.resize(17);
486
487 _points[ 0](0)=4.4579935677873917545062291115464e-03_R;
488 _points[ 1](0)=2.3340094123774273967021528207683e-02_R;
489 _points[ 2](0)=5.6707968769078239532713331556521e-02_R;
490 _points[ 3](0)=1.0355543293519706341349122696131e-01_R;
491 _points[ 4](0)=1.6246000342813654998162954391410e-01_R;
492 _points[ 5](0)=2.3163212577717218294679722573836e-01_R;
493 _points[ 6](0)=3.0897011775219590331752426128626e-01_R;
494 _points[ 7](0)=3.9212413472209565803361946333190e-01_R;
495 _points[ 8](0)=4.7856759685307958878371046285937e-01_R;
496 _points[ 9](0)=5.6567396688663433190330697600965e-01_R;
497 _points[10](0)=6.5079655845338226473148740732315e-01_R;
498 _points[11](0)=7.3134895273405138213302149556298e-01_R;
499 _points[12](0)=8.0488357852496649199917770139703e-01_R;
500 _points[13](0)=8.6916605956741361920444649801116e-01_R;
501 _points[14](0)=9.2224303459229840848710732823038e-01_R;
502 _points[15](0)=9.6250119782335004125046077538851e-01_R;
503 _points[16](0)=9.8871404063224375141712140225296e-01_R;
504
505 _weights[ 0]=1.1372703113196894148880104403419e-02_R;
506 _weights[ 1]=2.5642427920205179185750205247311e-02_R;
507 _weights[ 2]=3.8025728825742400201474917006665e-02_R;
508 _weights[ 3]=4.7641869374618441920575209265709e-02_R;
509 _weights[ 4]=5.3907931667527480191616020246527e-02_R;
510 _weights[ 5]=5.6573611382471512986991034182850e-02_R;
511 _weights[ 6]=5.5734917923560549577129019490753e-02_R;
512 _weights[ 7]=5.1809741929296333255214704762820e-02_R;
513 _weights[ 8]=4.5477790399142277497438924164211e-02_R;
514 _weights[ 9]=3.7592325487112238031431998524319e-02_R;
515 _weights[10]=2.9074524087705050563187355467924e-02_R;
516 _weights[11]=2.0803278010295362060012866375773e-02_R;
517 _weights[12]=1.3513697452300780909638958310491e-02_R;
518 _weights[13]=7.7164222148059386958884227660543e-03_R;
519 _weights[14]=3.6472304834214064450344565237838e-03_R;
520 _weights[15]=1.2526834393912207489106525201067e-03_R;
521 _weights[16]=2.1311628920693358082515074128342e-04_R;
522
523 return;
524 }
525
526 case THIRTYFOURTH:
527 case THIRTYFIFTH:
528 {
529 _points.resize (18);
530 _weights.resize(18);
531
532 _points[ 0](0)=4.0014793838673867970427199102708e-03_R;
533 _points[ 1](0)=2.0963648393766477995135600986561e-02_R;
534 _points[ 2](0)=5.0994041587890553966774921299853e-02_R;
535 _points[ 3](0)=9.3280395928544950777609058826066e-02_R;
536 _points[ 4](0)=1.4667010367761795715160882973461e-01_R;
537 _points[ 5](0)=2.0970703958884296672188171145203e-01_R;
538 _points[ 6](0)=2.8067179006017169910681926203455e-01_R;
539 _points[ 7](0)=3.5762864997663462939832714298390e-01_R;
540 _points[ 8](0)=4.3847844922413811765185426038741e-01_R;
541 _points[ 9](0)=5.2101582087077614731981479158547e-01_R;
542 _points[10](0)=6.0298936055983207213748070418747e-01_R;
543 _points[11](0)=6.8216303911365156501882207998153e-01_R;
544 _points[12](0)=7.5637719340615062679816733590978e-01_R;
545 _points[13](0)=8.2360742977486956587394885462062e-01_R;
546 _points[14](0)=8.8201982536207914673124120886230e-01_R;
547 _points[15](0)=9.3002088969969321648195850472769e-01_R;
548 _points[16](0)=9.6630075194563254241150674649068e-01_R;
549 _points[17](0)=9.8986684820259713441676302277596e-01_R;
550
551 _weights[ 0]=1.0214339435040633872267566728543e-02_R;
552 _weights[ 1]=2.3106350163377066931289331193145e-02_R;
553 _weights[ 2]=3.4471118921922024965038695158493e-02_R;
554 _weights[ 3]=4.3573907074643088262181650935306e-02_R;
555 _weights[ 4]=4.9902226917702713891102223856106e-02_R;
556 _weights[ 5]=5.3192334631835660026223777017865e-02_R;
557 _weights[ 6]=5.3445287802814027020361560753181e-02_R;
558 _weights[ 7]=5.0916928856374093181562996165432e-02_R;
559 _weights[ 8]=4.6082400990241280762086995392822e-02_R;
560 _weights[ 9]=3.9579162288607878726422969126448e-02_R;
561 _weights[10]=3.2134806127628549240737903166505e-02_R;
562 _weights[11]=2.4487590001291716597869859208141e-02_R;
563 _weights[12]=1.7308300480899289815470186505791e-02_R;
564 _weights[13]=1.1131870097409362452892993478578e-02_R;
565 _weights[14]=6.3060388823805337332782426625400e-03_R;
566 _weights[15]=2.9624430644328375036535062298419e-03_R;
567 _weights[16]=1.0130251793010471252471709101709e-03_R;
568 _weights[17]=1.7186908409819589231237151109171e-04_R;
569
570 return;
571 }
572
573 case THIRTYSIXTH:
574 case THIRTYSEVENTH:
575 {
576 _points.resize (19);
577 _weights.resize(19);
578
579 _points[ 0](0)=3.6116428185568930344532101262520e-03_R;
580 _points[ 1](0)=1.8931837031588217250264524316949e-02_R;
581 _points[ 2](0)=4.6097933048431083573924770835459e-02_R;
582 _points[ 3](0)=8.4447222784209820599847900451170e-02_R;
583 _points[ 4](0)=1.3303618855809877542408742397522e-01_R;
584 _points[ 5](0)=1.9066859490476335108747466488719e-01_R;
585 _points[ 6](0)=2.5592540348210296025204739729528e-01_R;
586 _points[ 7](0)=3.2719980076381171572842996527566e-01_R;
587 _points[ 8](0)=4.0273678616507709512304701110488e-01_R;
588 _points[ 9](0)=4.8067639357855190263322135248271e-01_R;
589 _points[10](0)=5.5909949264903198784692797587908e-01_R;
590 _points[11](0)=6.3607504487927089469109105709816e-01_R;
591 _points[12](0)=7.0970765165390239884374678311164e-01_R;
592 _points[13](0)=7.7818422297676161420929964704208e-01_R;
593 _points[14](0)=8.3981861570871107783863629442929e-01_R;
594 _points[15](0)=8.9309313498184497075098115456491e-01_R;
595 _points[16](0)=9.3669584807436508054390550208195e-01_R;
596 _points[17](0)=9.6955263708022088547192878623227e-01_R;
597 _points[18](0)=9.9085180527095568535309483522012e-01_R;
598
599 _weights[ 0]=9.2240377250330766917668248692203e-03_R;
600 _weights[ 1]=2.0924651751979890481445228332988e-02_R;
601 _weights[ 2]=3.1376275285732898854356814457609e-02_R;
602 _weights[ 3]=3.9962370048991741940293076442317e-02_R;
603 _weights[ 4]=4.6234928168578411765380785132191e-02_R;
604 _weights[ 5]=4.9934138240419379553284105838773e-02_R;
605 _weights[ 6]=5.1004186626719396295755229568486e-02_R;
606 _weights[ 7]=4.9591046468706580141316052533532e-02_R;
607 _weights[ 8]=4.6021985716138412908362881060678e-02_R;
