quadrature_gauss_1D.C
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00001 // The libMesh Finite Element Library. 00002 // Copyright (C) 2002-2014 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner 00003 00004 // This library is free software; you can redistribute it and/or 00005 // modify it under the terms of the GNU Lesser General Public 00006 // License as published by the Free Software Foundation; either 00007 // version 2.1 of the License, or (at your option) any later version. 00008 00009 // This library is distributed in the hope that it will be useful, 00010 // but WITHOUT ANY WARRANTY; without even the implied warranty of 00011 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 00012 // Lesser General Public License for more details. 00013 00014 // You should have received a copy of the GNU Lesser General Public 00015 // License along with this library; if not, write to the Free Software 00016 // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA 00017 00018 00019 00020 // C++ includes 00021 00022 // Local includes 00023 #include "libmesh/quadrature_gauss.h" 00024 00025 namespace libMesh 00026 { 00027 00028 00029 00030 void QGauss::init_1D(const ElemType, 00031 unsigned int p) 00032 { 00033 //---------------------------------------------------------------------- 00034 // 1D quadrature rules 00035 switch(_order + 2*p) 00036 { 00037 case CONSTANT: 00038 case FIRST: 00039 { 00040 _points.resize (1); 00041 _weights.resize(1); 00042 00043 _points[0](0) = 0.; 00044 00045 _weights[0] = 2.; 00046 00047 return; 00048 } 00049 case SECOND: 00050 case THIRD: 00051 { 00052 _points.resize (2); 00053 _weights.resize(2); 00054 00055 _points[0](0) = -5.7735026918962576450914878050196e-01L; // -sqrt(3)/3 00056 _points[1] = -_points[0]; 00057 00058 _weights[0] = 1.; 00059 _weights[1] = _weights[0]; 00060 00061 return; 00062 } 00063 case FOURTH: 00064 case FIFTH: 00065 { 00066 _points.resize (3); 00067 _weights.resize(3); 00068 00069 _points[ 0](0) = -7.7459666924148337703585307995648e-01L; 00070 _points[ 1](0) = 0.; 00071 _points[ 2] = -_points[0]; 00072 00073 _weights[ 0] = 5.5555555555555555555555555555556e-01L; 00074 _weights[ 1] = 8.8888888888888888888888888888889e-01L; 00075 _weights[ 2] = _weights[0]; 00076 00077 return; 00078 } 00079 case SIXTH: 00080 case SEVENTH: 00081 { 00082 _points.resize (4); 00083 _weights.resize(4); 00084 00085 _points[ 0](0) = -8.6113631159405257522394648889281e-01L; 00086 _points[ 1](0) = -3.3998104358485626480266575910324e-01L; 00087 _points[ 2] = -_points[1]; 00088 _points[ 3] = -_points[0]; 00089 00090 _weights[ 0] = 3.4785484513745385737306394922200e-01L; 00091 _weights[ 1] = 6.5214515486254614262693605077800e-01L; 00092 _weights[ 2] = _weights[1]; 00093 _weights[ 3] = _weights[0]; 00094 00095 return; 00096 } 00097 case EIGHTH: 00098 case NINTH: 00099 { 00100 _points.resize (5); 00101 _weights.resize(5); 00102 00103 _points[ 0](0) = -9.0617984593866399279762687829939e-01L; 00104 _points[ 1](0) = -5.3846931010568309103631442070021e-01L; 00105 _points[ 2](0) = 0.; 00106 _points[ 3] = -_points[1]; 00107 _points[ 4] = -_points[0]; 00108 00109 _weights[ 0] = 2.3692688505618908751426404071992e-01L; 00110 _weights[ 1] = 4.7862867049936646804129151483564e-01L; 00111 _weights[ 2] = 5.6888888888888888888888888888889e-01L; 00112 _weights[ 3] = _weights[1]; 00113 _weights[ 4] = _weights[0]; 00114 00115 return; 00116 } 