gmsh-TingyuanDoc  0.1
An Open-Source Timing-driven Analytical Mixed-size FPGA Placer
GaussQuadratureTri.cpp
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1 // Gmsh - Copyright (C) 1997-2022 C. Geuzaine, J.-F. Remacle
2 //
3 // See the LICENSE.txt file in the Gmsh root directory for license information.
4 // Please report all issues on https://gitlab.onelab.info/gmsh/gmsh/issues.
5 
6 #include <vector>
7 #include "GaussIntegration.h"
8 #include "GaussLegendre1D.h"
9 
10 IntPt GQT1[1] = {
11  {{0.333333333333333, 0.333333333333333, 0.}, 0.500000000000000}};
12 IntPt GQT2[3] = {
13  {{0.166666666666667, 0.166666666666667, 0.}, 0.166666666666667},
14  {{0.666666666666667, 0.166666666666667, 0.}, 0.166666666666667},
15  {{0.166666666666667, 0.666666666666667, 0.}, 0.166666666666667}};
16 
17 IntPt GQT3[4] = {
18  {{0.333333333333333, 0.333333333333333, 0.}, -0.281250000000000},
19  {{0.600000000000000, 0.200000000000000, 0.}, +0.260416666666667},
20  {{0.200000000000000, 0.600000000000000, 0.}, +0.260416666666667},
21  {{0.200000000000000, 0.200000000000000, 0.}, +0.260416666666667}};
22 
23 IntPt GQT4[6] = {
24  {{0.816847572980459, 0.091576213509771, 0.}, 0.054975871827661},
25  {{0.091576213509771, 0.816847572980459, 0.}, 0.054975871827661},
26  {{0.091576213509771, 0.091576213509771, 0.}, 0.054975871827661},
27  {{0.108103018168070, 0.445948490915965, 0.}, 0.111690794839005},
28  {{0.445948490915965, 0.108103018168070, 0.}, 0.111690794839005},
29  {{0.445948490915965, 0.445948490915965, 0.}, 0.111690794839005}};
30 
31 IntPt GQT5[7] = {
32  {{0.333333333333333, 0.333333333333333, 0.}, 0.112500000000000},
33  {{0.797426985353087, 0.101286507323456, 0.}, 0.062969590272414},
34  {{0.101286507323456, 0.797426985353087, 0.}, 0.062969590272414},
35  {{0.101286507323456, 0.101286507323456, 0.}, 0.062969590272414},
36  {{0.470142064105115, 0.059715871789770, 0.}, 0.066197076394253},
37  {{0.059715871789770, 0.470142064105115, 0.}, 0.066197076394253},
38  {{0.470142064105115, 0.470142064105115, 0.}, 0.066197076394253}};
39 
40 IntPt GQT6[12] = {
41  {{0.873821971016996, 0.063089014491502, 0.}, 0.025422453185104},
42  {{0.063089014491502, 0.873821971016996, 0.}, 0.025422453185104},
43  {{0.063089014491502, 0.063089014491502, 0.}, 0.025422453185104},
44  {{0.501426509658179, 0.249286745170910, 0.}, 0.058393137863189},
45  {{0.249286745170910, 0.501426509658179, 0.}, 0.058393137863189},
46  {{0.249286745170910, 0.249286745170910, 0.}, 0.058393137863189},
47  {{0.636502499121399, 0.310352451033785, 0.}, 0.041425537809187},
48  {{0.310352451033785, 0.636502499121399, 0.}, 0.041425537809187},
49  {{0.636502499121399, 0.053145049844816, 0.}, 0.041425537809187},
50  {{0.310352451033785, 0.053145049844816, 0.}, 0.041425537809187},
51  {{0.053145049844816, 0.310352451033785, 0.}, 0.041425537809187},
52  {{0.053145049844816, 0.636502499121399, 0.}, 0.041425537809187}};
53 
54 IntPt GQT7[13] = {
55  {{0.333333333333333, 0.333333333333333, 0.}, -0.074785022233841},
56  {{0.479308067841920, 0.260345966079040, 0.}, +0.087807628716604},
57  {{0.260345966079040, 0.479308067841920, 0.}, +0.087807628716604},
58  {{0.260345966079040, 0.260345966079040, 0.}, +0.087807628716604},
59  {{0.869739794195568, 0.065130102902216, 0.}, +0.026673617804419},
60  {{0.065130102902216, 0.869739794195568, 0.}, +0.026673617804419},
61  {{0.065130102902216, 0.065130102902216, 0.}, +0.026673617804419},
62  {{0.048690315425316, 0.312865496004874, 0.}, +0.038556880445128},
63  {{0.312865496004874, 0.048690315425316, 0.}, +0.038556880445128},
64  {{0.638444188569810, 0.048690315425316, 0.}, +0.038556880445128},
65  {{0.048690315425316, 0.638444188569810, 0.}, +0.038556880445128},
66  {{0.312865496004874, 0.638444188569810, 0.}, +0.038556880445128},
67  {{0.638444188569810, 0.312865496004874, 0.}, +0.038556880445128}
68 
69 };
70 
71 IntPt GQT8[16] = {
72  {{0.333333333333333, 0.333333333333333, 0.}, 0.072157803838894},
73  {{0.081414823414554, 0.459292588292723, 0.}, 0.047545817133643},
74  {{0.459292588292723, 0.081414823414554, 0.}, 0.047545817133643},
75  {{0.459292588292723, 0.459292588292723, 0.}, 0.047545817133643},
76  {{0.658861384496480, 0.170569307751760, 0.}, 0.051608685267359},
77  {{0.170569307751760, 0.658861384496480, 0.}, 0.051608685267359},
78  {{0.170569307751760, 0.170569307751760, 0.}, 0.051608685267359},
79  {{0.898905543365938, 0.050547228317031, 0.}, 0.016229248811599},
80  {{0.050547228317031, 0.898905543365938, 0.}, 0.016229248811599},
81  {{0.050547228317031, 0.050547228317031, 0.}, 0.016229248811599},
82  {{0.008394777409958, 0.728492392955404, 0.}, 0.013615157087217},
83  {{0.728492392955404, 0.008394777409958, 0.}, 0.013615157087217},
84  {{0.263112829634638, 0.008394777409958, 0.}, 0.013615157087217},
85  {{0.008394777409958, 0.263112829634638, 0.}, 0.013615157087217},
86  {{0.263112829634638, 0.728492392955404, 0.}, 0.013615157087217},
87  {{0.728492392955404, 0.263112829634638, 0.}, 0.013615157087217}};
88 
89 IntPt *GQT[9] = {GQT1, GQT1, GQT2, GQT3, GQT4, GQT5, GQT6, GQT7, GQT8};
90 int GQTnPt[9] = {1, 1, 3, 4, 6, 7, 12, 13, 16};
91 
92 // -----------------------------------------------------------------------------
94 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
95 
96 IntPt triP1Solin[1] = {
97  {{0.333333333333333, 0.333333333333333, 0.}, 0.500000000000000}};
98 // 0 negative weights, 0 points outside of the triangle, total sum of the
99 // weights is 0.5
100 
101 // -----------------------------------------------------------------------------
103 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
104 
105 IntPt triP2Solin[3] = {
106  {{0.166666666666667, 0.166666666666667, 0.}, 0.166666666666667},
107  {{0.166666666666667, 0.666666666666667, 0.}, 0.166666666666667},
108  {{0.666666666666667, 0.166666666666667, 0.}, 0.166666666666667}};
109 // 0 negative weights, 0 points outside of the triangle, total sum of the
110 // weights is 0.5
111 
112 // -----------------------------------------------------------------------------
114 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
115 
116 IntPt triP3Solin[4] = {
117  {{0.333333333333333, 0.333333333333333, 0.}, -0.281250000000000},
118  {{0.200000000000000, 0.200000000000000, 0.}, 0.260416666666667},
119  {{0.200000000000000, 0.600000000000000, 0.}, 0.260416666666667},
120  {{0.600000000000000, 0.200000000000000, 0.}, 0.260416666666667}};
121 // 1 negative weight, 0 points outside of the triangle, total sum of the
122 // weights is 0.5
123 
124 // -----------------------------------------------------------------------------
126 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
127 
128 IntPt triP4Solin[6] = {
129  {{0.445948490915965, 0.445948490915965, 0.}, 0.111690794839005},
130  {{0.445948490915965, 0.108103018168070, 0.}, 0.111690794839005},
131  {{0.108103018168070, 0.445948490915965, 0.}, 0.111690794839005},
132  {{0.091576213509771, 0.091576213509771, 0.}, 0.054975871827661},
133  {{0.091576213509771, 0.816847572980459, 0.}, 0.054975871827661},
134  {{0.816847572980459, 0.091576213509771, 0.}, 0.054975871827661}};
135 // 0 negative weights, 0 points outside of the triangle, total sum of the
