PolyDiM
C++ library for POLYtopal DIscretization Methods
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Quadrature_GaussLobatto1D.hpp
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1// _LICENSE_HEADER_
2//
3// Copyright (C) 2019 - 2025.
4// Terms register on the GPL-3.0 license.
5//
6// This file can be redistributed and/or modified under the license terms.
7//
8// See top level LICENSE file for more details.
9//
10// This file can be used citing references in CITATION.cff file.
11
12#ifndef __Quadrature_GaussLobatto1D_H
13#define __Quadrature_GaussLobatto1D_H
14
15#include "QuadratureData.hpp"
16
17namespace Gedim
18{
19namespace Quadrature
20{
22class Quadrature_GaussLobatto1D
23{
24 public:
25 static QuadratureData FillPointsAndWeights(const unsigned int &order)
26 {
27 QuadratureData quadrature_data;
28 auto &points = quadrature_data.Points;
29 auto &weights = quadrature_data.Weights;
30
31 switch (order)
32 {
33 case 0:
34 case 1: {
35 points.setZero(3, 2);
36 points(0, 0) = 0.0000000000000000e+00;
37 points(0, 1) = 1.0000000000000000e+00;
38 weights.resize(2);
39 weights[0] = 5.0000000000000000e-01;
40 weights[1] = 5.0000000000000000e-01;
41 }
42 break;
43 case 2:
44 case 3: {
45 points.setZero(3, 3);
46 points(0, 0) = 0.0000000000000000e+00;
47 points(0, 1) = 5.0000000000000000e-01;
48 points(0, 2) = 1.0000000000000000e+00;
49 weights.resize(3);
50 weights[0] = 1.6666666666666649e-01;
51 weights[1] = 6.6666666666666652e-01;
52 weights[2] = 1.6666666666666649e-01;
53 }
54 break;
55 case 4:
56 case 5: {
57 points.setZero(3, 4);
58 points(0, 0) = 0.0000000000000000e+00;
59 points(0, 1) = 2.7639320225002106e-01;
60 points(0, 2) = 7.2360679774997894e-01;
61 points(0, 3) = 1.0000000000000000e+00;
62 weights.resize(4);
63 weights[0] = 8.3333333333333329e-02;
64 weights[1] = 4.1666666666666663e-01;
65 weights[2] = 4.1666666666666663e-01;
66 weights[3] = 8.3333333333333329e-02;
67 }
68 break;
69 case 6:
70 case 7: {
71 points.setZero(3, 5);
72 points(0, 0) = 0.0000000000000000e+00;
73 points(0, 1) = 1.7267316464601151e-01;
74 points(0, 2) = 5.0000000000000000e-01;
75 points(0, 3) = 8.2732683535398843e-01;
76 points(0, 4) = 1.0000000000000000e+00;
77 weights.resize(5);
78 weights[0] = 5.0000000000000003e-02;
79 weights[1] = 2.7222222222222220e-01;
80 weights[2] = 3.5555555555555557e-01;
81 weights[3] = 2.7222222222222220e-01;
82 weights[4] = 5.0000000000000003e-02;
83 }
84 break;
85 case 8:
86 case 9: {
87 points.setZero(3, 6);
88 points(0, 0) = 0.0000000000000000e+00;
89 points(0, 1) = 1.1747233803526763e-01;
90 points(0, 2) = 3.5738424175967742e-01;
91 points(0, 3) = 6.4261575824032258e-01;
92 points(0, 4) = 8.8252766196473242e-01;
93 points(0, 5) = 1.0000000000000000e+00;
94 weights.resize(6);
95 weights[0] = 3.3333333333333333e-02;
96 weights[1] = 1.8923747814892350e-01;
97 weights[2] = 2.7742918851774317e-01;
98 weights[3] = 2.7742918851774317e-01;
99 weights[4] = 1.8923747814892350e-01;
100 weights[5] = 3.3333333333333333e-02;
101 }
102 break;
103 case 10:
104 case 11: {
105 points.setZero(3, 7);
106 points(0, 0) = 0.0000000000000000e+00;
107 points(0, 1) = 8.4888051860716518e-02;
108 points(0, 2) = 2.6557560326464291e-01;
109 points(0, 3) = 5.0000000000000000e-01;
110 points(0, 4) = 7.3442439673535709e-01;
111 points(0, 5) = 9.1511194813928354e-01;
112 points(0, 6) = 1.0000000000000000e+00;