608 _weights[ 9]=4.0768870871836685572301729841664e-02_R;
609 _weights[10]=3.4398957951907391429559705435925e-02_R;
610 _weights[11]=2.7518058144347978141481142479516e-02_R;
611 _weights[12]=2.0711672562757804879837159838775e-02_R;
612 _weights[13]=1.4489847112109724657001233005036e-02_R;
613 _weights[14]=9.2410919293165977626976877702861e-03_R;
614 _weights[15]=5.1997813282783796868055465441831e-03_R;
615 _weights[16]=2.4300917120432807075681660438661e-03_R;
616 _weights[17]=8.2788076092398219334600301771448e-04_R;
617 _weights[18]=1.4012759417838633744062778723898e-04_R;
618
619 return;
620 }
621
622 case THIRTYEIGHTH:
623 case THIRTYNINTH:
624 {
625 _points.resize (20);
626 _weights.resize(20);
627
628 _points[ 0](0)=3.2761066690500989752646761128711e-03_R;
629 _points[ 1](0)=1.7181218145255713738247704631582e-02_R;
630 _points[ 2](0)=4.1871431117765195244234634143709e-02_R;
631 _points[ 3](0)=7.6800837089621970481870523019947e-02_R;
632 _points[ 4](0)=1.2118986732367606561768615229454e-01_R;
633 _points[ 5](0)=1.7404711263554216522415793419966e-01_R;
634 _points[ 6](0)=2.3419188631359219089445571283230e-01_R;
635 _points[ 7](0)=3.0028067683595016436625841871717e-01_R;
636 _points[ 8](0)=3.7083718058439689644532207953771e-01_R;
637 _points[ 9](0)=4.4428528696301116212882391783598e-01_R;
638 _points[10](0)=5.1898428870357372961841176083024e-01_R;
639 _points[11](0)=5.9326553348350648796739308654437e-01_R;
640 _points[12](0)=6.6546969890551364795372958813385e-01_R;
641 _points[13](0)=7.3398385823565944973202719329584e-01_R;
642 _points[14](0)=7.9727750833659468770218885137527e-01_R;
643 _points[15](0)=8.5393675303589045708900439161802e-01_R;
644 _points[16](0)=9.0269587179345369227634694169967e-01_R;
645 _points[17](0)=9.4246554236318633869089187742766e-01_R;
646 _points[18](0)=9.7235694664743691118470187166465e-01_R;
647 _points[19](0)=9.9169995579293273076654365969470e-01_R;
648
649 _weights[ 0]=8.3708441762725569742347797346057e-03_R;
650 _weights[ 1]=1.9034969463701666952317752319364e-02_R;
651 _weights[ 2]=2.8668237379130596303519483134423e-02_R;
652 _weights[ 3]=3.6750239836647855880170014918540e-02_R;
653 _weights[ 4]=4.2890295837978204214146023790200e-02_R;
654 _weights[ 5]=4.6841691862557827847492882468251e-02_R;
655 _weights[ 6]=4.8516105059854090810181874268668e-02_R;
656 _weights[ 7]=4.7985461609943912515256158210751e-02_R;
657 _weights[ 8]=4.5470588941353475125260875269943e-02_R;
658 _weights[ 9]=4.1317706816665737825832945172262e-02_R;
659 _weights[10]=3.5964919153862747854063187859799e-02_R;
660 _weights[11]=2.9901741842629013049082489189589e-02_R;
661 _weights[12]=2.3625296173548892813066360441583e-02_R;
662 _weights[13]=1.7597066879206016267686128655074e-02_R;
663 _weights[14]=1.2204046126680104278798703245791e-02_R;
664 _weights[15]=7.7276679300514628735780671415898e-03_R;
665 _weights[16]=4.3232191126901531337390520742896e-03_R;
666 _weights[17]=2.0114576139640780069071394684122e-03_R;
667 _weights[18]=6.8306227608592198451771987553801e-04_R;
668 _weights[19]=1.1538190717568529014836276132844e-04_R;
669
670 return;
671 }
672
673 case FORTIETH:
674 case FORTYFIRST:
675 {
676 _points.resize (21);
677 _weights.resize(21);
678
679 _points[ 0](0)=2.9852372832130627418887840757498e-03_R;
680 _points[ 1](0)=1.5662280557573547332895610655678e-02_R;
681 _points[ 2](0)=3.8198288245073553344832819395658e-02_R;
682 _points[ 3](0)=7.0139619062325798139842656763758e-02_R;
683 _points[ 4](0)=1.1083667332036350223762530758616e-01_R;
684 _points[ 5](0)=1.5946112944406525026381380836555e-01_R;
685 _points[ 6](0)=2.1502318535802028508091216764592e-01_R;
686 _points[ 7](0)=2.7639177909378317240968620976306e-01_R;
687 _points[ 8](0)=3.4231763295873079372348132371246e-01_R;
688 _points[ 9](0)=4.1145869156190519892697533612651e-01_R;
689 _points[10](0)=4.8240744461243888053531852185958e-01_R;
690 _points[11](0)=5.5371958072829359140036561243486e-01_R;
691 _points[12](0)=6.2394338972128194749630581474409e-01_R;
692 _points[13](0)=6.9164931501296225721944667896925e-01_R;
693 _points[14](0)=7.5545905444968698626584997281486e-01_R;
694 _points[15](0)=8.1407361651269741678894410957934e-01_R;
695 _points[16](0)=8.6629975897095659707636330435792e-01_R;
696 _points[17](0)=9.1107426580261577477966643276619e-01_R;
697 _points[18](0)=9.4748554440639734668609897166113e-01_R;
698 _points[19](0)=9.7479197566036565307915209128675e-01_R;
699 _points[20](0)=9.9243549072562147749379027938900e-01_R;
700
701 _weights[ 0]=7.6306059065231890951709176867159e-03_R;
702 _weights[ 1]=1.7387926076195012545310092581185e-02_R;
703 _weights[ 2]=2.6287260083203306468723755830943e-02_R;
704 _weights[ 3]=3.3886790344403175515158905218748e-02_R;
705 _weights[ 4]=3.9845977571398966444570950002831e-02_R;
706 _weights[ 5]=4.3935570635150377464859835729052e-02_R;
707 _weights[ 6]=4.6050270723257502074077985626262e-02_R;
708 _weights[ 7]=4.6212552611022412660350368837561e-02_R;
709 _weights[ 8]=4.4566874686154606866984823191992e-02_R;
710 _weights[ 9]=4.1364760396997617354403702904192e-02_R;
711 _weights[10]=3.6942012648499385551903205764287e-02_R;
712 _weights[11]=3.1689953050127340376763333466278e-02_R;
713 _weights[12]=2.6023046795895555117823162899995e-02_R;
714 _weights[13]=2.0345549389821508292035088652126e-02_R;
715 _weights[14]=1.5019872613192784763520392446339e-02_R;
716 _weights[15]=1.0339209757970312663832726410241e-02_R;
717 _weights[16]=6.5065974236456053354067512991831e-03_R;
718 _weights[17]=3.6220528697449398652362737797211e-03_R;
719 _weights[18]=1.6787560215669155362763365937815e-03_R;
720 _weights[19]=5.6849852669976417861179123569953e-04_R;
721 _weights[20]=9.5861868529721828979599842865244e-05_R;
722
723 return;
724 }
725
726 case FORTYSECOND:
727 case FORTYTHIRD:
728 {
729 _points.resize (22);
730 _weights.resize(22);
731
732 _points[ 0](0)=2.7314460088842296840089704503200e-03_R;
733 _points[ 1](0)=1.4335933483699706185308039285053e-02_R;
734 _points[ 2](0)=3.4986328351216449387218814071085e-02_R;
735 _points[ 3](0)=6.4302641132158882531275071395686e-02_R;
736 _points[ 4](0)=1.0173934345216392401258226593794e-01_R;