136 // weights is 0.5
137 
138 // -----------------------------------------------------------------------------
140 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
141 
142 IntPt triP5Solin[7] = {
143  {{0.333333333333333, 0.333333333333333, 0.}, 0.112500000000000},
144  {{0.470142064105115, 0.470142064105115, 0.}, 0.066197076394253},
145  {{0.470142064105115, 0.059715871789770, 0.}, 0.066197076394253},
146  {{0.059715871789770, 0.470142064105115, 0.}, 0.066197076394253},
147  {{0.101286507323456, 0.101286507323456, 0.}, 0.062969590272414},
148  {{0.101286507323456, 0.797426985353087, 0.}, 0.062969590272414},
149  {{0.797426985353087, 0.101286507323456, 0.}, 0.062969590272414}};
150 // 0 negative weights, 0 points outside of the triangle, total sum of the
151 // weights is 0.5
152 
153 // -----------------------------------------------------------------------------
155 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
156 
157 IntPt triP6Solin[12] = {
158  {{0.249286745170910, 0.249286745170910, 0.}, 0.058393137863189},
159  {{0.249286745170910, 0.501426509658179, 0.}, 0.058393137863189},
160  {{0.501426509658179, 0.249286745170910, 0.}, 0.058393137863189},
161  {{0.063089014491502, 0.063089014491502, 0.}, 0.025422453185104},
162  {{0.063089014491502, 0.873821971016996, 0.}, 0.025422453185104},
163  {{0.873821971016996, 0.063089014491502, 0.}, 0.025422453185104},
164  {{0.310352451033785, 0.636502499121399, 0.}, 0.041425537809187},
165  {{0.636502499121399, 0.053145049844816, 0.}, 0.041425537809187},
166  {{0.053145049844816, 0.310352451033785, 0.}, 0.041425537809187},
167  {{0.310352451033785, 0.053145049844816, 0.}, 0.041425537809187},
168  {{0.636502499121399, 0.310352451033785, 0.}, 0.041425537809187},
169  {{0.053145049844816, 0.636502499121399, 0.}, 0.041425537809187}};
170 // 0 negative weights, 0 points outside of the triangle, total sum of the
171 // weights is 0.5
172 
173 // -----------------------------------------------------------------------------
175 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
176 
177 IntPt triP7Solin[13] = {
178  {{0.333333333333333, 0.333333333333333, 0.}, -0.074785022233841},
179  {{0.260345966079040, 0.260345966079040, 0.}, 0.087807628716604},
180  {{0.260345966079040, 0.479308067841920, 0.}, 0.087807628716604},
181  {{0.479308067841920, 0.260345966079040, 0.}, 0.087807628716604},
182  {{0.065130102902216, 0.065130102902216, 0.}, 0.026673617804419},
183  {{0.065130102902216, 0.869739794195568, 0.}, 0.026673617804419},
184  {{0.869739794195568, 0.065130102902216, 0.}, 0.026673617804419},
185  {{0.312865496004874, 0.638444188569810, 0.}, 0.038556880445128},
186  {{0.638444188569810, 0.048690315425316, 0.}, 0.038556880445128},
187  {{0.048690315425316, 0.312865496004874, 0.}, 0.038556880445128},
188  {{0.312865496004874, 0.048690315425316, 0.}, 0.038556880445128},
189  {{0.638444188569810, 0.312865496004874, 0.}, 0.038556880445128},
190  {{0.048690315425316, 0.638444188569810, 0.}, 0.038556880445128}};
191 // 1 negative weight, 0 points outside of the triangle, total sum of the
192 // weights is 0.5
193 
194 // -----------------------------------------------------------------------------
196 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
197 
198 IntPt triP8Solin[16] = {
199  {{0.333333333333333, 0.333333333333333, 0.}, 0.072157803838894},
200  {{0.459292588292723, 0.459292588292723, 0.}, 0.047545817133643},
201  {{0.459292588292723, 0.081414823414554, 0.}, 0.047545817133643},
202  {{0.081414823414554, 0.459292588292723, 0.}, 0.047545817133643},
203  {{0.170569307751760, 0.170569307751760, 0.}, 0.051608685267359},
204  {{0.170569307751760, 0.658861384496480, 0.}, 0.051608685267359},
205  {{0.658861384496480, 0.170569307751760, 0.}, 0.051608685267359},
206  {{0.050547228317031, 0.050547228317031, 0.}, 0.016229248811599},
207  {{0.050547228317031, 0.898905543365938, 0.}, 0.016229248811599},
208  {{0.898905543365938, 0.050547228317031, 0.}, 0.016229248811599},
209  {{0.263112829634638, 0.728492392955404, 0.}, 0.013615157087217},
210  {{0.728492392955404, 0.008394777409958, 0.}, 0.013615157087217},
211  {{0.008394777409958, 0.263112829634638, 0.}, 0.013615157087217},
212  {{0.263112829634638, 0.008394777409958, 0.}, 0.013615157087217},
213  {{0.728492392955404, 0.263112829634638, 0.}, 0.013615157087217},
214  {{0.008394777409958, 0.728492392955404, 0.}, 0.013615157087217}};
215 // 0 negative weights, 0 points outside of the triangle, total sum of the
216 // weights is 0.5
217 
218 // -----------------------------------------------------------------------------
220 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
221 
222 IntPt triP9Solin[19] = {
223  {{0.3333333333330, 0.3333333333333, 0.}, 0.04856789814140},
224  {{0.4896825191990, 0.4896825191990, 0.}, 0.01566735011355},
225  {{0.4896825191990, 0.0206349616025, 0.}, 0.01566735011355},
226  {{0.0206349616025, 0.4896825191990, 0.}, 0.01566735011355},
227  {{0.4370895914930, 0.4370895914930, 0.}, 0.03891377050240},
228  {{0.4370895914930, 0.1258208170140, 0.}, 0.03891377050240},
229  {{0.1258208170140, 0.4370895914930, 0.}, 0.03891377050240},
230  {{0.1882035356190, 0.1882035356190, 0.}, 0.03982386946360},
231  {{0.1882035356190, 0.6235929287620, 0.}, 0.03982386946360},
232  {{0.6235929287620, 0.1882035356190, 0.}, 0.03982386946360},
233  {{0.0447295133945, 0.0447295133945, 0.}, 0.01278883782935},
234  {{0.0447295133945, 0.9105409732110, 0.}, 0.01278883782935},
235  {{0.9105409732110, 0.0447295133945, 0.}, 0.01278883782935},
236  {{0.2219629891610, 0.7411985987840, 0.}, 0.02164176968865},
237  {{0.7411985987840, 0.0368384120547, 0.}, 0.02164176968865},
238  {{0.0368384120547, 0.2219629891610, 0.}, 0.02164176968865},
239  {{0.2219629891610, 0.0368384120547, 0.}, 0.02164176968865},
240  {{0.7411985987840, 0.2219629891610, 0.}, 0.02164176968865},
241  {{0.0368384120547, 0.7411985987840, 0.}, 0.02164176968865}};
242 // 0 negative weights, 0 points outside of the triangle, total sum of the
243 // weights is 0.5
244 
245 // -----------------------------------------------------------------------------
247 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
248 
249 IntPt triP10Solin[25] = {
250  {{0.3333333333330, 0.3333333333330, 0.}, 0.04540899519140},
251  {{0.4855776333840, 0.4855776333840, 0.}, 0.01836297887825},
252  {{0.4855776333840, 0.0288447332327, 0.}, 0.01836297887825},
253  {{0.0288447332327, 0.4855776333840, 0.}, 0.01836297887825},
254  {{0.1094815754850, 0.1094815754850, 0.}, 0.02266052971775},
255  {{0.1094815754850, 0.7810368490300, 0.}, 0.02266052971775},
256  {{0.7810368490300, 0.1094815754850, 0.}, 0.02266052971775},
257  {{0.3079398387640, 0.5503529418210, 0.}, 0.03637895842270},
258  {{0.5503529418210, 0.1417072194150, 0.}, 0.03637895842270},
259  {{0.1417072194150, 0.3079398387640, 0.}, 0.03637895842270},
260  {{0.3079398387640, 0.1417072194150, 0.}, 0.03637895842270},
261  {{0.5503529418210, 0.3079398387640, 0.}, 0.03637895842270},
262  {{0.1417072194150, 0.5503529418210, 0.}, 0.03637895842270},
263  {{0.2466725606400, 0.7283239045970, 0.}, 0.01416362126555},
264  {{0.7283239045970, 0.0250035347627, 0.}, 0.01416362126555},