113 weights.resize(7);
114 weights[0] = 2.3809523809523808e-02;
115 weights[1] = 1.3841302368078298e-01;
116 weights[2] = 2.1587269060493131e-01;
117 weights[3] = 2.4380952380952381e-01;
118 weights[4] = 2.1587269060493131e-01;
119 weights[5] = 1.3841302368078298e-01;
120 weights[6] = 2.3809523809523808e-02;
121 }
122 break;
123 case 12:
124 case 13: {
125 points.setZero(3, 8);
126 points(0, 0) = 0.0000000000000000e+00;
127 points(0, 1) = 6.4129925745196714e-02;
128 points(0, 2) = 2.0414990928342885e-01;
129 points(0, 3) = 3.9535039104876057e-01;
130 points(0, 4) = 6.0464960895123943e-01;
131 points(0, 5) = 7.9585009071657109e-01;
132 points(0, 6) = 9.3587007425480329e-01;
133 points(0, 7) = 1.0000000000000000e+00;
134 weights.resize(8);
135 weights[0] = 1.7857142857142856e-02;
136 weights[1] = 1.0535211357175302e-01;
137 weights[2] = 1.7056134624175218e-01;
138 weights[3] = 2.0622939732935194e-01;
139 weights[4] = 2.0622939732935194e-01;
140 weights[5] = 1.7056134624175218e-01;
141 weights[6] = 1.0535211357175302e-01;
142 weights[7] = 1.7857142857142856e-02;
143 }
144 break;
145 case 14:
146 case 15: {
147 points.setZero(3, 9);
148 points(0, 0) = 0.0000000000000000e+00;
149 points(0, 1) = 5.0121002294269912e-02;
150 points(0, 2) = 1.6140686024463113e-01;
151 points(0, 3) = 3.1844126808691092e-01;
152 points(0, 4) = 5.0000000000000000e-01;
153 points(0, 5) = 6.8155873191308913e-01;
154 points(0, 6) = 8.3859313975536887e-01;
155 points(0, 7) = 9.4987899770573003e-01;
156 points(0, 8) = 1.0000000000000000e+00;
157 weights.resize(9);
158 weights[0] = 1.3888888888888888e-02;
159 weights[1] = 8.2747680780402760e-02;
160 weights[2] = 1.3726935625008085e-01;
161 weights[3] = 1.7321425548652317e-01;
162 weights[4] = 1.8575963718820862e-01;
163 weights[5] = 1.7321425548652317e-01;
164 weights[6] = 1.3726935625008085e-01;
165 weights[7] = 8.2747680780402760e-02;
166 weights[8] = 1.3888888888888888e-02;
167 }
168 break;
169 case 16:
170 case 17:
171 points.resize(3, 10);
172 points(0, 0) = 0.0000000000000000e+00;
173 points(0, 1) = 4.0233045916770571e-02;
174 points(0, 2) = 1.3061306744724743e-01;
175 points(0, 3) = 2.6103752509477773e-01;
176 points(0, 4) = 4.1736052116680650e-01;
177 points(0, 5) = 5.8263947883319345e-01;
178 points(0, 6) = 7.3896247490522227e-01;
179 points(0, 7) = 8.6938693255275257e-01;
180 points(0, 8) = 9.5976695408322943e-01;
181 points(0, 9) = 1.0000000000000000e+00;
182 weights.resize(10);
183 weights[0] = 1.1111111111111112e-02;
184 weights[1] = 6.6652995425535030e-02;
185 weights[2] = 1.1244467103156322e-01;
186 weights[3] = 1.4602134183984189e-01;
187 weights[4] = 1.6376988059194872e-01;
188 weights[5] = 1.6376988059194872e-01;
189 weights[6] = 1.4602134183984189e-01;
190 weights[7] = 1.1244467103156322e-01;
191 weights[8] = 6.6652995425535030e-02;
192 weights[9] = 1.1111111111111112e-02;
193 break;
194 case 18:
195 case 19:
196 points.resize(3, 11);
197 points(0, 0) = 0.0000000000000000e+00;
198 points(0, 1) = 3.2999284795970418e-02;
199 points(0, 2) = 1.0775826316842779e-01;
200 points(0, 3) = 2.1738233650189748e-01;
201 points(0, 4) = 3.5212093220653029e-01;
202 points(0, 5) = 5.0000000000000000e-01;
203 points(0, 6) = 6.4787906779346971e-01;
204 points(0, 7) = 7.8261766349810258e-01;
205 points(0, 8) = 8.9224173683157226e-01;
206 points(0, 9) = 9.6700071520402964e-01;