737 _points[ 5](0)=1.4659920015766541692656584266952e-01_R;
738 _points[ 6](0)=1.9804660411818261484660504028001e-01_R;
739 _points[ 7](0)=2.5512320697168696957682873507625e-01_R;
740 _points[ 8](0)=3.1676578871044727183421117602379e-01_R;
741 _points[ 9](0)=3.8182606925675020305095127628112e-01_R;
742 _points[10](0)=4.4909210098681733251387195042393e-01_R;
743 _points[11](0)=5.1731084595099112005136286684174e-01_R;
744 _points[12](0)=5.8521151795129912975524533467408e-01_R;
745 _points[13](0)=6.5152925489581447403580682231185e-01_R;
746 _points[14](0)=7.1502868047476240261215783933800e-01_R;
747 _points[15](0)=7.7452691606482263532020273841099e-01_R;
748 _points[16](0)=8.2891561362172651235400549854277e-01_R;
749 _points[17](0)=8.7718159746542002099358323827803e-01_R;
750 _points[18](0)=9.1842572498984926327926994425432e-01_R;
751 _points[19](0)=9.5187959322971991452332541323047e-01_R;
752 _points[20](0)=9.7691966323712886717816657113704e-01_R;
753 _points[21](0)=9.9307748504434821490300210664154e-01_R;
754
755 _weights[ 0]=6.9842561136978136538216549700282e-03_R;
756 _weights[ 1]=1.5944053454778496864565929126309e-02_R;
757 _weights[ 2]=2.4184236671890499758870393233781e-02_R;
758 _weights[ 3]=3.1327596999375227892408958559682e-02_R;
759 _weights[ 4]=3.7077054093202864483217335909271e-02_R;
760 _weights[ 5]=4.1222404906411452577079119693783e-02_R;
761 _weights[ 6]=4.3651203786303462995293138094828e-02_R;
762 _weights[ 7]=4.4353370900419806188626977124445e-02_R;
763 _weights[ 8]=4.3418750145417827908334525766667e-02_R;
764 _weights[ 9]=4.1027795781940901638265438618895e-02_R;
765 _weights[10]=3.7436116466930019239662981188891e-02_R;
766 _weights[11]=3.2954058785385534039887856528676e-02_R;
767 _weights[12]=2.7922870823442631249079662456458e-02_R;
768 _weights[13]=2.2689228598160995380212860776143e-02_R;
769 _weights[14]=1.7580017560152292742735027157072e-02_R;
770 _weights[15]=1.2879230281365339696348205046681e-02_R;
771 _weights[16]=8.8086724401109070881737532508054e-03_R;
772 _weights[17]=5.5138751021276410109163746634529e-03_R;
773 _weights[18]=3.0562141131504037344643025112362e-03_R;
774 _weights[19]=1.4117668531394242829582650189559e-03_R;
775 _weights[20]=4.7692790565900675904839748933142e-04_R;
776 _weights[21]=8.0298216937450816028842814607537e-05_R;
777
778 return;
779 }
780
781 default:
782 libmesh_error_msg("Quadrature rule " << _order << " not supported!");
783 } // end switch(_order + 2*p)
784 } // end if ((_alpha == 1) && (_beta == 0))
785
786
787
788 else if ((_alpha == 2) && (_beta == 0))
789 {
790
791 switch(get_order())
792 {
793 case CONSTANT:
794 case FIRST:
795 {
796 _points.resize (1);
797 _weights.resize(1);
798
799 _points[0](0) = 0.25;
800
801 _weights[0] = 1/Real(3);
802
803 return;
804 }
805 case SECOND:
806 case THIRD:
807 {
808 _points.resize (2);
809 _weights.resize(2);
810
811 _points[ 0](0)=1.2251482265544137786674043037115e-01_R;
812 _points[ 1](0)=5.4415184401122528879992623629551e-01_R;
813
814 _weights[ 0]=2.3254745125350790274997694884235e-01_R;
815 _weights[ 1]=1.0078588207982543058335638449099e-01_R;
816
817 return;
818 }
819 case FOURTH:
820 case FIFTH:
821 {
822 _points.resize (3);
823 _weights.resize(3);
824
825 _points[ 0](0)=7.2994024073149732155837979012003e-02_R;
826 _points[ 1](0)=3.4700376603835188472176354340395e-01_R;
827 _points[ 2](0)=7.0500220988849838312239847758405e-01_R;
828
829 _weights[ 0]=1.5713636106488661331834482221327e-01_R;
830 _weights[ 1]=1.4624626925986602200351202036424e-01_R;
831 _weights[ 2]=2.9950703008580698011476490755827e-02_R;
832
833 return;
834 }
835 case SIXTH:
836 case SEVENTH:
837 {
838 _points.resize (4);
839 _weights.resize(4);
840
841 _points[ 0](0)=4.8500549446997329297067257098986e-02_R;
842 _points[ 1](0)=2.3860073755186230505898141272470e-01_R;
843 _points[ 2](0)=5.1704729510436750234057336938307e-01_R;
844 _points[ 3](0)=7.9585141789677286330337796079324e-01_R;
845
846 _weights[ 0]=1.1088841561127798368323131746895e-01_R;
847 _weights[ 1]=1.4345878979921420904832801427594e-01_R;
848 _weights[ 2]=6.8633887172923075317376345041811e-02_R;
849 _weights[ 3]=1.0352240749918065284397656546639e-02_R;
850
851 return;
852 }
853 case EIGHTH:
854 case NINTH:
855 {
856 _points.resize (5);
857 _weights.resize(5);
858
859 _points[ 0](0)=3.4578939918215091524457428631527e-02_R;
860 _points[ 1](0)=1.7348032077169572310459241798618e-01_R;
861 _points[ 2](0)=3.8988638706551932824089541038499e-01_R;
862 _points[ 3](0)=6.3433347263088677234716388892062e-01_R;
863 _points[ 4](0)=8.5105421294701641811622418741001e-01_R;
864
865 _weights[ 0]=8.1764784285770917904880732922352e-02_R;
866 _weights[ 1]=1.2619896189991148802883293516467e-01_R;
867 _weights[ 2]=8.9200161221590000186254493070384e-02_R;
868 _weights[ 3]=3.2055600722961919254748930556633e-02_R;
869 _weights[ 4]=4.1138252030990079586162416192983e-03_R;
870
871 return;
872 }
873 case TENTH:
874 case ELEVENTH:
875 {
876 _points.resize (6);
877 _weights.resize(6);
878
879 _points[ 0](0)=2.5904555093667192754643606997235e-02_R;
880 _points[ 1](0)=1.3156394165798513398691085074097e-01_R;
881 _points[ 2](0)=3.0243691802289123274990557791855e-01_R;
882 _points[ 3](0)=5.0903641316475208401103990516772e-01_R;
883 _points[ 4](0)=7.1568112731171391876766262459361e-01_R;
884 _points[ 5](0)=8.8680561617756186630126600601049e-01_R;
885
886 _weights[ 0]=6.2538702726580937878526556468332e-02_R;
887 _weights[ 1]=1.0737649973678063260575568234795e-01_R;
888 _weights[ 2]=9.4577186748541203568292051720052e-02_R;
889 _weights[ 3]=5.1289571129616210220129325076919e-02_R;
890 _weights[ 4]=1.5720297184945051327851262130020e-02_R;
891 _weights[ 5]=1.8310758068692977327784555900562e-03_R;
892
893 return;
894 }
895 case TWELFTH:
896 case THIRTEENTH:
897 {
898 _points.resize (7);
899 _weights.resize(7);
900
901 _points[ 0](0)=2.0132773773400507230501687117472e-02_R;
902 _points[ 1](0)=1.0308902914804901475222678600595e-01_R;
903 _points[ 2](0)=2.4055412604805753665369914150100e-01_R;
904 _points[ 3](0)=4.1400214459705974641828724885057e-01_R;