265  {{0.0250035347627, 0.2466725606400, 0.}, 0.01416362126555},
266  {{0.2466725606400, 0.0250035347627, 0.}, 0.01416362126555},
267  {{0.7283239045970, 0.2466725606400, 0.}, 0.01416362126555},
268  {{0.0250035347627, 0.7283239045970, 0.}, 0.01416362126555},
269  {{0.0668032510122, 0.9236559335870, 0.}, 0.00471083348185},
270  {{0.9236559335870, 0.0095408154003, 0.}, 0.00471083348185},
271  {{0.0095408154003, 0.0668032510122, 0.}, 0.00471083348185},
272  {{0.0668032510122, 0.0095408154003, 0.}, 0.00471083348185},
273  {{0.9236559335870, 0.0668032510122, 0.}, 0.00471083348185},
274  {{0.0095408154003, 0.9236559335870, 0.}, 0.00471083348185}};
275 // 0 negative weights, 0 points outside of the triangle, total sum of the
276 // weights is 0.5
277 
278 // -----------------------------------------------------------------------------
280 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
281 
282 IntPt triP11Solin[27] = {
283  {{+0.5346110482710, +0.5346110482710, 0.}, 0.00046350316448},
284  {{-0.0692220965415, +0.5346110482710, 0.}, 0.00046350316448},
285  {{+0.5346110482710, -0.0692220965415, 0.}, 0.00046350316448},
286  {{+0.3989693029660, +0.3989693029660, 0.}, 0.03857476745740},
287  {{+0.2020613940680, +0.3989693029660, 0.}, 0.03857476745740},
288  {{+0.3989693029660, +0.2020613940680, 0.}, 0.03857476745740},
289  {{+0.2033099004310, +0.2033099004310, 0.}, 0.02966148869040},
290  {{+0.5933801991370, +0.2033099004310, 0.}, 0.02966148869040},
291  {{+0.2033099004310, +0.5933801991370, 0.}, 0.02966148869040},
292  {{+0.1193509122830, +0.1193509122830, 0.}, 0.01809227025170},
293  {{+0.7612981754350, +0.1193509122830, 0.}, 0.01809227025170},
294  {{+0.1193509122830, +0.7612981754350, 0.}, 0.01809227025170},
295  {{+0.0323649481113, +0.0323649481113, 0.}, 0.00682986550135},
296  {{+0.9352701037770, +0.0323649481113, 0.}, 0.00682986550135},
297  {{+0.0323649481113, +0.9352701037770, 0.}, 0.00682986550135},
298  {{+0.5932012134280, +0.3566206482610, 0.}, 0.02616855598110},
299  {{+0.0501781383105, +0.5932012134280, 0.}, 0.02616855598110},
300  {{+0.3566206482610, +0.0501781383105, 0.}, 0.02616855598110},
301  {{+0.0501781383105, +0.3566206482610, 0.}, 0.02616855598110},
302  {{+0.3566206482610, +0.5932012134280, 0.}, 0.02616855598110},
303  {{+0.5932012134280, +0.0501781383105, 0.}, 0.02616855598110},
304  {{+0.8074890031600, +0.1714889803040, 0.}, 0.01035382981955},
305  {{+0.0210220165362, +0.8074890031600, 0.}, 0.01035382981955},
306  {{+0.1714889803040, +0.0210220165362, 0.}, 0.01035382981955},
307  {{+0.0210220165362, +0.1714889803040, 0.}, 0.01035382981955},
308  {{+0.1714889803040, +0.8074890031600, 0.}, 0.01035382981955},
309  {{+0.8074890031600, +0.0210220165362, 0.}, 0.01035382981955}};
310 // 0 negative weights, 3 points outside of the triangle, total sum of the
311 // weights is 0.5
312 
313 // -----------------------------------------------------------------------------
315 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
316 
317 IntPt triP12Solin[33] = {
318  {{0.4882173897740, 0.4882173897740, 0.}, 0.01286553322025},
319  {{0.4882173897740, 0.0235652204524, 0.}, 0.01286553322025},
320  {{0.0235652204524, 0.4882173897740, 0.}, 0.01286553322025},
321  {{0.4397243922940, 0.4397243922940, 0.}, 0.02184627226900},
322  {{0.4397243922940, 0.1205512154110, 0.}, 0.02184627226900},
323  {{0.1205512154110, 0.4397243922940, 0.}, 0.02184627226900},
324  {{0.2712103850120, 0.2712103850120, 0.}, 0.03142911210895},
325  {{0.2712103850120, 0.4575792299760, 0.}, 0.03142911210895},
326  {{0.4575792299760, 0.2712103850120, 0.}, 0.03142911210895},
327  {{0.1275761455420, 0.1275761455420, 0.}, 0.01739805646535},
328  {{0.1275761455420, 0.7448477089170, 0.}, 0.01739805646535},
329  {{0.7448477089170, 0.1275761455420, 0.}, 0.01739805646535},
330  {{0.0213173504532, 0.0213173504532, 0.}, 0.00308313052578},
331  {{0.0213173504532, 0.9573652990940, 0.}, 0.00308313052578},
332  {{0.9573652990940, 0.0213173504532, 0.}, 0.00308313052578},
333  {{0.2757132696860, 0.6089432357800, 0.}, 0.02018577888320},
334  {{0.6089432357800, 0.1153434945350, 0.}, 0.02018577888320},
335  {{0.1153434945350, 0.2757132696860, 0.}, 0.02018577888320},
336  {{0.2757132696860, 0.1153434945350, 0.}, 0.02018577888320},
337  {{0.6089432357800, 0.2757132696860, 0.}, 0.02018577888320},
338  {{0.1153434945350, 0.6089432357800, 0.}, 0.02018577888320},
339  {{0.2813255809900, 0.6958360867880, 0.}, 0.01117838660115},
340  {{0.6958360867880, 0.0228383322223, 0.}, 0.01117838660115},
341  {{0.0228383322223, 0.2813255809900, 0.}, 0.01117838660115},
342  {{0.2813255809900, 0.0228383322223, 0.}, 0.01117838660115},
343  {{0.6958360867880, 0.2813255809900, 0.}, 0.01117838660115},
344  {{0.0228383322223, 0.6958360867880, 0.}, 0.01117838660115},
345  {{0.1162519159080, 0.8580140335440, 0.}, 0.00865811555435},
346  {{0.8580140335440, 0.0257340505483, 0.}, 0.00865811555435},
347  {{0.0257340505483, 0.1162519159080, 0.}, 0.00865811555435},
348  {{0.1162519159080, 0.0257340505483, 0.}, 0.00865811555435},
349  {{0.8580140335440, 0.1162519159080, 0.}, 0.00865811555435},
350  {{0.0257340505483, 0.8580140335440, 0.}, 0.00865811555435}};
351 // 0 negative weights, 0 points outside of the triangle, total sum of the
352 // weights is 0.5
353 
354 // -----------------------------------------------------------------------------
356 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
357 
358 IntPt triP13Solin[37] = {
359  {{0.33333333333330, 0.33333333333330, 0.}, 0.026260461700400},
360  {{0.49504818494000, 0.49504818494000, 0.}, 0.005640072604650},
361  {{0.00990363012059, 0.49504818494000, 0.}, 0.005640072604650},
362  {{0.49504818494000, 0.00990363012059, 0.}, 0.005640072604650},
363  {{0.46871663511000, 0.46871663511000, 0.}, 0.015711759181250},
364  {{0.06256672978090, 0.46871663511000, 0.}, 0.015711759181250},
365  {{0.46871663511000, 0.06256672978090, 0.}, 0.015711759181250},
366  {{0.41452133680100, 0.41452133680100, 0.}, 0.023536251252100},
367  {{0.17095732639700, 0.41452133680100, 0.}, 0.023536251252100},
368  {{0.41452133680100, 0.17095732639700, 0.}, 0.023536251252100},
369  {{0.22939957204300, 0.22939957204300, 0.}, 0.023681793268200},
370  {{0.54120085591400, 0.22939957204300, 0.}, 0.023681793268200},
371  {{0.22939957204300, 0.54120085591400, 0.}, 0.023681793268200},
372  {{0.11442449519600, 0.11442449519600, 0.}, 0.015583764522900},
373  {{0.77115100960700, 0.11442449519600, 0.}, 0.015583764522900},
374  {{0.11442449519600, 0.77115100960700, 0.}, 0.015583764522900},
375  {{0.02481139136350, 0.02481139136350, 0.}, 0.003987885732535},
376  {{0.95037721727300, 0.02481139136350, 0.}, 0.003987885732535},
377  {{0.02481139136350, 0.95037721727300, 0.}, 0.003987885732535},
378  {{0.63635117456200, 0.26879499705900, 0.}, 0.018424201364350},
379  {{0.09485382837960, 0.63635117456200, 0.}, 0.018424201364350},
380  {{0.26879499705900, 0.09485382837960, 0.}, 0.018424201364350},
381  {{0.09485382837960, 0.26879499705900, 0.}, 0.018424201364350},
382  {{0.26879499705900, 0.63635117456200, 0.}, 0.018424201364350},
383  {{0.63635117456200, 0.09485382837960, 0.}, 0.018424201364350},