207 points(0, 10) = 1.0000000000000000e+00;
208 weights.resize(11);
209 weights[0] = 9.0909090909090905e-03;
210 weights[1] = 5.4806136633497413e-02;
211 weights[2] = 9.3584940890152596e-02;
212 weights[3] = 1.2402405213201415e-01;
213 weights[4] = 1.4343956238950392e-01;
214 weights[5] = 1.5010879772784536e-01;
215 weights[6] = 1.4343956238950392e-01;
216 weights[7] = 1.2402405213201415e-01;
217 weights[8] = 9.3584940890152596e-02;
218 weights[9] = 5.4806136633497413e-02;
219 weights[10] = 9.0909090909090905e-03;
220 break;
221 case 20:
222 case 21:
223 points.resize(3, 12);
224 points(0, 0) = 0.0000000000000000e+00;
225 points(0, 1) = 2.7550363888558915e-02;
226 points(0, 2) = 9.0360339177996685e-02;
227 points(0, 3) = 1.8356192348406969e-01;
228 points(0, 4) = 3.0023452951732554e-01;
229 points(0, 5) = 4.3172353357253623e-01;
230 points(0, 6) = 5.6827646642746377e-01;
231 points(0, 7) = 6.9976547048267446e-01;
232 points(0, 8) = 8.1643807651593026e-01;
233 points(0, 9) = 9.0963966082200332e-01;
234 points(0, 10) = 9.7244963611144108e-01;
235 points(0, 11) = 1.0000000000000000e+00;
236 weights.resize(12);
237 weights[0] = 7.5757575757575760e-03;
238 weights[1] = 4.5842258706598124e-02;
239 weights[2] = 7.8987352782185022e-02;
240 weights[3] = 1.0625420888051065e-01;
241 weights[4] = 1.2563780159960064e-01;
242 weights[5] = 1.3570262045534809e-01;
243 weights[6] = 1.3570262045534809e-01;
244 weights[7] = 1.2563780159960064e-01;
245 weights[8] = 1.0625420888051065e-01;
246 weights[9] = 7.8987352782185022e-02;
247 weights[10] = 4.5842258706598124e-02;
248 weights[11] = 7.5757575757575760e-03;
249 break;
250 case 22:
251 case 23:
252 points.resize(3, 13);
253 points(0, 0) = 0.0000000000000000e+00;
254 points(0, 1) = 2.3345076678918053e-02;
255 points(0, 2) = 7.6826217674063835e-02;
256 points(0, 3) = 1.5690576545912127e-01;
257 points(0, 4) = 2.5854508945433191e-01;
258 points(0, 5) = 3.7535653494688004e-01;
259 points(0, 6) = 5.0000000000000000e-01;
260 points(0, 7) = 6.2464346505311996e-01;
261 points(0, 8) = 7.4145491054566803e-01;
262 points(0, 9) = 8.4309423454087873e-01;
263 points(0, 10) = 9.2317378232593617e-01;
264 points(0, 11) = 9.7665492332108195e-01;
265 points(0, 12) = 1.0000000000000000e+00;
266 weights.resize(13);
267 weights[0] = 6.4102564102564100e-03;
268 weights[1] = 3.8900843373409481e-02;
269 weights[2] = 6.7490963344804200e-02;
270 weights[3] = 9.1823432601775085e-02;
271 weights[4] = 1.1038389678305506e-01;
272 weights[5] = 1.2200789515333813e-01;
273 weights[6] = 1.2596542466672336e-01;
274 weights[7] = 1.2200789515333813e-01;
275 weights[8] = 1.1038389678305506e-01;
276 weights[9] = 9.1823432601775085e-02;
277 weights[10] = 6.7490963344804200e-02;
278 weights[11] = 3.8900843373409481e-02;
279 weights[12] = 6.4102564102564100e-03;
280 break;
281 case 24:
282 case 25:
283 points.resize(3, 14);
284 points(0, 0) = 0.0000000000000000e+00;
285 points(0, 1) = 2.0032477366369539e-02;
286 points(0, 2) = 6.6099473084826388e-02;
287 points(0, 3) = 1.3556570045433691e-01;
288 points(0, 4) = 2.2468029853567645e-01;
289 points(0, 5) = 3.2863799332864357e-01;
290 points(0, 6) = 4.4183406555814808e-01;
291 points(0, 7) = 5.5816593444185192e-01;
292 points(0, 8) = 6.7136200667135637e-01;
293 points(0, 9) = 7.7531970146432361e-01;
294 points(0, 10) = 8.6443429954566309e-01;