905 _points[ 4](0)=6.0002151327899293019396877288994e-01_R;
906 _points[ 5](0)=7.7351724659143750111199899642603e-01_R;
907 _points[ 6](0)=9.1118316656300276363931736720905e-01_R;
908
909 _weights[ 0]=4.9276501776438120823429129084905e-02_R;
910 _weights[ 1]=9.0698824612686144536967479972374e-02_R;
911 _weights[ 2]=9.1733803279795254111416595896867e-02_R;
912 _weights[ 3]=6.3146378708891297709533940481199e-02_R;
913 _weights[ 4]=2.9422211289528614840745351985011e-02_R;
914 _weights[ 5]=8.1629256323046945072318090687213e-03_R;
915 _weights[ 6]=8.9268803368920680400902684425561e-04_R;
916
917 return;
918 }
919 case FOURTEENTH:
920 case FIFTEENTH:
921 {
922 _points.resize (8);
923 _weights.resize(8);
924
925 _points[ 0](0)=1.6097759551921033532013550096618e-02_R;
926 _points[ 1](0)=8.2900617485651102700366353380388e-02_R;
927 _points[ 2](0)=1.9547516848873991732426660953061e-01_R;
928 _points[ 3](0)=3.4165199147720222027296226216240e-01_R;
929 _points[ 4](0)=5.0559707818448917194006186500608e-01_R;
930 _points[ 5](0)=6.6955227182436145183011451055437e-01_R;
931 _points[ 6](0)=8.1577170358328376075475178697587e-01_R;
932 _points[ 7](0)=9.2850896495990689720101861784923e-01_R;
933
934 _weights[ 0]=3.9778957806690559830106455926398e-02_R;
935 _weights[ 1]=7.6818093267222624804506735068290e-02_R;
936 _weights[ 2]=8.5284769171938765209441226265186e-02_R;
937 _weights[ 3]=6.8447183421653272247027200610852e-02_R;
938 _weights[ 4]=4.0814426388544023186461596152148e-02_R;
939 _weights[ 5]=1.7246863780234982804243655774862e-02_R;
940 _weights[ 6]=4.4745217130144079957565210032836e-03_R;
941 _weights[ 7]=4.6851778403469725578994253231334e-04_R;
942
943 return;
944 }
945 case SIXTEENTH:
946 case SEVENTEENTH:
947 {
948 _points.resize (9);
949 _weights.resize(9);
950
951 _points[ 0](0)=1.3165885597114490545190537817972e-02_R;
952 _points[ 1](0)=6.8084529593767587476505856986822e-02_R;
953 _points[ 2](0)=1.6175951676407464206981091232919e-01_R;
954 _points[ 3](0)=2.8589108833922039772798956691264e-01_R;
955 _points[ 4](0)=4.2945364538781279250924800228659e-01_R;
956 _points[ 5](0)=5.7969405635116312626577241331199e-01_R;
957 _points[ 6](0)=7.2326857174033543181796015820021e-01_R;
958 _points[ 7](0)=8.4743684201323732017318042501962e-01_R;
959 _points[ 8](0)=9.4124586421327421141434212713498e-01_R;
960
961 _weights[ 0]=3.2760145111039721461819540084274e-02_R;
962 _weights[ 1]=6.5489537033396631781939107203912e-02_R;
963 _weights[ 2]=7.7673569160555504078595170478444e-02_R;
964 _weights[ 3]=6.9284395689804709215727785348892e-02_R;
965 _weights[ 4]=4.8540627864506507959528062424865e-02_R;
966 _weights[ 5]=2.6343280902549835737974696002673e-02_R;
967 _weights[ 6]=1.0406116579352237052426337235938e-02_R;
968 _weights[ 7]=2.5743986456087231023317159056037e-03_R;
969 _weights[ 8]=2.6126234651946294299091864873302e-04_R;
970
971 return;
972 }
973 case EIGHTTEENTH:
974 case NINETEENTH:
975 {
976 _points.resize (10);
977 _weights.resize(10);
978
979 _points[ 0](0)=1.0968452456174134250281032990432e-02_R;
980 _points[ 1](0)=5.6898150533657920711434859379121e-02_R;
981 _points[ 2](0)=1.3595023405022895426576342938519e-01_R;
982 _points[ 3](0)=2.4228119613252356111139455536509e-01_R;
983 _points[ 4](0)=3.6800785044933771760476956625017e-01_R;
984 _points[ 5](0)=5.0380712641487390700553064205723e-01_R;
985 _points[ 6](0)=6.3960948865470970932853650616696e-01_R;
986 _points[ 7](0)=7.6534767954810789620953312724460e-01_R;
987 _points[ 8](0)=8.7171007457440848761186134200542e-01_R;
988 _points[ 9](0)=9.5087429264052316644634948461033e-01_R;
989
990 _weights[ 0]=2.7434088710097496960451648584485e-02_R;
991 _weights[ 1]=5.6272936402808126282415832152709e-02_R;
992 _weights[ 2]=7.0069507708666334086372455308183e-02_R;
993 _weights[ 3]=6.7452219381437824970525794313691e-02_R;
994 _weights[ 4]=5.2883788766964158209884838942421e-02_R;
995 _weights[ 5]=3.3854565016814116044101071309373e-02_R;
996 _weights[ 6]=1.7197575046553008079137502323978e-02_R;
997 _weights[ 7]=6.4698890685585292297306065609276e-03_R;
998 _weights[ 8]=1.5455231947365786285853268147186e-03_R;
999 _weights[ 9]=1.5324003669716084212825702284675e-04_R;
1000
1001 return;
1002 }
1003 case TWENTIETH:
1004 case TWENTYFIRST:
1005 {
1006 _points.resize (11);
1007 _weights.resize(11);
1008
1009 _points[ 0](0)=9.2789738313488342029466103013448e-03_R;
1010 _points[ 1](0)=4.8249692094286258286483723731132e-02_R;
1011 _points[ 2](0)=1.1578862662939522596030591825565e-01_R;
1012 _points[ 3](0)=2.0766834159705988244389542530053e-01_R;
1013 _points[ 4](0)=3.1811795190623396637744646657914e-01_R;
1014 _points[ 5](0)=4.4019839985886246708268132217632e-01_R;
1015 _points[ 6](0)=5.6623983915456831356751247193488e-01_R;
1016 _points[ 7](0)=6.8832423986295668569553397580809e-01_R;
1017 _points[ 8](0)=7.9878435859091464197460872800735e-01_R;
1018 _points[ 9](0)=8.9069109935439218915081289990608e-01_R;
1019 _points[10](0)=9.5832514378664820192443912466615e-01_R;
1020
1021 _weights[ 0]=2.3300850051388377415061404350855e-02_R;
1022 _weights[ 1]=4.8745861030664491864450329028080e-02_R;
1023 _weights[ 2]=6.2979543000367394338333998811129e-02_R;
1024 _weights[ 3]=6.4183559349755944992539371306173e-02_R;
1025 _weights[ 4]=5.4632222321044926070678715192708e-02_R;
1026 _weights[ 5]=3.9290217798435612246535835921329e-02_R;
1027 _weights[ 6]=2.3589663538806928649316661943808e-02_R;
1028 _weights[ 7]=1.1414590918097618249921262806781e-02_R;
1029 _weights[ 8]=4.1400042632190223547676874553245e-03_R;
1030 _weights[ 9]=9.6302057554323908320037373956771e-04_R;
1031 _weights[10]=9.3800486009778068527692777578977e-05_R;
1032
1033 return;
1034 }
1035 case TWENTYSECOND:
1036 case TWENTYTHIRD:
1037 {
1038 _points.resize (12);
1039 _weights.resize(12);
1040
1041 _points[ 0](0)=7.9520457026384368762190933400404e-03_R;
1042 _points[ 1](0)=4.1427810454294590790770165194795e-02_R;
1043 _points[ 2](0)=9.9757625542614157066081703480300e-02_R;
1044 _points[ 3](0)=1.7981078905242324954164334430721e-01_R;
1045 _points[ 4](0)=2.7727345779931511981753891831052e-01_R;
1046 _points[ 5](0)=3.8689200999768979166563470380544e-01_R;