00117 case TENTH: 00118 case ELEVENTH: 00119 { 00120 _points.resize (6); 00121 _weights.resize(6); 00122 00123 _points[ 0](0) = -9.3246951420315202781230155449399e-01L; 00124 _points[ 1](0) = -6.6120938646626451366139959501991e-01L; 00125 _points[ 2](0) = -2.3861918608319690863050172168071e-01L; 00126 _points[ 3] = -_points[2]; 00127 _points[ 4] = -_points[1]; 00128 _points[ 5] = -_points[0]; 00129 00130 _weights[ 0] = 1.7132449237917034504029614217273e-01L; 00131 _weights[ 1] = 3.6076157304813860756983351383772e-01L; 00132 _weights[ 2] = 4.6791393457269104738987034398955e-01L; 00133 _weights[ 3] = _weights[2]; 00134 _weights[ 4] = _weights[1]; 00135 _weights[ 5] = _weights[0]; 00136 00137 return; 00138 } 00139 case TWELFTH: 00140 case THIRTEENTH: 00141 { 00142 _points.resize (7); 00143 _weights.resize(7); 00144 00145 _points[ 0](0) = -9.4910791234275852452618968404785e-01L; 00146 _points[ 1](0) = -7.4153118559939443986386477328079e-01L; 00147 _points[ 2](0) = -4.0584515137739716690660641207696e-01L; 00148 _points[ 3](0) = 0.; 00149 _points[ 4] = -_points[2]; 00150 _points[ 5] = -_points[1]; 00151 _points[ 6] = -_points[0]; 00152 00153 _weights[ 0] = 1.2948496616886969327061143267908e-01L; 00154 _weights[ 1] = 2.7970539148927666790146777142378e-01L; 00155 _weights[ 2] = 3.8183005050511894495036977548898e-01L; 00156 _weights[ 3] = 4.1795918367346938775510204081633e-01L; 00157 _weights[ 4] = _weights[2]; 00158 _weights[ 5] = _weights[1]; 00159 _weights[ 6] = _weights[0]; 00160 00161 return; 00162 } 00163 case FOURTEENTH: 00164 case FIFTEENTH: 00165 { 00166 _points.resize (8); 00167 _weights.resize(8); 00168 00169 _points[ 0](0) = -9.6028985649753623168356086856947e-01L; 00170 _points[ 1](0) = -7.9666647741362673959155393647583e-01L; 00171 _points[ 2](0) = -5.2553240991632898581773904918925e-01L; 00172 _points[ 3](0) = -1.8343464249564980493947614236018e-01L; 00173 _points[ 4] = -_points[3]; 00174 _points[ 5] = -_points[2]; 00175 _points[ 6] = -_points[1]; 00176 _points[ 7] = -_points[0]; 00177 00178 _weights[ 0] = 1.0122853629037625915253135430996e-01L; 00179 _weights[ 1] = 2.2238103445337447054435599442624e-01L; 00180 _weights[ 2] = 3.1370664587788728733796220198660e-01L; 00181 _weights[ 3] = 3.6268378337836198296515044927720e-01L; 00182 _weights[ 4] = _weights[3]; 00183 _weights[ 5] = _weights[2]; 00184 _weights[ 6] = _weights[1]; 00185 _weights[ 7] = _weights[0]; 00186 00187 return; 00188 } 00189 case SIXTEENTH: 00190 case SEVENTEENTH: 00191 { 00192 _points.resize (9); 00193 _weights.resize(9); 00194 00195 _points[ 0](0) = -9.6816023950762608983557620290367e-01L; 00196 _points[ 1](0) = -8.3603110732663579429942978806973e-01L; 00197 _points[ 2](0) = -6.1337143270059039730870203934147e-01L; 00198 _points[ 3](0) = -3.2425342340380892903853801464334e-01L; 00199 _points[ 4](0) = 0.; 00200 _points[ 5] = -_points[3]; 00201 _points[ 6] = -_points[2]; 00202 _points[ 7] = -_points[1]; 00203 _points[ 8] = -_points[0]; 00204 00205 _weights[ 0] = 8.1274388361574411971892158110524e-02L; 00206 _weights[ 1] = 1.8064816069485740405847203124291e-01L; 00207 _weights[ 2] = 2.6061069640293546231874286941863e-01L; 00208 _weights[ 3] = 3.1234707704000284006863040658444e-01L; 00209 _weights[ 4] = 3.3023935500125976316452506928697e-01L; 00210 _weights[ 5] = _weights[3]; 00211 _weights[ 6] = _weights[2]; 00212 _weights[ 7] = _weights[1]; 00213 _weights[ 8] = _weights[0]; 00214 