295 points(0, 11) = 9.3390052691517367e-01;
296 points(0, 12) = 9.7996752263363041e-01;
297 points(0, 13) = 1.0000000000000000e+00;
298 weights.resize(14);
299 weights[0] = 5.4945054945054949e-03;
300 weights[1] = 3.3418642248840585e-02;
301 weights[2] = 5.8293327949355746e-02;
302 weights[3] = 8.0010925881476000e-02;
303 weights[4] = 9.7413074686708026e-02;
304 weights[5] = 1.0956312650488541e-01;
305 weights[6] = 1.1580639723422859e-01;
306 weights[7] = 1.1580639723422849e-01;
307 weights[8] = 1.0956312650488541e-01;
308 weights[9] = 9.7413074686708026e-02;
309 weights[10] = 8.0010925881476000e-02;
310 weights[11] = 5.8293327949355746e-02;
311 weights[12] = 3.3418642248840585e-02;
312 weights[13] = 5.4945054945054949e-03;
313 break;
314 case 26:
315 case 27:
316 points.resize(3, 15);
317 points(0, 0) = 0.0000000000000000e+00;
318 points(0, 1) = 1.7377036748080721e-02;
319 points(0, 2) = 5.7458977888511842e-02;
320 points(0, 3) = 1.1824015502409241e-01;
321 points(0, 4) = 1.9687339726507713e-01;
322 points(0, 5) = 2.8968097264316373e-01;
323 points(0, 6) = 3.9232302231810290e-01;
324 points(0, 7) = 5.0000000000000000e-01;
325 points(0, 8) = 6.0767697768189710e-01;
326 points(0, 9) = 7.1031902735683627e-01;
327 points(0, 10) = 8.0312660273492287e-01;
328 points(0, 11) = 8.8175984497590765e-01;
329 points(0, 12) = 9.4254102211148816e-01;
330 points(0, 13) = 9.8262296325191922e-01;
331 points(0, 14) = 1.0000000000000000e+00;
332 weights.resize(15);
333 weights[0] = 4.7619047619047623e-03;
334 weights[1] = 2.9014946514300668e-02;
335 weights[2] = 5.0830035162859062e-02;
336 weights[3] = 7.0255849901214015e-02;
337 weights[4] = 8.6394823626800440e-02;
338 weights[5] = 9.8493617982306686e-02;
339 weights[6] = 1.0598679296341047e-01;
340 weights[7] = 1.0852405817440783e-01;
341 weights[8] = 1.0598679296341047e-01;
342 weights[9] = 9.8493617982306686e-02;
343 weights[10] = 8.6394823626800440e-02;
344 weights[11] = 7.0255849901214015e-02;
345 weights[12] = 5.0830035162859062e-02;
346 weights[13] = 2.9014946514300668e-02;
347 weights[14] = 4.7619047619047623e-03;
348 break;
349 case 28:
350 case 29:
351 points.resize(3, 16);
352 points(0, 0) = 0.0000000000000000e+00;
353 points(0, 1) = 1.5215976864891012e-02;
354 points(0, 2) = 5.0399733453263984e-02;
355 points(0, 3) = 1.0399585406909245e-01;
356 points(0, 4) = 1.7380564855875347e-01;
357 points(0, 5) = 2.5697028905643116e-01;
358 points(0, 6) = 3.5008476554961843e-01;
359 points(0, 7) = 4.4933686323902527e-01;
360 points(0, 8) = 5.5066313676097467e-01;
361 points(0, 9) = 6.4991523445038157e-01;
362 points(0, 10) = 7.4302971094356884e-01;
363 points(0, 11) = 8.2619435144124653e-01;
364 points(0, 12) = 8.9600414593090760e-01;
365 points(0, 13) = 9.4960026654673602e-01;
366 points(0, 14) = 9.8478402313510904e-01;
367 points(0, 15) = 1.0000000000000000e+00;
368 weights.resize(16);
369 weights[0] = 4.1666666666666666e-03;
370 weights[1] = 2.5425180502960013e-02;
371 weights[2] = 4.4696848662965347e-02;
372 weights[3] = 6.2127691066257026e-02;
373 weights[4] = 7.7013490403582130e-02;
374 weights[5] = 8.8745956695852057e-02;
375 weights[6] = 9.6845011912601808e-02;
376 weights[7] = 1.0097915408911501e-01;
377 weights[8] = 1.0097915408911501e-01;
378 weights[9] = 9.6845011912601808e-02;
379 weights[10] = 8.8745956695852057e-02;
380 weights[11] = 7.7013490403582130e-02;