1047 _points[ 6](0)=5.0275736044903220327930927843912e-01_R;
1048 _points[ 7](0)=6.1862386345845604629354886189114e-01_R;
1049 _points[ 8](0)=7.2824645295307268642888033006114e-01_R;
1050 _points[ 9](0)=8.2571851421478690176408336295370e-01_R;
1051 _points[10](0)=9.0579507354454372680179647039974e-01_R;
1052 _points[11](0)=9.6420653529267155121295530627839e-01_R;
1053
1054 _weights[ 0]=2.0031112584748752943807724216722e-02_R;
1055 _weights[ 1]=4.2556615367405637772968490900760e-02_R;
1056 _weights[ 2]=5.6584184749474069646478036154467e-02_R;
1057 _weights[ 3]=6.0250607487604518170935343500906e-02_R;
1058 _weights[ 4]=5.4573941164231582825558709780290e-02_R;
1059 _weights[ 5]=4.2764763570188902317265936785879e-02_R;
1060 _weights[ 6]=2.8908051838727360494403492180206e-02_R;
1061 _weights[ 7]=1.6547343644609412101387213540038e-02_R;
1062 _weights[ 8]=7.7163670238864266187877366246530e-03_R;
1063 _weights[ 9]=2.7208421441038393545415361663513e-03_R;
1064 _weights[10]=6.1995339854451942336673117135933e-04_R;
1065 _weights[11]=5.9550359808311663832382311702501e-05_R;
1066
1067 return;
1068 }
1069
1070 case TWENTYFOURTH:
1071 case TWENTYFIFTH:
1072 {
1073 _points.resize (13);
1074 _weights.resize(13);
1075
1076 _points[ 0](0)=6.8908313099587313966815341534070e-03_R;
1077 _points[ 1](0)=3.5953362700170095501132811969521e-02_R;
1078 _points[ 2](0)=8.6811780157585433284280307690601e-02_R;
1079 _points[ 3](0)=1.5709997419650927473052206555148e-01_R;
1080 _points[ 4](0)=2.4353289958712844441903410356775e-01_R;
1081 _points[ 5](0)=3.4206951264607532347450799656627e-01_R;
1082 _points[ 6](0)=4.4810263890570985362873430879398e-01_R;
1083 _points[ 7](0)=5.5667462262945501069694664236208e-01_R;
1084 _points[ 8](0)=6.6270931356038854232146315212326e-01_R;
1085 _points[ 9](0)=7.6124976630827697227665952639343e-01_R;
1086 _points[10](0)=8.4769104394723239091031404895142e-01_R;
1087 _points[11](0)=9.1799964553720667953362597028835e-01_R;
1088 _points[12](0)=9.6892889422858896211181181730274e-01_R;
1089
1090 _weights[ 0]=1.7401228610061845488081141733526e-02_R;
1091 _weights[ 1]=3.7426708168844039953666298186474e-02_R;
1092 _weights[ 2]=5.0909830712695019092906847187640e-02_R;
1093 _weights[ 3]=5.6111537130827396185039872203667e-02_R;
1094 _weights[ 4]=5.3340021605871745725401666422880e-02_R;
1095 _weights[ 5]=4.4624600755614954430566337477243e-02_R;
1096 _weights[ 6]=3.2940451678432790083648445397381e-02_R;
1097 _weights[ 7]=2.1254996714756613031113108888658e-02_R;
1098 _weights[ 8]=1.1728259593101880662970381149369e-02_R;
1099 _weights[ 9]=5.3135693388326384480559144318474e-03_R;
1100 _weights[10]=1.8323911392393785873485644191745e-03_R;
1101 _weights[11]=4.1072089179088541678428389490865e-04_R;
1102 _weights[12]=3.9016993264146227750471940564101e-05_R;
1103
1104 return;
1105 }
1106
1107 case TWENTYSIXTH:
1108 case TWENTYSEVENTH:
1109 {
1110 _points.resize (14);
1111 _weights.resize(14);
1112
1113 _points[ 0](0)=6.0288088710666481700887477121600e-03_R;
1114 _points[ 1](0)=3.1494259818657590707306712766317e-02_R;
1115 _points[ 2](0)=7.6213622474853867586406786340023e-02_R;
1116 _points[ 3](0)=1.3836652595947406914513833295825e-01_R;
1117 _points[ 4](0)=2.1540975706889557490069553208515e-01_R;
1118 _points[ 5](0)=3.0418952814165630963236635490440e-01_R;
1119 _points[ 6](0)=4.0107137869715435758118603205199e-01_R;
1120 _points[ 7](0)=5.0208913974997841006932539804960e-01_R;
1121 _points[ 8](0)=6.0310739672759678368189556654036e-01_R;
1122 _points[ 9](0)=6.9999091716990649741073666393849e-01_R;
1123 _points[10](0)=7.8877423843456071534030488559891e-01_R;
1124 _points[11](0)=8.6582490073159695367114083518102e-01_R;
1125 _points[12](0)=9.2799573874675232498377812203940e-01_R;
1126 _points[13](0)=9.7277712074118323045296336316727e-01_R;
1127
1128 _weights[ 0]=1.5255206119448295373511341972378e-02_R;
1129 _weights[ 1]=3.3139595469960559875930225836517e-02_R;
1130 _weights[ 2]=4.5914772114671178911403799944693e-02_R;
1131 _weights[ 3]=5.2025865410701701832827358849471e-02_R;
1132 _weights[ 4]=5.1389924039471503273808065266413e-02_R;
1133 _weights[ 5]=4.5253432254460881465122373566022e-02_R;
1134 _weights[ 6]=3.5739010292514612984162525810346e-02_R;
1135 _weights[ 7]=2.5216183536839055034306220202219e-02_R;
1136 _weights[ 8]=1.5694332285072957184930434798487e-02_R;
1137 _weights[ 9]=8.4129767371364622096077152778570e-03_R;
1138 _weights[10]=3.7248756752828588215538124784652e-03_R;
1139 _weights[11]=1.2617838951574880413283334197260e-03_R;
1140 _weights[12]=2.7909934094687847008945560658272e-04_R;
1141 _weights[13]=2.6276161668899854751670304157309e-05_R;
1142
1143 return;
1144 }
1145
1146 case TWENTYEIGHTH:
1147 case TWENTYNINTH:
1148 {
1149 _points.resize (15);
1150 _weights.resize(15);
1151
1152 _points[ 0](0)=5.3190520028437405909978402739774e-03_R;
1153 _points[ 1](0)=2.7814561918260051571980709238074e-02_R;
1154 _points[ 2](0)=6.7431865838998613384568577571818e-02_R;
1155 _points[ 3](0)=1.2274828621549783933958732401303e-01_R;
1156 _points[ 4](0)=1.9176570627765362550282684505042e-01_R;
1157 _points[ 5](0)=2.7198996592948620305633800793026e-01_R;
1158 _points[ 6](0)=3.6052169358705764815778444077840e-01_R;
1159 _points[ 7](0)=4.5416123575447709916009624996188e-01_R;
1160 _points[ 8](0)=5.4952435559355131365468962196031e-01_R;
1161 _points[ 9](0)=6.4316460176878493853949400884187e-01_R;
1162 _points[10](0)=7.3169797305252320629933948467521e-01_R;
1163 _points[11](0)=8.1192547727500966668969312120195e-01_R;
1164 _points[12](0)=8.8094952871531360238808055493652e-01_R;
1165 _points[13](0)=9.3628182173551874210251937228715e-01_R;
1166 _points[14](0)=9.7595387433502370956200384127912e-01_R;
1167
1168 _weights[ 0]=1.3481662725134304090265733542410e-02_R;
1169 _weights[ 1]=2.9527650756798205089388266870014e-02_R;
1170 _weights[ 2]=4.1531307651604265373799456795289e-02_R;
1171 _weights[ 3]=4.8132057668529815888404876719886e-02_R;
1172 _weights[ 4]=4.9041267894409180565196427508457e-02_R;
1173 _weights[ 5]=4.4991555820615933365730152800755e-02_R;
1174 _weights[ 6]=3.7473875792101303095319296790068e-02_R;