384  {{0.69016915998700, 0.29173006673400, 0.}, 0.008700731651900},
385  {{0.01810077327880, 0.69016915998700, 0.}, 0.008700731651900},
386  {{0.29173006673400, 0.01810077327880, 0.}, 0.008700731651900},
387  {{0.01810077327880, 0.29173006673400, 0.}, 0.008700731651900},
388  {{0.29173006673400, 0.69016915998700, 0.}, 0.008700731651900},
389  {{0.69016915998700, 0.01810077327880, 0.}, 0.008700731651900},
390  {{0.85140953783400, 0.12635738549200, 0.}, 0.007760893419500},
391  {{0.02223307667410, 0.85140953783400, 0.}, 0.007760893419500},
392  {{0.12635738549200, 0.02223307667410, 0.}, 0.007760893419500},
393  {{0.02223307667410, 0.12635738549200, 0.}, 0.007760893419500},
394  {{0.12635738549200, 0.85140953783400, 0.}, 0.007760893419500},
395  {{0.85140953783400, 0.02223307667410, 0.}, 0.007760893419500}};
396 // 0 negative weights, 0 points outside of the triangle, total sum of the
397 // weights is 0.5
398 
399 // -----------------------------------------------------------------------------
401 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
402 
403 IntPt triP14Solin[42] = {
404  {{0.48896391036200, 0.48896391036200, 0.}, 0.01094179068470},
405  {{0.02207217927560, 0.48896391036200, 0.}, 0.01094179068470},
406  {{0.48896391036200, 0.02207217927560, 0.}, 0.01094179068470},
407  {{0.41764471934000, 0.41764471934000, 0.}, 0.01639417677205},
408  {{0.16471056131900, 0.41764471934000, 0.}, 0.01639417677205},
409  {{0.41764471934000, 0.16471056131900, 0.}, 0.01639417677205},
410  {{0.27347752830900, 0.27347752830900, 0.}, 0.02588705225365},
411  {{0.45304494338200, 0.27347752830900, 0.}, 0.02588705225365},
412  {{0.27347752830900, 0.45304494338200, 0.}, 0.02588705225365},
413  {{0.17720553241300, 0.17720553241300, 0.}, 0.02108129436850},
414  {{0.64558893517500, 0.17720553241300, 0.}, 0.02108129436850},
415  {{0.17720553241300, 0.64558893517500, 0.}, 0.02108129436850},
416  {{0.06179988309090, 0.06179988309090, 0.}, 0.00721684983490},
417  {{0.87640023381800, 0.06179988309090, 0.}, 0.00721684983490},
418  {{0.06179988309090, 0.87640023381800, 0.}, 0.00721684983490},
419  {{0.01939096124870, 0.01939096124870, 0.}, 0.00246170180120},
420  {{0.96121807750300, 0.01939096124870, 0.}, 0.00246170180120},
421  {{0.01939096124870, 0.96121807750300, 0.}, 0.00246170180120},
422  {{0.77060855477500, 0.17226668782100, 0.}, 0.01233287660630},
423  {{0.05712475740360, 0.77060855477500, 0.}, 0.01233287660630},
424  {{0.17226668782100, 0.05712475740360, 0.}, 0.01233287660630},
425  {{0.05712475740360, 0.17226668782100, 0.}, 0.01233287660630},
426  {{0.17226668782100, 0.77060855477500, 0.}, 0.01233287660630},
427  {{0.77060855477500, 0.05712475740360, 0.}, 0.01233287660630},
428  {{0.57022229084700, 0.33686145979600, 0.}, 0.01928575539355},
429  {{0.09291624935700, 0.57022229084700, 0.}, 0.01928575539355},
430  {{0.33686145979600, 0.09291624935700, 0.}, 0.01928575539355},
431  {{0.09291624935700, 0.33686145979600, 0.}, 0.01928575539355},
432  {{0.33686145979600, 0.57022229084700, 0.}, 0.01928575539355},
433  {{0.57022229084700, 0.09291624935700, 0.}, 0.01928575539355},
434  {{0.68698016780800, 0.29837288213600, 0.}, 0.00721815405675},
435  {{0.01464695005570, 0.68698016780800, 0.}, 0.00721815405675},
436  {{0.29837288213600, 0.01464695005570, 0.}, 0.00721815405675},
437  {{0.01464695005570, 0.29837288213600, 0.}, 0.00721815405675},
438  {{0.29837288213600, 0.68698016780800, 0.}, 0.00721815405675},
439  {{0.68698016780800, 0.01464695005570, 0.}, 0.00721815405675},
440  {{0.87975717137000, 0.11897449769700, 0.}, 0.00250511441925},
441  {{0.00126833093287, 0.87975717137000, 0.}, 0.00250511441925},
442  {{0.11897449769700, 0.00126833093287, 0.}, 0.00250511441925},
443  {{0.00126833093287, 0.11897449769700, 0.}, 0.00250511441925},
444  {{0.11897449769700, 0.87975717137000, 0.}, 0.00250511441925},
445  {{0.87975717137000, 0.00126833093287, 0.}, 0.00250511441925}};
446 // 0 negative weights, 0 points outside of the triangle, total sum of the
447 // weights is 0.5
448 
449 // -----------------------------------------------------------------------------
451 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
452 
453 IntPt triP15Solin[48] = {
454  {{+0.5069729168580, +0.5069729168580, 0.}, 0.000958437821425},
455  {{-0.0139458337165, +0.5069729168580, 0.}, 0.000958437821425},
456  {{+0.5069729168580, -0.0139458337165, 0.}, 0.000958437821425},
457  {{+0.4314063542830, +0.4314063542830, 0.}, 0.022124513635550},
458  {{+0.1371872914340, +0.4314063542830, 0.}, 0.022124513635550},
459  {{+0.4314063542830, +0.1371872914340, 0.}, 0.022124513635550},
460  {{+0.2776936448470, +0.2776936448470, 0.}, 0.025593274359450},
461  {{+0.4446127103060, +0.2776936448470, 0.}, 0.025593274359450},
462  {{+0.2776936448470, +0.4446127103060, 0.}, 0.025593274359450},
463  {{+0.1264648910410, +0.1264648910410, 0.}, 0.011843867935350},
464  {{+0.7470702179170, +0.1264648910410, 0.}, 0.011843867935350},
465  {{+0.1264648910410, +0.7470702179170, 0.}, 0.011843867935350},
466  {{+0.0708083859747, +0.0708083859747, 0.}, 0.006644887845000},
467  {{+0.8583832280510, +0.0708083859747, 0.}, 0.006644887845000},
468  {{+0.0708083859747, +0.8583832280510, 0.}, 0.006644887845000},
469  {{+0.0189651702411, +0.0189651702411, 0.}, 0.002374458304095},
470  {{+0.9620696595180, +0.0189651702411, 0.}, 0.002374458304095},
471  {{+0.0189651702411, +0.9620696595180, 0.}, 0.002374458304095},
472  {{+0.6049544668930, +0.2613113711400, 0.}, 0.019275036299800},
473  {{+0.1337341619670, +0.6049544668930, 0.}, 0.019275036299800},
474  {{+0.2613113711400, +0.1337341619670, 0.}, 0.019275036299800},
475  {{+0.1337341619670, +0.2613113711400, 0.}, 0.019275036299800},
476  {{+0.2613113711400, +0.6049544668930, 0.}, 0.019275036299800},
477  {{+0.6049544668930, +0.1337341619670, 0.}, 0.019275036299800},
478  {{+0.5755865555130, +0.3880467670900, 0.}, 0.013607907160300},
479  {{+0.0363666773969, +0.5755865555130, 0.}, 0.013607907160300},
480  {{+0.3880467670900, +0.0363666773969, 0.}, 0.013607907160300},
481  {{+0.0363666773969, +0.3880467670900, 0.}, 0.013607907160300},
482  {{+0.3880467670900, +0.5755865555130, 0.}, 0.013607907160300},
483  {{+0.5755865555130, +0.0363666773969, 0.}, 0.013607907160300},
484  {{+0.7244626630770, +0.2857122200500, 0.}, 0.001091038683400},
485  {{-0.0101748831266, +0.7244626630770, 0.}, 0.001091038683400},
486  {{+0.2857122200500, -0.0101748831266, 0.}, 0.001091038683400},
487  {{-0.0101748831266, +0.2857122200500, 0.}, 0.001091038683400},
488  {{+0.2857122200500, +0.7244626630770, 0.}, 0.001091038683400},
489  {{+0.7244626630770, -0.0101748831266, 0.}, 0.001091038683400},
490  {{+0.7475564660520, +0.2155996640720, 0.}, 0.010752659923850},
491  {{+0.0368438698759, +0.7475564660520, 0.}, 0.010752659923850},
492  {{+0.2155996640720, +0.0368438698759, 0.}, 0.010752659923850},
493  {{+0.0368438698759, +0.2155996640720, 0.}, 0.010752659923850},
494  {{+0.2155996640720, +0.7475564660520, 0.}, 0.010752659923850},
495  {{+0.7475564660520, +0.0368438698759, 0.}, 0.010752659923850},
496  {{+0.8839645740920, +0.1035756165760, 0.}, 0.003836971315525},
497  {{+0.0124598093312, +0.8839645740920, 0.}, 0.003836971315525},