381 weights[12] = 6.2127691066257026e-02;
382 weights[13] = 4.4696848662965347e-02;
383 weights[14] = 2.5425180502960013e-02;
384 weights[15] = 4.1666666666666666e-03;
385 break;
386 case 30:
387 case 31:
388 points.resize(3, 17);
389 points(0, 0) = 0.0000000000000000e+00;
390 points(0, 1) = 1.3433911684290811e-02;
391 points(0, 2) = 4.4560002042213220e-02;
392 points(0, 3) = 9.2151874389114874e-02;
393 points(0, 4) = 1.5448550968615765e-01;
394 points(0, 5) = 2.2930730033494923e-01;
395 points(0, 6) = 3.1391278321726146e-01;
396 points(0, 7) = 4.0524401324084131e-01;
397 points(0, 8) = 5.0000000000000000e-01;
398 points(0, 9) = 5.9475598675915875e-01;
399 points(0, 10) = 6.8608721678273854e-01;
400 points(0, 11) = 7.7069269966505072e-01;
401 points(0, 12) = 8.4551449031384229e-01;
402 points(0, 13) = 9.0784812561088513e-01;
403 points(0, 14) = 9.5543999795778678e-01;
404 points(0, 15) = 9.8656608831570924e-01;
405 points(0, 16) = 1.0000000000000000e+00;
406 weights.resize(17);
407 weights[0] = 3.6764705882352941e-03;
408 weights[1] = 2.2460970271627068e-02;
409 weights[2] = 3.9599135251843547e-02;
410 weights[3] = 5.5296454503514073e-02;
411 weights[4] = 6.8993873100963291e-02;
412 weights[5] = 8.0197330998810740e-02;
413 weights[6] = 8.8502126757828856e-02;
414 weights[7] = 9.3608169838809638e-02;
415 weights[8] = 9.5330937376734717e-02;
416 weights[9] = 9.3608169838809638e-02;
417 weights[10] = 8.8502126757828856e-02;
418 weights[11] = 8.0197330998810740e-02;
419 weights[12] = 6.8993873100963291e-02;
420 weights[13] = 5.5296454503514073e-02;
421 weights[14] = 3.9599135251843547e-02;
422 weights[15] = 2.2460970271627068e-02;
423 weights[16] = 3.6764705882352941e-03;
424 break;
425 case 32:
426 case 33:
427 points.resize(3, 18);
428 points(0, 0) = 0.0000000000000000e+00;
429 points(0, 1) = 1.1947221293900745e-02;
430 points(0, 2) = 3.9675407326233036e-02;
431 points(0, 3) = 8.2203232390954895e-02;
432 points(0, 4) = 1.3816033535837868e-01;
433 points(0, 5) = 2.0574758284066913e-01;
434 points(0, 6) = 2.8279248154393799e-01;
435 points(0, 7) = 3.6681867356085951e-01;
436 points(0, 8) = 4.5512545325767395e-01;
437 points(0, 9) = 5.4487454674232605e-01;
438 points(0, 10) = 6.3318132643914049e-01;
439 points(0, 11) = 7.1720751845606201e-01;
440 points(0, 12) = 7.9425241715933081e-01;
441 points(0, 13) = 8.6183966464162132e-01;
442 points(0, 14) = 9.1779676760904505e-01;
443 points(0, 15) = 9.6032459267376691e-01;
444 points(0, 16) = 9.8805277870609931e-01;
445 points(0, 17) = 1.0000000000000000e+00;
446 weights.resize(18);
447 weights[0] = 3.2679738562091504e-03;
448 weights[1] = 1.9985314405456974e-02;
449 weights[2] = 3.5318583442816825e-02;
450 weights[3] = 4.9508135858751391e-02;
451 weights[4] = 6.2105266566483540e-02;
452 weights[5] = 7.2705980786901159e-02;
453 weights[6] = 8.0969758618801208e-02;
454 weights[7] = 8.6631054744728181e-02;
455 weights[8] = 8.9507931719851538e-02;
456 weights[9] = 8.9507931719851538e-02;
457 weights[10] = 8.6631054744728181e-02;
458 weights[11] = 8.0969758618801208e-02;
459 weights[12] = 7.2705980786901159e-02;
460 weights[13] = 6.2105266566483540e-02;
461 weights[14] = 4.9508135858751391e-02;
462 weights[15] = 3.5318583442816825e-02;
463 weights[16] = 1.9985314405456974e-02;
464 weights[17] = 3.2679738562091504e-03;
465 break;
466 case 34:
467 case 35:
468 points.resize(3, 19);