1175 _weights[ 7]=2.8326553174241247644068974123766e-02_R;
1176 _weights[ 8]=1.9293416585274520485988288429744e-02_R;
1177 _weights[ 9]=1.1668582484776638563534331197891e-02_R;
1178 _weights[10]=6.1110501102060490412153142922240e-03_R;
1179 _weights[11]=2.6556629857743191811282114211333e-03_R;
1180 _weights[12]=8.8657363523409667398227745346013e-04_R;
1181 _weights[13]=1.9398726306394554934013378631178e-04_R;
1182 _weights[14]=1.8128785569508725971591601924058e-05_R;
1183
1184 return;
1185 }
1186
1187
1188 case THIRTIETH:
1189 case THIRTYFIRST:
1190 {
1191 _points.resize (16);
1192 _weights.resize(16);
1193
1194 _points[ 0](0)=4.7276871229345922061506104450645e-03_R;
1195 _points[ 1](0)=2.4742967619434984512603456269536e-02_R;
1196 _points[ 2](0)=6.0076437716637992275242255328112e-02_R;
1197 _points[ 3](0)=1.0960060925877060286789758461950e-01_R;
1198 _points[ 4](0)=1.7172475948300210790307417791270e-01_R;
1199 _points[ 5](0)=2.4445243174451137730207656160275e-01_R;
1200 _points[ 6](0)=3.2544621002412961482683685190181e-01_R;
1201 _points[ 7](0)=4.1210296411685959691728421362251e-01_R;
1202 _points[ 8](0)=5.0163755615318759370013043235084e-01_R;
1203 _points[ 9](0)=5.9117238531650308897076051877634e-01_R;
1204 _points[10](0)=6.7782991741456081130251277264148e-01_R;
1205 _points[11](0)=7.5882525794914141335427940535114e-01_R;
1206 _points[12](0)=8.3155588302646195188920635482406e-01_R;
1207 _points[13](0)=8.9368597454880401881486969876816e-01_R;
1208 _points[14](0)=9.4322428571224559352545066239296e-01_R;
1209 _points[15](0)=9.7860643749869701257280091378128e-01_R;
1210
1211 _weights[ 0]=1.1999405624691969586506695404143e-02_R;
1212 _weights[ 1]=2.6460842517339527040437264564557e-02_R;
1213 _weights[ 2]=3.7685824681918572833315081444311e-02_R;
1214 _weights[ 3]=4.4496573472543214976151049587710e-02_R;
1215 _weights[ 4]=4.6506239397362658797012521100333e-02_R;
1216 _weights[ 5]=4.4112657675899371113911374089320e-02_R;
1217 _weights[ 6]=3.8348046951185955673582690910292e-02_R;
1218 _weights[ 7]=3.0612037917837609541948834407964e-02_R;
1219 _weights[ 8]=2.2357185649529930223334734263644e-02_R;
1220 _weights[ 9]=1.4803776657751738340239250997704e-02_R;
1221 _weights[10]=8.7475454956120699745801506391282e-03_R;
1222 _weights[11]=4.4948488514798588832066397608164e-03_R;
1223 _weights[12]=1.9235319260667742273824398535627e-03_R;
1224 _weights[13]=6.3445999956883686801084896849641e-04_R;
1225 _weights[14]=1.3757810397555175246959527906570e-04_R;
1226 _weights[15]=1.2778410569693501244162062287056e-05_R;
1227
1228 return;
1229 }
1230
1231
1232 case THIRTYSECOND:
1233 case THIRTYTHIRD:
1234 {
1235 _points.resize (17);
1236 _weights.resize(17);
1237
1238 _points[ 0](0)=4.2297654864907678749919877813007e-03_R;
1239 _points[ 1](0)=2.2152705311830232294209002101573e-02_R;
1240 _points[ 2](0)=5.3856014827184829566760322013645e-02_R;
1241 _points[ 3](0)=9.8434936830541362494246924237098e-02_R;
1242 _points[ 4](0)=1.5460792826588562987838903880788e-01_R;
1243 _points[ 5](0)=2.2075922519215138391363787768336e-01_R;
1244 _points[ 6](0)=2.9498586629802348865100598497056e-01_R;
1245 _points[ 7](0)=3.7515254164081788200834771392226e-01_R;
1246 _points[ 8](0)=4.5895305335301908085933451474375e-01_R;
1247 _points[ 9](0)=5.4397667809047570974515217435547e-01_R;
1248 _points[10](0)=6.2777753854681427256560538094776e-01_R;
1249 _points[11](0)=7.0794500138508556794362242607309e-01_R;
1250 _points[12](0)=7.8217310308122112810113854015572e-01_R;
1251 _points[13](0)=8.4832708570995060757906353137179e-01_R;
1252 _points[14](0)=9.0450542331432870037906100932836e-01_R;
1253 _points[15](0)=9.4909701659654457024654762835657e-01_R;
1254 _points[16](0)=9.8084389384741256367666372092760e-01_R;
1255
1256 _weights[ 0]=1.0748151030768621662834062204936e-02_R;
1257 _weights[ 1]=2.3837762018703244620506074665265e-02_R;
1258 _weights[ 2]=3.4307889795671880028436869439002e-02_R;
1259 _weights[ 3]=4.1143975847068207121110777965721e-02_R;
1260 _weights[ 4]=4.3922618772592577808611328095136e-02_R;
1261 _weights[ 5]=4.2825403927934553301439133345126e-02_R;
1262 _weights[ 6]=3.8555241947102353628223582107170e-02_R;
1263 _weights[ 7]=3.2163570112378639217164962127759e-02_R;
1264 _weights[ 8]=2.4829256111976082802381065145755e-02_R;
1265 _weights[ 9]=1.7638789331050110518481458865839e-02_R;
1266 _weights[10]=1.1413642238636687747573403275566e-02_R;
1267 _weights[11]=6.6164197603617147286557116199452e-03_R;
1268 _weights[12]=3.3465172918198153715474254116460e-03_R;
1269 _weights[13]=1.4138837589561322316624033902623e-03_R;
1270 _weights[14]=4.6167405877711308077043506706165e-04_R;
1271 _weights[15]=9.9356525335473959962406835119113e-05_R;
1272 _weights[16]=9.1808042001255039722337720228143e-06_R;
1273
1274 return;
1275 }
1276
1277 case THIRTYFOURTH:
1278 case THIRTYFIFTH:
1279 {
1280 _points.resize (18);
1281 _weights.resize(18);
1282
1283 _points[ 0](0)=3.8065822475018763836485343548908e-03_R;
1284 _points[ 1](0)=1.9948351047343018666301273550578e-02_R;
1285 _points[ 2](0)=4.8549645304224630965525818224597e-02_R;
1286 _points[ 3](0)=8.8876259116497388048181392194957e-02_R;
1287 _points[ 4](0)=1.3988457083516926493003835526765e-01_R;
1288 _points[ 5](0)=2.0025369592363033820671255853211e-01_R;
1289 _points[ 6](0)=2.6842018278660208442014712803618e-01_R;
1290 _points[ 7](0)=3.4261859780200830045140484446480e-01_R;
1291 _points[ 8](0)=4.2092727587031795580391095608392e-01_R;
1292 _points[ 9](0)=5.0131810275027358836467598537906e-01_R;
1293 _points[10](0)=5.8170905267091792822883758529331e-01_R;
1294 _points[11](0)=6.6001812722531554655212340270381e-01_R;
1295 _points[12](0)=7.3421730813501325031921736140253e-01_R;
1296 _points[13](0)=8.0238514983641747020667379058517e-01_R;
1297 _points[14](0)=8.6275672070005501336081662021610e-01_R;
1298 _points[15](0)=9.1376986411079293616612318979159e-01_R;
1299 _points[16](0)=9.5410789551731665881890309384613e-01_R;
1300 _points[17](0)=9.8274840759428696063307389954630e-01_R;
1301
1302 _weights[ 0]=9.6823988037660231774964807691529e-03_R;
1303 _weights[ 1]=2.1578772679193827027157750409882e-02_R;