498  {{+0.1035756165760, +0.0124598093312, 0.}, 0.003836971315525},
499  {{+0.0124598093312, +0.1035756165760, 0.}, 0.003836971315525},
500  {{+0.1035756165760, +0.8839645740920, 0.}, 0.003836971315525},
501  {{+0.8839645740920, +0.0124598093312, 0.}, 0.003836971315525}};
502 // 0 negative weights, 9 points outside of the triangle, total sum of the
503 // weights is 0.5
504 
505 // -----------------------------------------------------------------------------
507 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
508 
509 IntPt triP16Solin[52] = {
510  {{+0.33333333333330, +0.33333333333330, 0.}, 0.023437848713800},
511  {{+0.49738054194800, +0.49738054194800, 0.}, 0.003202939289290},
512  {{+0.00523891610312, +0.49738054194800, 0.}, 0.003202939289290},
513  {{+0.49738054194800, +0.00523891610312, 0.}, 0.003202939289290},
514  {{+0.41346943854900, +0.41346943854900, 0.}, 0.020855148369700},
515  {{+0.17306112290100, +0.41346943854900, 0.}, 0.020855148369700},
516  {{+0.41346943854900, +0.17306112290100, 0.}, 0.020855148369700},
517  {{+0.47045859906700, +0.47045859906700, 0.}, 0.013445742125050},
518  {{+0.05908280186600, +0.47045859906700, 0.}, 0.013445742125050},
519  {{+0.47045859906700, +0.05908280186600, 0.}, 0.013445742125050},
520  {{+0.24055374997000, +0.24055374997000, 0.}, 0.021066261380800},
521  {{+0.51889250006100, +0.24055374997000, 0.}, 0.021066261380800},
522  {{+0.24055374997000, +0.51889250006100, 0.}, 0.021066261380800},
523  {{+0.14796579422300, +0.14796579422300, 0.}, 0.015000133421400},
524  {{+0.70406841155500, +0.14796579422300, 0.}, 0.015000133421400},
525  {{+0.14796579422300, +0.70406841155500, 0.}, 0.015000133421400},
526  {{+0.07546518765750, +0.07546518765750, 0.}, 0.007100049462500},
527  {{+0.84906962468500, +0.07546518765750, 0.}, 0.007100049462500},
528  {{+0.07546518765750, +0.84906962468500, 0.}, 0.007100049462500},
529  {{+0.01659640262300, +0.01659640262300, 0.}, 0.001791231175635},
530  {{+0.96680719475400, +0.01659640262300, 0.}, 0.001791231175635},
531  {{+0.01659640262300, +0.96680719475400, 0.}, 0.001791231175635},
532  {{+0.59986871117500, +0.29655559658000, 0.}, 0.016386573730300},
533  {{+0.10357569224500, +0.59986871117500, 0.}, 0.016386573730300},
534  {{+0.29655559658000, +0.10357569224500, 0.}, 0.016386573730300},
535  {{+0.10357569224500, +0.29655559658000, 0.}, 0.016386573730300},
536  {{+0.29655559658000, +0.59986871117500, 0.}, 0.016386573730300},
537  {{+0.59986871117500, +0.10357569224500, 0.}, 0.016386573730300},
538  {{+0.64219352494200, +0.33772306340300, 0.}, 0.007649153124200},
539  {{+0.02008341165540, +0.64219352494200, 0.}, 0.007649153124200},
540  {{+0.33772306340300, +0.02008341165540, 0.}, 0.007649153124200},
541  {{+0.02008341165540, +0.33772306340300, 0.}, 0.007649153124200},
542  {{+0.33772306340300, +0.64219352494200, 0.}, 0.007649153124200},
543  {{+0.64219352494200, +0.02008341165540, 0.}, 0.007649153124200},
544  {{+0.79959272097100, +0.20474828164300, 0.}, 0.001193122096420},
545  {{-0.00434100261414, +0.79959272097100, 0.}, 0.001193122096420},
546  {{+0.20474828164300, -0.00434100261414, 0.}, 0.001193122096420},
547  {{-0.00434100261414, +0.20474828164300, 0.}, 0.001193122096420},
548  {{+0.20474828164300, +0.79959272097100, 0.}, 0.001193122096420},
549  {{+0.79959272097100, -0.00434100261414, 0.}, 0.001193122096420},
550  {{+0.76869972140100, +0.18935849213100, 0.}, 0.009542396377950},
551  {{+0.04194178646800, +0.76869972140100, 0.}, 0.009542396377950},
552  {{+0.18935849213100, +0.04194178646800, 0.}, 0.009542396377950},
553  {{+0.04194178646800, +0.18935849213100, 0.}, 0.009542396377950},
554  {{+0.18935849213100, +0.76869972140100, 0.}, 0.009542396377950},
555  {{+0.76869972140100, +0.04194178646800, 0.}, 0.009542396377950},
556  {{+0.90039906408700, +0.08528361568270, 0.}, 0.003425027273270},
557  {{+0.01431732023070, +0.90039906408700, 0.}, 0.003425027273270},
558  {{+0.08528361568270, +0.01431732023070, 0.}, 0.003425027273270},
559  {{+0.01431732023070, +0.08528361568270, 0.}, 0.003425027273270},
560  {{+0.08528361568270, +0.90039906408700, 0.}, 0.003425027273270},
561  {{+0.90039906408700, +0.01431732023070, 0.}, 0.003425027273270}};
562 // 0 negative weights, 6 points outside of the triangle, total sum of the
563 // weights is 0.5
564 
565 // -----------------------------------------------------------------------------
567 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
568 
569 IntPt triP17Solin[61] = {
570  {{0.33333333333330, 0.33333333333330, 0.}, 0.016718599645400},
571  {{0.49717054055700, 0.49717054055700, 0.}, 0.002546707720255},
572  {{0.00565891888645, 0.49717054055700, 0.}, 0.002546707720255},
573  {{0.49717054055700, 0.00565891888645, 0.}, 0.002546707720255},
574  {{0.48217632262500, 0.48217632262500, 0.}, 0.007335432263800},
575  {{0.03564735475080, 0.48217632262500, 0.}, 0.007335432263800},
576  {{0.48217632262500, 0.03564735475080, 0.}, 0.007335432263800},
577  {{0.45023996902100, 0.45023996902100, 0.}, 0.012175439176850},
578  {{0.09952006195840, 0.45023996902100, 0.}, 0.012175439176850},
579  {{0.45023996902100, 0.09952006195840, 0.}, 0.012175439176850},
580  {{0.40026623937700, 0.40026623937700, 0.}, 0.015553775434500},
581  {{0.19946752124500, 0.40026623937700, 0.}, 0.015553775434500},
582  {{0.40026623937700, 0.19946752124500, 0.}, 0.015553775434500},
583  {{0.25214126797100, 0.25214126797100, 0.}, 0.015628555609300},
584  {{0.49571746405800, 0.25214126797100, 0.}, 0.015628555609300},
585  {{0.25214126797100, 0.49571746405800, 0.}, 0.015628555609300},
586  {{0.16204700465800, 0.16204700465800, 0.}, 0.012407827169850},
587  {{0.67590599068300, 0.16204700465800, 0.}, 0.012407827169850},
588  {{0.16204700465800, 0.67590599068300, 0.}, 0.012407827169850},
589  {{0.07587588226070, 0.07587588226070, 0.}, 0.007028036535300},
590  {{0.84824823547900, 0.07587588226070, 0.}, 0.007028036535300},
591  {{0.07587588226070, 0.84824823547900, 0.}, 0.007028036535300},
592  {{0.01565472696780, 0.01565472696780, 0.}, 0.001597338086890},
593  {{0.96869054606400, 0.01565472696780, 0.}, 0.001597338086890},
594  {{0.01565472696780, 0.96869054606400, 0.}, 0.001597338086890},
595  {{0.65549320380900, 0.33431986736400, 0.}, 0.004059827659495},
596  {{0.01018692882690, 0.65549320380900, 0.}, 0.004059827659495},
597  {{0.33431986736400, 0.01018692882690, 0.}, 0.004059827659495},
598  {{0.01018692882690, 0.33431986736400, 0.}, 0.004059827659495},
599  {{0.33431986736400, 0.65549320380900, 0.}, 0.004059827659495},
600  {{0.65549320380900, 0.01018692882690, 0.}, 0.004059827659495},
601  {{0.57233759053200, 0.29222153779700, 0.}, 0.013402871141600},
602  {{0.13544087167100, 0.57233759053200, 0.}, 0.013402871141600},
603  {{0.29222153779700, 0.13544087167100, 0.}, 0.013402871141600},
604  {{0.13544087167100, 0.29222153779700, 0.}, 0.013402871141600},
605  {{0.29222153779700, 0.57233759053200, 0.}, 0.013402871141600},
606  {{0.57233759053200, 0.13544087167100, 0.}, 0.013402871141600},
607  {{0.62600119028600, 0.31957488542300, 0.}, 0.009229996605400},
608  {{0.05442392429060, 0.62600119028600, 0.}, 0.009229996605400},