00215 return; 00216 } 00217 case EIGHTTEENTH: 00218 case NINETEENTH: 00219 { 00220 _points.resize (10); 00221 _weights.resize(10); 00222 00223 _points[ 0](0) = -9.7390652851717172007796401208445e-01L; 00224 _points[ 1](0) = -8.6506336668898451073209668842349e-01L; 00225 _points[ 2](0) = -6.7940956829902440623432736511487e-01L; 00226 _points[ 3](0) = -4.3339539412924719079926594316578e-01L; 00227 _points[ 4](0) = -1.4887433898163121088482600112972e-01L; 00228 _points[ 5] = -_points[4]; 00229 _points[ 6] = -_points[3]; 00230 _points[ 7] = -_points[2]; 00231 _points[ 8] = -_points[1]; 00232 _points[ 9] = -_points[0]; 00233 00234 _weights[ 0] = 6.6671344308688137593568809893332e-02L; 00235 _weights[ 1] = 1.4945134915058059314577633965770e-01L; 00236 _weights[ 2] = 2.1908636251598204399553493422816e-01L; 00237 _weights[ 3] = 2.6926671930999635509122692156947e-01L; 00238 _weights[ 4] = 2.9552422471475287017389299465134e-01L; 00239 _weights[ 5] = _weights[4]; 00240 _weights[ 6] = _weights[3]; 00241 _weights[ 7] = _weights[2]; 00242 _weights[ 8] = _weights[1]; 00243 _weights[ 9] = _weights[0]; 00244 00245 return; 00246 } 00247 00248 case TWENTIETH: 00249 case TWENTYFIRST: 00250 { 00251 _points.resize (11); 00252 _weights.resize(11); 00253 00254 _points[ 0](0) = -9.7822865814605699280393800112286e-01L; 00255 _points[ 1](0) = -8.8706259976809529907515776930393e-01L; 00256 _points[ 2](0) = -7.3015200557404932409341625203115e-01L; 00257 _points[ 3](0) = -5.1909612920681181592572566945861e-01L; 00258 _points[ 4](0) = -2.6954315595234497233153198540086e-01L; 00259 _points[ 5](0) = 0.; 00260 _points[ 6] = -_points[4]; 00261 _points[ 7] = -_points[3]; 00262 _points[ 8] = -_points[2]; 00263 _points[ 9] = -_points[1]; 00264 _points[10] = -_points[0]; 00265 00266 _weights[ 0] = 5.5668567116173666482753720442549e-02L; 00267 _weights[ 1] = 1.2558036946490462463469429922394e-01L; 00268 _weights[ 2] = 1.8629021092773425142609764143166e-01L; 00269 _weights[ 3] = 2.3319376459199047991852370484318e-01L; 00270 _weights[ 4] = 2.6280454451024666218068886989051e-01L; 00271 _weights[ 5] = 2.7292508677790063071448352833634e-01L; 00272 _weights[ 6] = _weights[4]; 00273 _weights[ 7] = _weights[3]; 00274 _weights[ 8] = _weights[2]; 00275 _weights[ 9] = _weights[1]; 00276 _weights[10] = _weights[0]; 00277 00278 return; 00279 } 00280 00281 case TWENTYSECOND: 00282 case TWENTYTHIRD: 00283 { 00284 _points.resize (12); 00285 _weights.resize(12); 00286 00287 _points[ 0](0) = -9.8156063424671925069054909014928e-01L; 00288 _points[ 1](0) = -9.0411725637047485667846586611910e-01L; 00289 _points[ 2](0) = -7.6990267419430468703689383321282e-01L; 00290 _points[ 3](0) = -5.8731795428661744729670241894053e-01L; 00291 _points[ 4](0) = -3.6783149899818019375269153664372e-01L; 00292 _points[ 5](0) = -1.2523340851146891547244136946385e-01L; 00293 _points[ 6] = -_points[5]; 00294 _points[ 7] = -_points[4]; 00295 _points[ 8] = -_points[3]; 00296 _points[ 9] = -_points[2]; 00297 _points[10] = -_points[1]; 00298 _points[11] = -_points[0]; 00299 00300 _weights[ 0] = 4.7175336386511827194615961485017e-02L; 00301 _weights[ 1] = 1.0693932599531843096025471819400e-01L; 00302 _weights[ 2] = 1.6007832854334622633465252954336e-01L; 00303 _weights[ 3] = 2.0316742672306592174906445580980e-01L; 00304 _weights[ 4] = 2.3349253653835480876084989892483e-01L; 00305 _weights[ 5] = 2.4914704581340278500056243604295e-01L; 00306 _weights[ 6] = _weights[5]; 00307 _weights[ 7] = _weights[4]; 00308 _weights[ 8] = _weights[3]; 00309 _weights[ 9] = _weights[2]; 00310 _weights[10] = _weights[1]; 00311 _weights[11] = _weights[0]; 00312 00313 return; 00314 } 00315 00316 case TWENTYFOURTH: 00317 case TWENTYFIFTH: 00318 { 00319 _points.resize (13); 00320 _weights.resize(13); 00321 00322 _points[ 0](0) = -9.8418305471858814947282944880711e-01L; 00323 _points[ 1](0) = -9.1759839922297796520654783650072e-01L; 00324 _points[ 2](0) = -8.0157809073330991279420648958286e-01L; 00325 _points[ 3](0) = -6.4234933944034022064398460699552e-01L; 00326 _points[ 4](0) = -4.4849275103644685287791285212764e-01L; 00327 _points[ 5](0) = -2.3045831595513479406552812109799e-01L; 00328 _points[ 6](0) = 0.; 00329 _points[ 7] = -_points[5]; 00330 _points[ 8] = -_points[4]; 00331 _points[ 9] = -_points[3]; 00332 _points[10] = -_points[2]; 00333 _points[11] = -_points[1]; 00334 _points[12] = -_points[0]; 00335 00336 _weights[ 0] = 4.0484004765315879520021592200986e-02L; 00337 _weights[ 1] = 9.2121499837728447914421775953797e-02L; 00338 _weights[ 2] = 1.3887351021978723846360177686887e-01L; 00339 _weights[ 3] = 1.7814598076194573828004669199610e-01L; 00340 _weights[ 4] = 2.0781604753688850231252321930605e-01L; 00341 _weights[ 5] = 2.2628318026289723841209018603978e-01L; 00342 _weights[ 6] = 2.3255155323087391019458951526884e-01L; 00343 _weights[ 7] = _weights[5]; 00344 _weights[ 8] = _weights[4]; 00345 _weights[ 9] = _weights[3]; 00346 _weights[10] = _weights[2]; 00347 _weights[11] = _weights[1]; 00348 _weights[12] = _weights[0]; 00349 00350 return; 00351 } 00352 00353 case TWENTYSIXTH: 00354 case TWENTYSEVENTH: 00355 { 00356 _points.resize (14); 00357 _weights.resize(14); 00358 00359 _points[ 0](0) = -9.8628380869681233884159726670405e-01L; 00360 _points[ 1](0) = -9.2843488366357351733639113937787e-01L; 00361 _points[ 2](0) = -8.2720131506976499318979474265039e-01L; 00362 _points[ 3](0) = -6.8729290481168547014801980301933e-01L; 00363 _points[ 4](0) = -5.1524863635815409196529071855119e-01L; 00364 _points[ 5](0) = -3.1911236892788976043567182416848e-01L; 00365 _points[ 6](0) = -1.0805494870734366206624465021983e-01L; 00366 _points[ 7] = -_points[6]; 00367 _points[ 8] = -_points[5]; 00368 _points[ 9] = -_points[4]; 00369 _points[10] = -_points[3]; 00370 _points[11] = -_points[2]; 00371 _points[12] = -_points[1]; 00372 _points[13] = -_points[0]; 00373 00374 _weights[ 0] = 3.5119460331751863031832876138192e-02L; 00375 _weights[ 1] = 8.0158087159760209805633277062854e-02L; 00376 _weights[ 2] = 1.2151857068790318468941480907248e-01L; 00377 _weights[ 3] = 1.5720316715819353456960193862384e-01L; 00378 _weights[ 4] = 1.8553839747793781374171659012516e-01L; 00379 _weights[ 5] = 2.0519846372129560396592406566122e-01L; 00380 _weights[ 6] = 2.1526385346315779019587644331626e-01L; 00381 _weights[ 7] = _weights[6]; 00382 _weights[ 8] = _weights[5]; 00383 _weights[ 9] = _weights[4]; 00384 _weights[10] = _weights[3]; 00385 _weights[11] = _weights[2]; 00386 _weights[12] = _weights[1]; 00387 _weights[13] = _weights[0]; 00388 00389 return; 00390 } 00391 00392 case TWENTYEIGHTH: 00393 case TWENTYNINTH: 00394 { 00395 _points.resize (15); 00396 _weights.resize(15); 00397 00398 _points[ 0](0) = -9.8799251802048542848956571858661e-01L; 00399 _points[ 1](0) = -9.3727339240070590430775894771021e-01L; 00400 _points[ 