1304 _weights[ 2]=3.1333907671729513327950397913143e-02_R;
1305 _weights[ 3]=3.8075134253447687665457823100366e-02_R;
1306 _weights[ 4]=4.1377182287519565332651504100178e-02_R;
1307 _weights[ 5]=4.1283665809957749414286828772884e-02_R;
1308 _weights[ 6]=3.8262794672349299757849656256339e-02_R;
1309 _weights[ 7]=3.3095976202072497795672769135623e-02_R;
1310 _weights[ 8]=2.6723424368960119486097972811646e-02_R;
1311 _weights[ 9]=2.0078641696369720179443819032712e-02_R;
1312 _weights[10]=1.3943897653647906425703531920973e-02_R;
1313 _weights[11]=8.8522782250949774435502470347624e-03_R;
1314 _weights[12]=5.0502487883546813166841235600508e-03_R;
1315 _weights[13]=2.5207216384362558022745702364513e-03_R;
1316 _weights[14]=1.0535502839571923712409403476880e-03_R;
1317 _weights[15]=3.4109120368765498289598525047321e-04_R;
1318 _weights[16]=7.2937008664118705328162954331465e-05_R;
1319 _weights[17]=6.7100861245431215907697266774769e-06_R;
1320
1321 return;
1322 }
1323
1324 case THIRTYSIXTH:
1325 case THIRTYSEVENTH:
1326 {
1327 _points.resize (19);
1328 _weights.resize(19);
1329
1330 _points[ 0](0)=3.4438904038624902806940509331722e-03_R;
1331 _points[ 1](0)=1.8056978337900562863030093954343e-02_R;
1332 _points[ 2](0)=4.3987395090842734455198832773659e-02_R;
1333 _points[ 3](0)=8.0633276366661415469721776663016e-02_R;
1334 _points[ 4](0)=1.2713640986156026953002535083969e-01_R;
1335 _points[ 5](0)=1.8240698366909185313069695387128e-01_R;
1336 _points[ 6](0)=2.4514956909516857055249217701821e-01_R;
1337 _points[ 7](0)=3.1389356741821822415240859865307e-01_R;
1338 _points[ 8](0)=3.8702770276933220341545290751683e-01_R;
1339 _points[ 9](0)=4.6283779855202027820220487054694e-01_R;
1340 _points[10](0)=5.3954696279208808766943066332998e-01_R;
1341 _points[11](0)=6.1535724480454716546694016358337e-01_R;
1342 _points[12](0)=6.8849179091409498918986551203802e-01_R;
1343 _points[13](0)=7.5723651917329793549736932794667e-01_R;
1344 _points[14](0)=8.1998035706323733537954006841029e-01_R;
1345 _points[15](0)=8.7525316298382668006594890887609e-01_R;
1346 _points[16](0)=9.2176068172914004889937421632274e-01_R;
1347 _points[17](0)=9.5841690242340714510347790926694e-01_R;
1348 _points[18](0)=9.8438280655170201067612761745569e-01_R;
1349
1350 _weights[ 0]=8.7672970568792323661393261305840e-03_R;
1351 _weights[ 1]=1.9620856340232434512901283777202e-02_R;
1352 _weights[ 2]=2.8708149778704086122791006941433e-02_R;
1353 _weights[ 3]=3.5278117199476000434599584597235e-02_R;
1354 _weights[ 4]=3.8922386222261737550985848811514e-02_R;
1355 _weights[ 5]=3.9598248214880677015066061570123e-02_R;
1356 _weights[ 6]=3.7607500520347543950912173611332e-02_R;
1357 _weights[ 7]=3.3525068070610283960905700567460e-02_R;
1358 _weights[ 8]=2.8091607936102907649141378579235e-02_R;
1359 _weights[ 9]=2.2090563149823990465333672755377e-02_R;
1360 _weights[10]=1.6231815321996325630177612472423e-02_R;
1361 _weights[11]=1.1061440629037007897211784796273e-02_R;
1362 _weights[12]=6.9108110779321981973514541466546e-03_R;
1363 _weights[13]=3.8897848125530902102984958782958e-03_R;
1364 _weights[14]=1.9197884726923132048372710905667e-03_R;
1365 _weights[15]=7.9504432544855937325482850317179e-04_R;
1366 _weights[16]=2.5553085889097125647555166013802e-04_R;
1367 _weights[17]=5.4342643132004416773622274012570e-05_R;
1368 _weights[18]=4.9807023319691181766751703037610e-06_R;
1369
1370 return;
1371 }
1372
1373 case THIRTYEIGHTH:
1374 case THIRTYNINTH:
1375 {
1376 _points.resize (20);
1377 _weights.resize(20);
1378
1379 _points[ 0](0)=3.1306837407435895621501417495463e-03_R;
1380 _points[ 1](0)=1.6422088133987832902541614256258e-02_R;
1381 _points[ 2](0)=4.0036900461906780996320149828793e-02_R;
1382 _points[ 3](0)=7.3477191785285283057566545285874e-02_R;
1383 _points[ 4](0)=1.1603090765548680494669743156748e-01_R;
1384 _points[ 5](0)=1.6679125348100943001298070145849e-01_R;
1385 _points[ 6](0)=2.2467641938430503840938196483210e-01_R;
1386 _points[ 7](0)=2.8845271218127238477194070665240e-01_R;
1387 _points[ 8](0)=3.5676087010245310564705506663326e-01_R;
1388 _points[ 9](0)=4.2814504093325668461542503477245e-01_R;
1389 _points[10](0)=5.0108381548284855137062465413693e-01_R;
1390 _points[11](0)=5.7402265818282687172751219665371e-01_R;
1391 _points[12](0)=6.4540704577736756661732083476397e-01_R;
1392 _points[13](0)=7.1371561101528768074208343535393e-01_R;
1393 _points[14](0)=7.7749259203548675355112594583658e-01_R;
1394 _points[15](0)=8.3537891463156172517151839471341e-01_R;
1395 _points[16](0)=8.8614130291454714368728293036495e-01_R;
1396 _points[17](0)=9.2869901491875054534509783716727e-01_R;
1397 _points[18](0)=9.6214871215049818970916080642292e-01_R;
1398 _points[19](0)=9.8579578884064184668002313135922e-01_R;
1399
1400 _weights[ 0]=7.9757927362766516852273101574255e-03_R;
1401 _weights[ 1]=1.7913752325738559101773958866323e-02_R;
1402 _weights[ 2]=2.6382564429125584794513408474046e-02_R;
1403 _weights[ 3]=3.2734644317573148047479656498988e-02_R;
1404 _weights[ 4]=3.6587916553227064986609295576925e-02_R;
1405 _weights[ 5]=3.7847390376922340715354694449373e-02_R;
1406 _weights[ 6]=3.6697420472018132713254249570653e-02_R;
1407 _weights[ 7]=3.3556431453475493479002714822739e-02_R;
1408 _weights[ 8]=2.9002404745589285169916357261403e-02_R;
1409 _weights[ 9]=2.3682290414246053980866450266495e-02_R;
1410 _weights[10]=1.8220503418268691551843315309759e-02_R;
1411 _weights[11]=1.3140919256661651742108133720781e-02_R;
1412 _weights[12]=8.8135560782433553289252731679767e-03_R;
1413 _weights[13]=5.4320908061230274500120111426487e-03_R;
1414 _weights[14]=3.0224891709073793749184859780611e-03_R;
1415 _weights[15]=1.4774444419714858062838576456553e-03_R;
1416 _weights[16]=6.0704570426725825415272373108771e-04_R;
1417 _weights[17]=1.9388830961751181076983851525948e-04_R;
1418 _weights[18]=4.1039102087320205549074040898061e-05_R;
1419 _weights[19]=3.7492209933371347725241368372638e-06_R;
1420
1421 return;
1422 }
1423
1424
1425 case FORTIETH:
1426 case FORTYFIRST:
1427 {
1428 _points.resize (21);
1429 _weights.resize(21);
1430