609  {{0.31957488542300, 0.05442392429060, 0.}, 0.009229996605400},
610  {{0.05442392429060, 0.31957488542300, 0.}, 0.009229996605400},
611  {{0.31957488542300, 0.62600119028600, 0.}, 0.009229996605400},
612  {{0.62600119028600, 0.05442392429060, 0.}, 0.009229996605400},
613  {{0.79642721497400, 0.19070422419200, 0.}, 0.004238434267165},
614  {{0.01286856083360, 0.79642721497400, 0.}, 0.004238434267165},
615  {{0.19070422419200, 0.01286856083360, 0.}, 0.004238434267165},
616  {{0.01286856083360, 0.19070422419200, 0.}, 0.004238434267165},
617  {{0.19070422419200, 0.79642721497400, 0.}, 0.004238434267165},
618  {{0.79642721497400, 0.01286856083360, 0.}, 0.004238434267165},
619  {{0.75235100593800, 0.18048321164900, 0.}, 0.009146398385000},
620  {{0.06716578241350, 0.75235100593800, 0.}, 0.009146398385000},
621  {{0.18048321164900, 0.06716578241350, 0.}, 0.009146398385000},
622  {{0.06716578241350, 0.18048321164900, 0.}, 0.009146398385000},
623  {{0.18048321164900, 0.75235100593800, 0.}, 0.009146398385000},
624  {{0.75235100593800, 0.06716578241350, 0.}, 0.009146398385000},
625  {{0.90462550409600, 0.08071131367960, 0.}, 0.003332816002085},
626  {{0.01466318222480, 0.90462550409600, 0.}, 0.003332816002085},
627  {{0.08071131367960, 0.01466318222480, 0.}, 0.003332816002085},
628  {{0.01466318222480, 0.08071131367960, 0.}, 0.003332816002085},
629  {{0.08071131367960, 0.90462550409600, 0.}, 0.003332816002085},
630  {{0.90462550409600, 0.01466318222480, 0.}, 0.003332816002085}};
631 // 0 negative weights, 0 points outside of the triangle, total sum of the
632 // weights is 0.5
633 
634 // -----------------------------------------------------------------------------
636 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
637 
638 IntPt triP18Solin[70] = {
639  {{+0.33333333333330, +0.33333333333330, 0.}, +0.015404969968800},
640  {{+0.49334480863100, +0.49334480863100, 0.}, +0.004536218339700},
641  {{+0.01331038273820, +0.49334480863100, 0.}, +0.004536218339700},
642  {{+0.49334480863100, +0.01331038273820, 0.}, +0.004536218339700},
643  {{+0.46921059424200, +0.46921059424200, 0.}, +0.009380658469800},
644  {{+0.06157881151610, +0.46921059424200, 0.}, +0.009380658469800},
645  {{+0.46921059424200, +0.06157881151610, 0.}, +0.009380658469800},
646  {{+0.43628139588700, +0.43628139588700, 0.}, +0.009720548992750},
647  {{+0.12743720822600, +0.43628139588700, 0.}, +0.009720548992750},
648  {{+0.43628139588700, +0.12743720822600, 0.}, +0.009720548992750},
649  {{+0.39484617067300, +0.39484617067300, 0.}, +0.013876974305400},
650  {{+0.21030765865300, +0.39484617067300, 0.}, +0.013876974305400},
651  {{+0.39484617067300, +0.21030765865300, 0.}, +0.013876974305400},
652  {{+0.24979456880300, +0.24979456880300, 0.}, +0.016128112675750},
653  {{+0.50041086239400, +0.24979456880300, 0.}, +0.016128112675750},
654  {{+0.24979456880300, +0.50041086239400, 0.}, +0.016128112675750},
655  {{+0.16143219374400, +0.16143219374400, 0.}, +0.012537016308450},
656  {{+0.67713561251200, +0.16143219374400, 0.}, +0.012537016308450},
657  {{+0.16143219374400, +0.67713561251200, 0.}, +0.012537016308450},
658  {{+0.07659822748540, +0.07659822748540, 0.}, +0.007635963985900},
659  {{+0.84680354502900, +0.07659822748540, 0.}, +0.007635963985900},
660  {{+0.07659822748540, +0.84680354502900, 0.}, +0.007635963985900},
661  {{+0.02425243935350, +0.02425243935350, 0.}, +0.003396961011480},
662  {{+0.95149512129300, +0.02425243935350, 0.}, +0.003396961011480},
663  {{+0.02425243935350, +0.95149512129300, 0.}, +0.003396961011480},
664  {{+0.04314636721700, +0.04314636721700, 0.}, -0.001111549364960},
665  {{+0.91370726556600, +0.04314636721700, 0.}, -0.001111549364960},
666  {{+0.04314636721700, +0.91370726556600, 0.}, -0.001111549364960},
667  {{+0.63265796885700, +0.35891149494100, 0.}, +0.003165957038205},
668  {{+0.00843053620242, +0.63265796885700, 0.}, +0.003165957038205},
669  {{+0.35891149494100, +0.00843053620242, 0.}, +0.003165957038205},
670  {{+0.00843053620242, +0.35891149494100, 0.}, +0.003165957038205},
671  {{+0.35891149494100, +0.63265796885700, 0.}, +0.003165957038205},
672  {{+0.63265796885700, +0.00843053620242, 0.}, +0.003165957038205},
673  {{+0.57441097151100, +0.29440247675200, 0.}, +0.013628769024550},
674  {{+0.13118655173700, +0.57441097151100, 0.}, +0.013628769024550},
675  {{+0.29440247675200, +0.13118655173700, 0.}, +0.013628769024550},
676  {{+0.13118655173700, +0.29440247675200, 0.}, +0.013628769024550},
677  {{+0.29440247675200, +0.57441097151100, 0.}, +0.013628769024550},
678  {{+0.57441097151100, +0.13118655173700, 0.}, +0.013628769024550},
679  {{+0.62477904679300, +0.32501780164200, 0.}, +0.008838392824750},
680  {{+0.05020315156570, +0.62477904679300, 0.}, +0.008838392824750},
681  {{+0.32501780164200, +0.05020315156570, 0.}, +0.008838392824750},
682  {{+0.05020315156570, +0.32501780164200, 0.}, +0.008838392824750},
683  {{+0.32501780164200, +0.62477904679300, 0.}, +0.008838392824750},
684  {{+0.62477904679300, +0.05020315156570, 0.}, +0.008838392824750},
685  {{+0.74893317652300, +0.18473755966600, 0.}, +0.009189742319050},
686  {{+0.06632926381090, +0.74893317652300, 0.}, +0.009189742319050},
687  {{+0.18473755966600, +0.06632926381090, 0.}, +0.009189742319050},
688  {{+0.06632926381090, +0.18473755966600, 0.}, +0.009189742319050},
689  {{+0.18473755966600, +0.74893317652300, 0.}, +0.009189742319050},
690  {{+0.74893317652300, +0.06632926381090, 0.}, +0.009189742319050},
691  {{+0.76920700542000, +0.21879680001300, 0.}, +0.004052366404095},
692  {{+0.01199619456620, +0.76920700542000, 0.}, +0.004052366404095},
693  {{+0.21879680001300, +0.01199619456620, 0.}, +0.004052366404095},
694  {{+0.01199619456620, +0.21879680001300, 0.}, +0.004052366404095},
695  {{+0.21879680001300, +0.76920700542000, 0.}, +0.004052366404095},
696  {{+0.76920700542000, +0.01199619456620, 0.}, +0.004052366404095},
697  {{+0.88396230227300, +0.10117959713600, 0.}, +0.003817064535365},
698  {{+0.01485810059010, +0.88396230227300, 0.}, +0.003817064535365},
699  {{+0.10117959713600, +0.01485810059010, 0.}, +0.003817064535365},
700  {{+0.01485810059010, +0.10117959713600, 0.}, +0.003817064535365},
701  {{+0.10117959713600, +0.88396230227300, 0.}, +0.003817064535365},
702  {{+0.88396230227300, +0.01485810059010, 0.}, +0.003817064535365},
703  {{+1.01434726001000, +0.02087475528260, 0.}, +2.3093830397e-05},
704  {{-0.03522201528790, +1.01434726001000, 0.}, +2.3093830397e-05},
705  {{+0.02087475528260, -0.03522201528790, 0.}, +2.3093830397e-05},
706  {{-0.03522201528790, +0.02087475528260, 0.}, +2.3093830397e-05},
707  {{+0.02087475528260, +1.01434726001000, 0.}, +2.3093830397e-05},
708  {{+1.01434726001000, -0.03522201528790, 0.}, +2.3093830397e-05}};
709 // 3 negative weights, 6 points outside of the triangle, total sum of the
710 // weights is 0.5
711 
712 // -----------------------------------------------------------------------------
714 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
715 
716 IntPt triP19Solin[73] = {
717  {{0.33333333333330, 0.33333333333330, 0.}, 0.016453165694450},
718  {{0.48960998707300, 0.48960998707300, 0.}, 0.005165365945650},
719  {{0.02078002585400, 0.48960998707300, 0.}, 0.005165365945650},