2](0) = -8.4820658341042721620064832077422e-01L; 00401 _points[ 3](0) = -7.2441773136017004741618605461394e-01L; 00402 _points[ 4](0) = -5.7097217260853884753722673725391e-01L; 00403 _points[ 5](0) = -3.9415134707756336989720737098105e-01L; 00404 _points[ 6](0) = -2.0119409399743452230062830339460e-01L; 00405 _points[ 7](0) = 0.; 00406 _points[ 8] = -_points[6]; 00407 _points[ 9] = -_points[5]; 00408 _points[10] = -_points[4]; 00409 _points[11] = -_points[3]; 00410 _points[12] = -_points[2]; 00411 _points[13] = -_points[1]; 00412 _points[14] = -_points[0]; 00413 00414 _weights[ 0] = 3.0753241996117268354628393577204e-02L; 00415 _weights[ 1] = 7.0366047488108124709267416450667e-02L; 00416 _weights[ 2] = 1.0715922046717193501186954668587e-01L; 00417 _weights[ 3] = 1.3957067792615431444780479451103e-01L; 00418 _weights[ 4] = 1.6626920581699393355320086048121e-01L; 00419 _weights[ 5] = 1.8616100001556221102680056186642e-01L; 00420 _weights[ 6] = 1.9843148532711157645611832644384e-01L; 00421 _weights[ 7] = 2.0257824192556127288062019996752e-01L; 00422 _weights[ 8] = _weights[6]; 00423 _weights[ 9] = _weights[5]; 00424 _weights[10] = _weights[4]; 00425 _weights[11] = _weights[3]; 00426 _weights[12] = _weights[2]; 00427 _weights[13] = _weights[1]; 00428 _weights[14] = _weights[0]; 00429 00430 return; 00431 } 00432 00433 case THIRTIETH: 00434 case THIRTYFIRST: 00435 { 00436 _points.resize (16); 00437 _weights.resize(16); 00438 00439 _points[ 0](0) = -9.8940093499164993259615417345033e-01L; 00440 _points[ 1](0) = -9.4457502307323257607798841553461e-01L; 00441 _points[ 2](0) = -8.6563120238783174388046789771239e-01L; 00442 _points[ 3](0) = -7.5540440835500303389510119484744e-01L; 00443 _points[ 4](0) = -6.1787624440264374844667176404879e-01L; 00444 _points[ 5](0) = -4.5801677765722738634241944298358e-01L; 00445 _points[ 6](0) = -2.8160355077925891323046050146050e-01L; 00446 _points[ 7](0) = -9.5012509837637440185319335424958e-02L; 00447 _points[ 8] = -_points[7]; 00448 _points[ 9] = -_points[6]; 00449 _points[10] = -_points[5]; 00450 _points[11] = -_points[4]; 00451 _points[12] = -_points[3]; 00452 _points[13] = -_points[2]; 00453 _points[14] = -_points[1]; 00454 _points[15] = -_points[0]; 00455 00456 _weights[ 0] = 2.7152459411754094851780572456018e-02L; 00457 _weights[ 1] = 6.2253523938647892862843836994378e-02L; 00458 _weights[ 2] = 9.5158511682492784809925107602246e-02L; 00459 _weights[ 3] = 1.2462897125553387205247628219202e-01L; 00460 _weights[ 4] = 1.4959598881657673208150173054748e-01L; 00461 _weights[ 5] = 1.6915651939500253818931207903033e-01L; 00462 _weights[ 6] = 1.8260341504492358886676366796922e-01L; 00463 _weights[ 7] = 1.8945061045506849628539672320828e-01L; 00464 _weights[ 8] = _weights[7]; 00465 _weights[ 9] = _weights[6]; 00466 _weights[10] = _weights[5]; 00467 _weights[11] = _weights[4]; 00468 _weights[12] = _weights[3]; 00469 _weights[13] = _weights[2]; 00470 _weights[14] = _weights[1]; 00471 _weights[15] = _weights[0]; 00472 00473 return; 00474 } 00475 00476 case THIRTYSECOND: 00477 case THIRTYTHIRD: 00478 { 00479 _points.resize (17); 00480 _weights.resize(17); 00481 00482 _points[ 0](0) = -9.9057547531441733567543401994067e-01L; 00483 _points[ 1](0) = -9.5067552176876776122271695789580e-01L; 00484 _points[ 2](0) = -8.8023915372698590212295569448816e-01L; 00485 _points[ 3](0) = -7.8151400389680140692523005552048e-01L; 00486 _points[ 4](0) = -6.5767115921669076585030221664300e-01L; 