1431 _points[ 0](0)=2.8583506000918943222556277168267e-03_R;
1432 _points[ 1](0)=1.4999364972075522340357135916023e-02_R;
1433 _points[ 2](0)=3.6593863281140122626545055282186e-02_R;
1434 _points[ 3](0)=6.7226441667938638526563947674675e-02_R;
1435 _points[ 4](0)=1.0630147973769311755044868847393e-01_R;
1436 _points[ 5](0)=1.5305857495571921224970195300963e-01_R;
1437 _points[ 6](0)=2.0658770608253356867698033417515e-01_R;
1438 _points[ 7](0)=2.6584701401081590981089215154372e-01_R;
1439 _points[ 8](0)=3.2968309899010272373734914205452e-01_R;
1440 _points[ 9](0)=3.9685347698561900950394342909483e-01_R;
1441 _points[10](0)=4.6605076663517464847296649003812e-01_R;
1442 _points[11](0)=5.3592813869303216093268951839176e-01_R;
1443 _points[12](0)=6.0512553397610192844810985230774e-01_R;
1444 _points[13](0)=6.7229614098692961628997049948121e-01_R;
1445 _points[14](0)=7.3613262059728734846410297670221e-01_R;
1446 _points[15](0)=7.9539257374613146232498650332774e-01_R;
1447 _points[16](0)=8.4892277353768883984401746895126e-01_R;
1448 _points[17](0)=8.9568174292546676052820257429765e-01_R;
1449 _points[18](0)=9.3476043640122994798279429359660e-01_R;
1450 _points[19](0)=9.6540160736574245809294907904429e-01_R;
1451 _points[20](0)=9.8702556657875783654690055164718e-01_R;
1452
1453 _weights[ 0]=7.2866317313744308995629793584932e-03_R;
1454 _weights[ 1]=1.6417061144242818824757454238052e-02_R;
1455 _weights[ 2]=2.4316074956305588348553255406534e-02_R;
1456 _weights[ 3]=3.0423854654878694196479542521305e-02_R;
1457 _weights[ 4]=3.4388553550627421941340376509459e-02_R;
1458 _weights[ 5]=3.6085277384893044986268336555960e-02_R;
1459 _weights[ 6]=3.5615944774693119613624648820995e-02_R;
1460 _weights[ 7]=3.3281046762833346236473134492600e-02_R;
1461 _weights[ 8]=2.9528072702082493907799384765866e-02_R;
1462 _weights[ 9]=2.4885083875255978309567929915161e-02_R;
1463 _weights[10]=1.9889780066352815019424534213776e-02_R;
1464 _weights[11]=1.5024528041917190276613254752701e-02_R;
1465 _weights[12]=1.0666270365508680718786852036243e-02_R;
1466 _weights[13]=7.0573209743621604363614669672455e-03_R;
1467 _weights[14]=4.2993100642134152210363702100934e-03_R;
1468 _weights[15]=2.3686215346115318974092271035074e-03_R;
1469 _weights[16]=1.1482414207164748272703814817286e-03_R;
1470 _weights[17]=4.6857361253397420043294612589344e-04_R;
1471 _weights[18]=1.4884999898655056859287865070751e-04_R;
1472 _weights[19]=3.1377233396792732027953172274463e-05_R;
1473 _weights[20]=2.8584835468101709504260347382715e-06_R;
1474
1475 return;
1476 }
1477
1478 case FORTYSECOND:
1479 case FORTYTHIRD:
1480 {
1481 _points.resize (22);
1482 _weights.resize(22);
1483
1484 _points[ 0](0)=2.6200747203711594248593674552649e-03_R;
1485 _points[ 1](0)=1.3753657987385804025756750709059e-02_R;
1486 _points[ 2](0)=3.3575226848026692714308191640158e-02_R;
1487 _points[ 3](0)=6.1735561623069601690826574395308e-02_R;
1488 _points[ 4](0)=9.7732696675368642458479884996723e-02_R;
1489 _points[ 5](0)=1.4092439775695158519450619775816e-01_R;
1490 _points[ 6](0)=1.9053995518421662849913969152881e-01_R;
1491 _points[ 7](0)=2.4569399962450332222446519900435e-01_R;
1492 _points[ 8](0)=3.0540231844259902315260853518244e-01_R;
1493 _points[ 9](0)=3.6859942495594128250321664201293e-01_R;
1494 _points[10](0)=4.3415757484015513750820121247106e-01_R;
1495 _points[11](0)=5.0090689264793505011775015892772e-01_R;
1496 _points[12](0)=5.6765625027260978702177266771788e-01_R;
1497 _points[13](0)=6.3321452557266284279166256182373e-01_R;
1498 _points[14](0)=6.9641186298595172661126707689713e-01_R;
1499 _points[15](0)=7.5612055917893487122928793527786e-01_R;
1500 _points[16](0)=8.1127520683922050787811864631196e-01_R;
1501 _points[17](0)=8.6089175276286621730656128908876e-01_R;
1502 _points[18](0)=9.0408517849775272066170136431884e-01_R;
1503 _points[19](0)=9.4008566921081846961603077466108e-01_R;
1504 _points[20](0)=9.6825388381656365288164210087944e-01_R;
1505 _points[21](0)=9.8810245999087788318348935085438e-01_R;
1506
1507 _weights[ 0]=6.6829315239216368796332393406135e-03_R;
1508 _weights[ 1]=1.5098062421623821319493004238262e-02_R;
1509 _weights[ 2]=2.2473713734526648003280648297671e-02_R;
1510 _weights[ 3]=2.8324458025288763364233486167273e-02_R;
1511 _weights[ 4]=3.2329473952869436965326587507885e-02_R;
1512 _weights[ 5]=3.4348599664417779736425965942178e-02_R;
1513 _weights[ 6]=3.4426309828130701949676126316990e-02_R;
1514 _weights[ 7]=3.2774586900497126738748991342107e-02_R;
1515 _weights[ 8]=2.9737336628427308246400548097974e-02_R;
1516 _weights[ 9]=2.5741821234796918381507016798653e-02_R;
1517 _weights[10]=2.1244167813524304464862872202199e-02_R;
1518 _weights[11]=1.6676482379699419616981906191727e-02_R;
1519 _weights[12]=1.2402453510959574984251948178874e-02_R;
1520 _weights[13]=8.6866984738749141556196547655377e-03_R;
1521 _weights[14]=5.6807683849250404394970034550940e-03_R;
1522 _weights[15]=3.4260685209698087638377353482425e-03_R;
1523 _weights[16]=1.8713879532585689543042377871244e-03_R;
1524 _weights[17]=9.0066625279251987400261357834378e-04_R;
1525 _weights[18]=3.6536328467284676654467859219800e-04_R;
1526 _weights[19]=1.1551470917602499323205530447797e-04_R;
1527 _weights[20]=2.4263177919766775694554800111547e-05_R;
1528 _weights[21]=2.2049570604019597784590797971169e-06_R;
1529
1530 return;
1531 }
1532
1533
1534 default:
1535 libmesh_error_msg("Quadrature rule " << _order << " not supported!");
1536 } // end switch(_order + 2*p)
1537 } // end else if ((_alpha == 2) && (_beta == 0))
1538
1539 else
1540 {
1541 libMesh::err << "Unsupported combination of (alpha,beta) = ("
1542 << _alpha
1543 << ","
1544 << _beta
1545 << ") requested in Jacobi-Gauss quadrature rule."
1546 << std::endl;
1547 }
1548}
1549
1550} // 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::QJacobi::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_jacobi_1D.C:26
libMesh
The libMesh namespace provides an interface to certain functionality in the library.
libMesh::err
OStreamProxy err
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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