720  {{0.48960998707300, 0.02078002585400, 0.}, 0.005165365945650},
721  {{0.45453689269800, 0.45453689269800, 0.}, 0.011193623631500},
722  {{0.09092621460420, 0.45453689269800, 0.}, 0.011193623631500},
723  {{0.45453689269800, 0.09092621460420, 0.}, 0.011193623631500},
724  {{0.40141668064900, 0.40141668064900, 0.}, 0.015133062934750},
725  {{0.19716663870100, 0.40141668064900, 0.}, 0.015133062934750},
726  {{0.40141668064900, 0.19716663870100, 0.}, 0.015133062934750},
727  {{0.25555165440300, 0.25555165440300, 0.}, 0.015245483901100},
728  {{0.48889669119400, 0.25555165440300, 0.}, 0.015245483901100},
729  {{0.25555165440300, 0.48889669119400, 0.}, 0.015245483901100},
730  {{0.17707794215200, 0.17707794215200, 0.}, 0.012079606370800},
731  {{0.64584411569600, 0.17707794215200, 0.}, 0.012079606370800},
732  {{0.17707794215200, 0.64584411569600, 0.}, 0.012079606370800},
733  {{0.11006105322800, 0.11006105322800, 0.}, 0.008025401793400},
734  {{0.77987789354400, 0.11006105322800, 0.}, 0.008025401793400},
735  {{0.11006105322800, 0.77987789354400, 0.}, 0.008025401793400},
736  {{0.05552862425180, 0.05552862425180, 0.}, 0.004042290130890},
737  {{0.88894275149600, 0.05552862425180, 0.}, 0.004042290130890},
738  {{0.05552862425180, 0.88894275149600, 0.}, 0.004042290130890},
739  {{0.01262186377720, 0.01262186377720, 0.}, 0.001039681013740},
740  {{0.97475627244600, 0.01262186377720, 0.}, 0.001039681013740},
741  {{0.01262186377720, 0.97475627244600, 0.}, 0.001039681013740},
742  {{0.60063379479500, 0.39575478735700, 0.}, 0.001942438452490},
743  {{0.00361141784841, 0.60063379479500, 0.}, 0.001942438452490},
744  {{0.39575478735700, 0.00361141784841, 0.}, 0.001942438452490},
745  {{0.00361141784841, 0.39575478735700, 0.}, 0.001942438452490},
746  {{0.39575478735700, 0.60063379479500, 0.}, 0.001942438452490},
747  {{0.60063379479500, 0.00361141784841, 0.}, 0.001942438452490},
748  {{0.55760326158900, 0.30792998388000, 0.}, 0.012787080306000},
749  {{0.13446675453100, 0.55760326158900, 0.}, 0.012787080306000},
750  {{0.30792998388000, 0.13446675453100, 0.}, 0.012787080306000},
751  {{0.13446675453100, 0.30792998388000, 0.}, 0.012787080306000},
752  {{0.30792998388000, 0.55760326158900, 0.}, 0.012787080306000},
753  {{0.55760326158900, 0.13446675453100, 0.}, 0.012787080306000},
754  {{0.72098702581700, 0.26456694840700, 0.}, 0.004440451786670},
755  {{0.01444602577610, 0.72098702581700, 0.}, 0.004440451786670},
756  {{0.26456694840700, 0.01444602577610, 0.}, 0.004440451786670},
757  {{0.01444602577610, 0.26456694840700, 0.}, 0.004440451786670},
758  {{0.26456694840700, 0.72098702581700, 0.}, 0.004440451786670},
759  {{0.72098702581700, 0.01444602577610, 0.}, 0.004440451786670},
760  {{0.59452706895600, 0.35853935220600, 0.}, 0.008062273380850},
761  {{0.04693357883820, 0.59452706895600, 0.}, 0.008062273380850},
762  {{0.35853935220600, 0.04693357883820, 0.}, 0.008062273380850},
763  {{0.04693357883820, 0.35853935220600, 0.}, 0.008062273380850},
764  {{0.35853935220600, 0.59452706895600, 0.}, 0.008062273380850},
765  {{0.59452706895600, 0.04693357883820, 0.}, 0.008062273380850},
766  {{0.83933147368100, 0.15780740596900, 0.}, 0.001245970908745},
767  {{0.00286112035057, 0.83933147368100, 0.}, 0.001245970908745},
768  {{0.15780740596900, 0.00286112035057, 0.}, 0.001245970908745},
769  {{0.00286112035057, 0.15780740596900, 0.}, 0.001245970908745},
770  {{0.15780740596900, 0.83933147368100, 0.}, 0.001245970908745},
771  {{0.83933147368100, 0.00286112035057, 0.}, 0.001245970908745},
772  {{0.70108797892600, 0.07505059697590, 0.}, 0.009121420059500},
773  {{0.22386142409800, 0.70108797892600, 0.}, 0.009121420059500},
774  {{0.07505059697590, 0.22386142409800, 0.}, 0.009121420059500},
775  {{0.22386142409800, 0.07505059697590, 0.}, 0.009121420059500},
776  {{0.07505059697590, 0.70108797892600, 0.}, 0.009121420059500},
777  {{0.70108797892600, 0.22386142409800, 0.}, 0.009121420059500},
778  {{0.82293132407000, 0.14242160111300, 0.}, 0.005129281868100},
779  {{0.03464707481680, 0.82293132407000, 0.}, 0.005129281868100},
780  {{0.14242160111300, 0.03464707481680, 0.}, 0.005129281868100},
781  {{0.03464707481680, 0.14242160111300, 0.}, 0.005129281868100},
782  {{0.14242160111300, 0.82293132407000, 0.}, 0.005129281868100},
783  {{0.82293132407000, 0.03464707481680, 0.}, 0.005129281868100},
784  {{0.92434425262100, 0.06549462808290, 0.}, 0.001899964427650},
785  {{0.01016111929630, 0.92434425262100, 0.}, 0.001899964427650},
786  {{0.06549462808290, 0.01016111929630, 0.}, 0.001899964427650},
787  {{0.01016111929630, 0.06549462808290, 0.}, 0.001899964427650},
788  {{0.06549462808290, 0.92434425262100, 0.}, 0.001899964427650},
789  {{0.92434425262100, 0.01016111929630, 0.}, 0.001899964427650}};
790 // 0 negative weights, 0 points outside of the triangle, total sum of the
791 // weights is 0.5
792 
793 // -----------------------------------------------------------------------------
795 /* 'Higher-order Finite Elements', P.Solin, K.Segeth and I. Dolezel */
796 
797 IntPt triP20Solin[79] = {
798  {{+0.3333333333333, +0.3333333333333, 0.}, +0.016528527770800},
799  {{+0.5009504643520, +0.5009504643520, 0.}, +0.000433509592831},
800  {{-0.0019009287044, +0.5009504643520, 0.}, +0.000433509592831},
801  {{+0.5009504643520, -0.0019009287044, 0.}, +0.000433509592831},
802  {{+0.4882129579350, +0.4882129579350, 0.}, +0.005830026358200},
803  {{+0.0235740841305, +0.4882129579350, 0.}, +0.005830026358200},
804  {{+0.4882129579350, +0.0235740841305, 0.}, +0.005830026358200},
805  {{+0.4551366869500, +0.4551366869500, 0.}, +0.011438468178200},
806  {{+0.0897266360994, +0.4551366869500, 0.}, +0.011438468178200},
807  {{+0.4551366869500, +0.0897266360994, 0.}, +0.011438468178200},
808  {{+0.4019962593180, +0.4019962593180, 0.}, +0.015224491336950},
809  {{+0.1960074813630, +0.4019962593180, 0.}, +0.015224491336950},
810  {{+0.4019962593180, +0.1960074813630, 0.}, +0.015224491336950},
811  {{+0.2558929097590, +0.2558929097590, 0.}, +0.015312445862700},
812  {{+0.4882141804810, +0.2558929097590, 0.}, +0.015312445862700},
813  {{+0.2558929097590, +0.4882141804810, 0.}, +0.015312445862700},
814  {{+0.1764882559950, +0.1764882559950, 0.}, +0.012184028838400},
815  {{+0.6470234880100, +0.1764882559950, 0.}, +0.012184028838400},
816  {{+0.1764882559950, +0.6470234880100, 0.}, +0.012184028838400},
817  {{+0.1041708553370, +0.1041708553370, 0.}, +0.007998716016000},
818  {{+0.7916582893260, +0.1041708553370, 0.}, +0.007998716016000},
819  {{+0.1041708553370, +0.7916582893260, 0.}, +0.007998716016000},
820  {{+0.0530689638409, +0.0530689638409, 0.}, +0.003849150907800},
821  {{+0.8938620723180, +0.0530689638409, 0.}, +0.003849150907800},
822  {{+0.0530689638409, +0.8938620723180, 0.}, +0.003849150907800},
823  {{+0.0416187151960, +0.0416187151960, 0.}, -0.000316030248744},
824  {{+0.9167625696080, +0.0416187151960, 0.}, -0.000316030248744},
825  {{+0.0416187151960, +0.9167625696080, 0.}, -0.000316030248744},
826  {{+0.0115819214068, +0.0115819214068, 0.}, +0.000875567150595},
827  {{+0.9768361571860, +0.0115819214068, 0.}, +0.000875567150595},