469 points(0, 0) = 0.0000000000000000e+00;
470 points(0, 1) = 1.0694116888959992e-02;
471 points(0, 2) = 3.5549235923706846e-02;
472 points(0, 3) = 7.3769711101676960e-02;
473 points(0, 4) = 1.2425289872369349e-01;
474 points(0, 5) = 1.8554593136738973e-01;
475 points(0, 6) = 2.5588535715964322e-01;
476 points(0, 7) = 3.3324757608775069e-01;
477 points(0, 8) = 4.1540698829535921e-01;
478 points(0, 9) = 5.0000000000000000e-01;
479 points(0, 10) = 5.8459301170464073e-01;
480 points(0, 11) = 6.6675242391224931e-01;
481 points(0, 12) = 7.4411464284035678e-01;
482 points(0, 13) = 8.1445406863261027e-01;
483 points(0, 14) = 8.7574710127630651e-01;
484 points(0, 15) = 9.2623028889832304e-01;
485 points(0, 16) = 9.6445076407629315e-01;
486 points(0, 17) = 9.8930588311103995e-01;
487 points(0, 18) = 1.0000000000000000e+00;
488 weights.resize(19);
489 weights[0] = 2.9239766081871343e-03;
490 weights[1] = 1.7896682593088322e-02;
491 weights[2] = 3.1690945881314866e-02;
492 weights[3] = 4.4565878549603526e-02;
493 weights[4] = 5.6157670738652458e-02;
494 weights[5] = 6.6133640224375345e-02;
495 weights[6] = 7.4206971297969423e-02;
496 weights[7] = 8.0145462022030600e-02;
497 weights[8] = 8.3778292263571391e-02;
498 weights[9] = 8.5000959642413623e-02;
499 weights[10] = 8.3778292263571391e-02;
500 weights[11] = 8.0145462022030600e-02;
501 weights[12] = 7.4206971297969423e-02;
502 weights[13] = 6.6133640224375345e-02;
503 weights[14] = 5.6157670738652458e-02;
504 weights[15] = 4.4565878549603526e-02;
505 weights[16] = 3.1690945881314866e-02;
506 weights[17] = 1.7896682593088322e-02;
507 weights[18] = 2.9239766081871343e-03;
508 break;
509 case 36:
510 case 37:
511 points.resize(3, 20);
512 points(0, 0) = 0.0000000000000000e+00;
513 points(0, 1) = 9.6281475530429206e-03;
514 points(0, 2) = 3.2032750593667281e-02;
515 points(0, 3) = 6.6561010955024924e-02;
516 points(0, 4) = 1.1231586952397205e-01;
517 points(0, 5) = 1.6811179885484434e-01;
518 points(0, 6) = 2.3250356798405686e-01;
519 points(0, 7) = 3.0382340814304531e-01;
520 points(0, 8) = 3.8022414703850677e-01;
521 points(0, 9) = 4.5972703138058907e-01;
522 points(0, 10) = 5.4027296861941088e-01;
523 points(0, 11) = 6.1977585296149329e-01;
524 points(0, 12) = 6.9617659185695469e-01;
525 points(0, 13) = 7.6749643201594320e-01;
526 points(0, 14) = 8.3188820114515560e-01;
527 points(0, 15) = 8.8768413047602790e-01;
528 points(0, 16) = 9.3343898904497502e-01;
529 points(0, 17) = 9.6796724940633272e-01;
530 points(0, 18) = 9.9037185244695713e-01;
531 points(0, 19) = 1.0000000000000000e+00;
532 weights.resize(20);
533 weights[0] = 2.6315789473684210e-03;
534 weights[1] = 1.6118561594244466e-02;
535 weights[2] = 2.8590901063783401e-02;
536 weights[3] = 4.0315881998059834e-02;
537 weights[4] = 5.0995749849725339e-02;
538 weights[5] = 6.0354613814337328e-02;
539 weights[6] = 6.8150241179362109e-02;
540 weights[7] = 7.4180777035458417e-02;
541 weights[8] = 7.8290051323737717e-02;
542 weights[9] = 8.0371643193922884e-02;
543 weights[10] = 8.0371643193922884e-02;
544 weights[11] = 7.8290051323737717e-02;
545 weights[12] = 7.4180777035458417e-02;
546 weights[13] = 6.8150241179362109e-02;
547 weights[14] = 6.0354613814337328e-02;
548 weights[15] = 5.0995749849725339e-02;
549 weights[16] = 4.0315881998059834e-02;
550 weights[17] = 2.8590901063783401e-02;