828  {{+0.0115819214068, +0.9768361571860, 0.}, +0.000875567150595},
829  {{+0.6064026461060, +0.3448557702290, 0.}, +0.008232919594800},
830  {{+0.0487415836648, +0.6064026461060, 0.}, +0.008232919594800},
831  {{+0.3448557702290, +0.0487415836648, 0.}, +0.008232919594800},
832  {{+0.0487415836648, +0.3448557702290, 0.}, +0.008232919594800},
833  {{+0.3448557702290, +0.6064026461060, 0.}, +0.008232919594800},
834  {{+0.6064026461060, +0.0487415836648, 0.}, +0.008232919594800},
835  {{+0.6158426144570, +0.3778432695950, 0.}, +0.002419516770245},
836  {{+0.0063141159486, +0.6158426144570, 0.}, +0.002419516770245},
837  {{+0.3778432695950, +0.0063141159486, 0.}, +0.002419516770245},
838  {{+0.0063141159486, +0.3778432695950, 0.}, +0.002419516770245},
839  {{+0.3778432695950, +0.6158426144570, 0.}, +0.002419516770245},
840  {{+0.6158426144570, +0.0063141159486, 0.}, +0.002419516770245},
841  {{+0.5590480003900, +0.3066354790620, 0.}, +0.012902453267350},
842  {{+0.1343165205470, +0.5590480003900, 0.}, +0.012902453267350},
843  {{+0.3066354790620, +0.1343165205470, 0.}, +0.012902453267350},
844  {{+0.1343165205470, +0.3066354790620, 0.}, +0.012902453267350},
845  {{+0.3066354790620, +0.5590480003900, 0.}, +0.012902453267350},
846  {{+0.5590480003900, +0.1343165205470, 0.}, +0.012902453267350},
847  {{+0.7366067432630, +0.2494193627750, 0.}, +0.004235545527220},
848  {{+0.0139738939624, +0.7366067432630, 0.}, +0.004235545527220},
849  {{+0.2494193627750, +0.0139738939624, 0.}, +0.004235545527220},
850  {{+0.0139738939624, +0.2494193627750, 0.}, +0.004235545527220},
851  {{+0.2494193627750, +0.7366067432630, 0.}, +0.004235545527220},
852  {{+0.7366067432630, +0.0139738939624, 0.}, +0.004235545527220},
853  {{+0.7116751422870, +0.2127757248030, 0.}, +0.009177457053150},
854  {{+0.0755491329098, +0.7116751422870, 0.}, +0.009177457053150},
855  {{+0.2127757248030, +0.0755491329098, 0.}, +0.009177457053150},
856  {{+0.0755491329098, +0.2127757248030, 0.}, +0.009177457053150},
857  {{+0.2127757248030, +0.7116751422870, 0.}, +0.009177457053150},
858  {{+0.7116751422870, +0.0755491329098, 0.}, +0.009177457053150},
859  {{+0.8614027171550, +0.1469654360530, 0.}, +0.000352202338954},
860  {{-0.0083681532082, +0.8614027171550, 0.}, +0.000352202338954},
861  {{+0.1469654360530, -0.0083681532082, 0.}, +0.000352202338954},
862  {{-0.0083681532082, +0.1469654360530, 0.}, +0.000352202338954},
863  {{+0.1469654360530, +0.8614027171550, 0.}, +0.000352202338954},
864  {{+0.8614027171550, -0.0083681532082, 0.}, +0.000352202338954},
865  {{+0.8355869579120, +0.1377269788290, 0.}, +0.005056342463750},
866  {{+0.0266860632587, +0.8355869579120, 0.}, +0.005056342463750},
867  {{+0.1377269788290, +0.0266860632587, 0.}, +0.005056342463750},
868  {{+0.0266860632587, +0.1377269788290, 0.}, +0.005056342463750},
869  {{+0.1377269788290, +0.8355869579120, 0.}, +0.005056342463750},
870  {{+0.8355869579120, +0.0266860632587, 0.}, +0.005056342463750},
871  {{+0.9297561715570, +0.0596961091490, 0.}, +0.001786954692975},
872  {{+0.0105477192941, +0.9297561715570, 0.}, +0.001786954692975},
873  {{+0.0596961091490, +0.0105477192941, 0.}, +0.001786954692975},
874  {{+0.0105477192941, +0.0596961091490, 0.}, +0.001786954692975},
875  {{+0.0596961091490, +0.9297561715570, 0.}, +0.001786954692975},
876  {{+0.9297561715570, +0.0105477192941, 0.}, +0.001786954692975}};
877 // 3 negative weights, 9 points outside of the triangle, total sum of the
878 // weights is 0.5
879 
880 static IntPt *GQTSolin[21] = {
881  triP1Solin, triP1Solin, triP2Solin, triP3Solin, triP4Solin, triP5Solin,
882  triP6Solin, triP7Solin, triP8Solin, triP9Solin, triP10Solin, triP11Solin,
883  triP12Solin, triP13Solin, triP14Solin, triP15Solin, triP16Solin, triP17Solin,
884  triP18Solin, triP19Solin, triP20Solin};
885 static int GQTnPtSolin[21] = {1, 1, 3, 4, 6, 7, 12, 13, 16, 19, 25,
886  27, 33, 37, 42, 48, 52, 61, 70, 73, 79};
887 static std::vector<IntPt *> GQTGL(40, nullptr);
888 
889 IntPt *getGQTPts(int order, bool forceTensorRule)
890 {
891  if(!forceTensorRule && order < 21) return GQTSolin[order];
892  if(static_cast<int>(GQTGL.size()) < order + 1)
893  GQTGL.resize(order + 1, nullptr);
894  if(!GQTGL[order]) {
895  int n = (order + 3) / 2;
896  int npts = n * n;
897  IntPt *intpt = new IntPt[npts];
898  GaussLegendreTri(n, n, intpt);
899  GQTGL[order] = intpt;
900  }
901  return GQTGL[order];
902 }
903 
904 int getNGQTPts(int order, bool forceTensorRule)
905 {
906  if(!forceTensorRule && order < 21) return GQTnPtSolin[order];
907  return ((order + 3) / 2) * ((order + 3) / 2);
908 }
getNGQTPts
int getNGQTPts(int order, bool forceTensorRule)
Definition: GaussQuadratureTri.cpp:904
triP10Solin
IntPt triP10Solin[25]
Definition: GaussQuadratureTri.cpp:249
GaussLegendre1D.h
triP6Solin
IntPt triP6Solin[12]
Definition: GaussQuadratureTri.cpp:157
GQTnPt
int GQTnPt[9]
Definition: GaussQuadratureTri.cpp:90
triP11Solin
IntPt triP11Solin[27]
Definition: GaussQuadratureTri.cpp:282
triP9Solin
IntPt triP9Solin[19]
Definition: GaussQuadratureTri.cpp:222
triP20Solin
IntPt triP20Solin[79]
Definition: GaussQuadratureTri.cpp:797
triP18Solin
IntPt triP18Solin[70]
Definition: GaussQuadratureTri.cpp:638
GaussIntegration.h
triP17Solin
IntPt triP17Solin[61]
Definition: GaussQuadratureTri.cpp:569
GQTSolin
static IntPt * GQTSolin[21]
Definition: GaussQuadratureTri.cpp:880
GaussLegendreTri
int GaussLegendreTri(int n1, int n2, IntPt *pts)
Definition: GaussLegendreSimplex.cpp:54
triP15Solin
IntPt triP15Solin[48]
Definition: GaussQuadratureTri.cpp:453
GQT5
IntPt GQT5[7]
Definition: GaussQuadratureTri.cpp:31
triP4Solin
IntPt triP4Solin[6]
Definition: GaussQuadratureTri.cpp:128
triP12Solin
IntPt triP12Solin[33]
Definition: GaussQuadratureTri.cpp:317
GQT7
IntPt GQT7[13]
Definition: GaussQuadratureTri.cpp:54
GQT8
IntPt GQT8[16]
Definition: GaussQuadratureTri.cpp:71
triP3Solin
IntPt triP3Solin[4]
Definition: GaussQuadratureTri.cpp:116
triP8Solin
IntPt triP8Solin[16]
Definition: GaussQuadratureTri.cpp:198
GQT4
IntPt GQT4[6]
Definition: GaussQuadratureTri.cpp:23
GQT
IntPt * GQT[9]
Definition: GaussQuadratureTri.cpp:89
triP19Solin
IntPt triP19Solin[73]
Definition: GaussQuadratureTri.cpp:716
GQT6
IntPt GQT6[12]
Definition: GaussQuadratureTri.cpp:40
GQT1
IntPt GQT1[1]
Definition: GaussQuadratureTri.cpp:10
IntPt
Definition: GaussIntegration.h:12
triP14Solin
IntPt triP14Solin[42]
Definition: GaussQuadratureTri.cpp:403
getGQTPts
IntPt * getGQTPts(int order, bool forceTensorRule)
Definition: GaussQuadratureTri.cpp:889
triP16Solin
IntPt triP16Solin[52]
Definition: GaussQuadratureTri.cpp:509
triP13Solin
IntPt triP13Solin[37]
Definition: GaussQuadratureTri.cpp:358
triP2Solin
IntPt triP2Solin[3]
Definition: GaussQuadratureTri.cpp:105
triP1Solin
IntPt triP1Solin[1]
Definition: GaussQuadratureTri.cpp:96
GQTGL
static std::vector< IntPt * > GQTGL(40, nullptr)
GQT2
IntPt GQT2[3]
Definition: GaussQuadratureTri.cpp:12
triP7Solin
IntPt triP7Solin[13]
Definition: GaussQuadratureTri.cpp:177
GQTnPtSolin
static int GQTnPtSolin[21]
Definition: GaussQuadratureTri.cpp:885
triP5Solin
IntPt triP5Solin[7]
Definition: GaussQuadratureTri.cpp:142
GQT3
IntPt GQT3[4]
Definition: GaussQuadratureTri.cpp:17