551 weights[18] = 1.6118561594244466e-02;
552 weights[19] = 2.6315789473684210e-03;
553 break;
554 case 38:
555 case 39:
556 points.resize(3, 21);
557 points(0, 0) = 0.0000000000000000e+00;
558 points(0, 1) = 8.7138516977259828e-03;
559 points(0, 2) = 2.9011851520127252e-02;
560 points(0, 3) = 6.0352622338204764e-02;
561 points(0, 4) = 1.0199903696114382e-01;
562 points(0, 5) = 1.5297448696888838e-01;
563 points(0, 6) = 2.1208401986908465e-01;
564 points(0, 7) = 2.7794210836049893e-01;
565 points(0, 8) = 3.4900507174561757e-01;
566 points(0, 9) = 4.2360724209890727e-01;
567 points(0, 10) = 5.0000000000000000e-01;
568 points(0, 11) = 5.7639275790109279e-01;
569 points(0, 12) = 6.5099492825438243e-01;
570 points(0, 13) = 7.2205789163950107e-01;
571 points(0, 14) = 7.8791598013091535e-01;
572 points(0, 15) = 8.4702551303111162e-01;
573 points(0, 16) = 8.9800096303885613e-01;
574 points(0, 17) = 9.3964737766179529e-01;
575 points(0, 18) = 9.7098814847987280e-01;
576 points(0, 19) = 9.9128614830227402e-01;
577 points(0, 20) = 1.0000000000000000e+00;
578 weights.resize(21);
579 weights[0] = 2.3809523809523812e-03;
580 weights[1] = 1.4592420049252782e-02;
581 weights[2] = 2.5921584500424821e-02;
582 weights[3] = 3.6636959092537086e-02;
583 weights[4] = 4.6492733978942997e-02;
584 weights[5] = 5.5258541609561632e-02;
585 weights[6] = 6.2729060595434455e-02;
586 weights[7] = 6.8729231430020646e-02;
587 weights[8] = 7.3118431223988686e-02;
588 weights[9] = 7.5793787555840680e-02;
589 weights[10] = 7.6692595166087479e-02;
590 weights[11] = 7.5793787555840680e-02;
591 weights[12] = 7.3118431223988686e-02;
592 weights[13] = 6.8729231430020646e-02;
593 weights[14] = 6.2729060595434455e-02;
594 weights[15] = 5.5258541609561632e-02;
595 weights[16] = 4.6492733978942997e-02;
596 weights[17] = 3.6636959092537086e-02;
597 weights[18] = 2.5921584500424821e-02;
598 weights[19] = 1.4592420049252782e-02;
599 weights[20] = 2.3809523809523812e-03;
600 break;
601 case 40:
602 case 41:
603 points.resize(3, 22);
604 points(0, 0) = 0.0000000000000000e+00;
605 points(0, 1) = 7.9237807711768915e-03;
606 points(0, 2) = 2.6397858000385688e-02;
607 points(0, 3) = 5.4968854904547726e-02;
608 points(0, 4) = 9.3025536194039415e-02;
609 points(0, 5) = 1.3975638001939894e-01;
610 points(0, 6) = 1.9416528085787049e-01;
611 points(0, 7) = 2.5509256240504885e-01;
612 points(0, 8) = 3.2123964493054025e-01;
613 points(0, 9) = 3.9119670742035750e-01;
614 points(0, 10) = 4.6347272999455080e-01;
615 points(0, 11) = 5.3652727000544920e-01;
616 points(0, 12) = 6.0880329257964250e-01;
617 points(0, 13) = 6.7876035506945975e-01;
618 points(0, 14) = 7.4490743759495115e-01;
619 points(0, 15) = 8.0583471914212956e-01;
620 points(0, 16) = 8.6024361998060106e-01;
621 points(0, 17) = 9.0697446380596058e-01;
622 points(0, 18) = 9.4503114509545227e-01;
623 points(0, 19) = 9.7360214199961437e-01;
624 points(0, 20) = 9.9207621922882305e-01;
625 points(0, 21) = 1.0000000000000000e+00;
626 weights.resize(22);
627 weights[0] = 2.1645021645021645e-03;
628 weights[1] = 1.3272873841250830e-02;
629 weights[2] = 2.3607232646870410e-02;
630 weights[3] = 3.3432802932276483e-02;
631 weights[4] = 4.2545030195919264e-02;
632 weights[5] = 5.0750287400823844e-02;
633 weights[6] = 5.7873822326969582e-02;
634 weights[7] = 6.3763848326715153e-02;
635 weights[8] = 6.8294844306870731e-02;
636 weights[9] = 7.1370246135680757e-02;
637 weights[10] = 7.2924509722120862e-02;
638 weights[11] = 7.2924509722120862e-02;
639 weights[12] = 7.1370246135680757e-02;
640 weights[13] = 6.8294844306870731e-02;
641 weights[14] = 6.3763848326715153e-02;
642 weights[15] = 5.7873822326969582e-02;
643 weights[16] = 5.0750287400823844e-02;
644 weights[17] = 4.2545030195919264e-02;
645 weights[18] = 3.3432802932276483e-02;
646 weights[19] = 2.3607232646870410e-02;
647 weights[20] = 1.3272873841250830e-02;
648 weights[21] = 2.1645021645021645e-03;
649 break;
650 case 42:
651 case 43:
652 points.resize(3, 23);
653 points(0, 0) = 0.0000000000000000e+00;
654 points(0, 1) = 7.2364220606337404e-03;
655 points(0, 2) = 2.4121022144644899e-02;
656 points(0, 3) = 5.0270720979827488e-02;
657 points(0, 4) = 8.5174451674357055e-02;
658 points(0, 5) = 1.2815247941396968e-01;
659 points(0, 6) = 1.7836817776993191e-01;
660 points(0, 7) = 2.3484411443157793e-01;
661 points(0, 8) = 2.9648103104276258e-01;
662 points(0, 9) = 3.6207922552710348e-01;
663 points(0, 10) = 4.3036189797966579e-01;
664 points(0, 11) = 5.0000000000000000e-01;
665 points(0, 12) = 5.6963810202033416e-01;
666 points(0, 13) = 6.3792077447289652e-01;
667 points(0, 14) = 7.0351896895723742e-01;
668 points(0, 15) = 7.6515588556842207e-01;
669 points(0, 16) = 8.2163182223006803e-01;
670 points(0, 17) = 8.7184752058603032e-01;
671 points(0, 18) = 9.1482554832564289e-01;
672 points(0, 19) = 9.4972927902017257e-01;
673 points(0, 20) = 9.7587897785535516e-01;
674 points(0, 21) = 9.9276357793936620e-01;
675 points(0, 22) = 1.0000000000000000e+00;
676 weights.resize(23);
677 weights[0] = 1.9762845849802370e-03;
678 weights[1] = 1.2124300385765858e-02;
679 weights[2] = 2.1587935585120871e-02;
680 weights[3] = 3.0626238564777111e-02;
681 weights[4] = 3.9067724737784998e-02;
682 weights[5] = 4.6748623081756188e-02;
683 weights[6] = 5.3519550862168308e-02;
684 weights[7] = 5.9248755331374525e-02;
685 weights[8] = 6.3824737350879387e-02;
686 weights[9] = 6.7158436319301920e-02;
687 weights[10] = 6.9184968192903706e-02;
688 weights[11] = 6.9864890006373678e-02;
689 weights[12] = 6.9184968192903706e-02;
690 weights[13] = 6.7158436319301920e-02;
691 weights[14] = 6.3824737350879387e-02;
692 weights[15] = 5.9248755331374525e-02;
693 weights[16] = 5.3519550862168308e-02;
694 weights[17] = 4.6748623081756188e-02;
695 weights[18] = 3.9067724737784998e-02;
696 weights[19] = 3.0626238564777111e-02;
697 weights[20] = 2.1587935585120871e-02;
698 weights[21] = 1.2124300385765858e-02;
699 weights[22] = 1.9762845849802370e-03;
700 break;
701 default:
702 throw std::runtime_error("Wrong initialization of 1D Gauss Lobatto quadrature. Order not supported.");
703 }
704
705 return quadrature_data;
706 }
707};
708} // namespace Quadrature
709} // namespace Gedim
710
711#endif // __Quadrature_GaussLobatto1D_H
Gedim::Eigen_Array
Eigen column vector.
Definition Eigen_Array.hpp:23
Gedim::Quadrature::Quadrature_GaussLobatto1D
Gauss quadrature rule for segments.
Definition Quadrature_GaussLobatto1D.hpp:23
Gedim::Quadrature::Quadrature_GaussLobatto1D::FillPointsAndWeights
static QuadratureData FillPointsAndWeights(const unsigned int &order)
Definition Quadrature_GaussLobatto1D.hpp:25
Gedim
Definition Eigen_Array.cpp:22
Gedim::Quadrature::QuadratureData
Definition QuadratureData.hpp:22