00487 _points[ 5](0) = -5.1269053708647696788624656862955e-01L; 00488 _points[ 6](0) = -3.5123176345387631529718551709535e-01L; 00489 _points[ 7](0) = -1.7848418149584785585067749365407e-01L; 00490 _points[ 8](0) = 0.; 00491 _points[ 9] = -_points[7]; 00492 _points[10] = -_points[6]; 00493 _points[11] = -_points[5]; 00494 _points[12] = -_points[4]; 00495 _points[13] = -_points[3]; 00496 _points[14] = -_points[2]; 00497 _points[15] = -_points[1]; 00498 _points[16] = -_points[0]; 00499 00500 _weights[ 0] = 2.4148302868547931960110026287565e-02L; 00501 _weights[ 1] = 5.5459529373987201129440165358245e-02L; 00502 _weights[ 2] = 8.5036148317179180883535370191062e-02L; 00503 _weights[ 3] = 1.1188384719340397109478838562636e-01L; 00504 _weights[ 4] = 1.3513636846852547328631998170235e-01L; 00505 _weights[ 5] = 1.5404576107681028808143159480196e-01L; 00506 _weights[ 6] = 1.6800410215645004450997066378832e-01L; 00507 _weights[ 7] = 1.7656270536699264632527099011320e-01L; 00508 _weights[ 8] = 1.7944647035620652545826564426189e-01L; 00509 _weights[ 9] = _weights[7]; 00510 _weights[10] = _weights[6]; 00511 _weights[11] = _weights[5]; 00512 _weights[12] = _weights[4]; 00513 _weights[13] = _weights[3]; 00514 _weights[14] = _weights[2]; 00515 _weights[15] = _weights[1]; 00516 _weights[16] = _weights[0]; 00517 00518 return; 00519 } 00520 00521 case THIRTYFOURTH: 00522 case THIRTYFIFTH: 00523 { 00524 _points.resize (18); 00525 _weights.resize(18); 00526 00527 _points[ 0](0) = -9.9156516842093094673001600470615e-01L; 00528 _points[ 1](0) = -9.5582394957139775518119589292978e-01L; 00529 _points[ 2](0) = -8.9260246649755573920606059112715e-01L; 00530 _points[ 3](0) = -8.0370495897252311568241745501459e-01L; 00531 _points[ 4](0) = -6.9168704306035320787489108128885e-01L; 00532 _points[ 5](0) = -5.5977083107394753460787154852533e-01L; 00533 _points[ 6](0) = -4.1175116146284264603593179383305e-01L; 00534 _points[ 7](0) = -2.5188622569150550958897285487791e-01L; 00535 _points[ 8](0) = -8.4775013041735301242261852935784e-02L; 00536 _points[ 9] = -_points[8]; 00537 _points[10] = -_points[7]; 00538 _points[11] = -_points[6]; 00539 _points[12] = -_points[5]; 00540 _points[13] = -_points[4]; 00541 _points[14] = -_points[3]; 00542 _points[15] = -_points[2]; 00543 _points[16] = -_points[1]; 00544 _points[17] = -_points[0]; 00545 00546 _weights[ 0] = 2.1616013526483310313342710266452e-02L; 00547 _weights[ 1] = 4.9714548894969796453334946202639e-02L; 00548 _weights[ 2] = 7.6425730254889056529129677616637e-02L; 00549 _weights[ 3] = 1.0094204410628716556281398492483e-01L; 00550 _weights[ 4] = 1.2255520671147846018451912680020e-01L; 00551 _weights[ 5] = 1.4064291467065065120473130375195e-01L; 00552 _weights[ 6] = 1.5468467512626524492541800383637e-01L; 00553 _weights[ 7] = 1.6427648374583272298605377646593e-01L; 00554 _weights[ 8] = 1.6914238296314359184065647013499e-01L; 00555 _weights[ 9] = _weights[8]; 00556 _weights[10] = _weights[7]; 00557 _weights[11] = _weights[6]; 00558 _weights[12] = _weights[5]; 00559 _weights[13] = _weights[4]; 00560 _weights[14] = _weights[3]; 00561 _weights[15] = _weights[2]; 00562 _weights[16] = _weights[1]; 00563 _weights[17] = _weights[0]; 00564 00565 return; 00566 } 00567 00568 case THIRTYSIXTH: 00569 case THIRTYSEVENTH: 00570 { 00571 _points.resize (19); 00572 _weights.resize(19); 00573 00574 _points[ 0](0) = -9.9240684384358440318901767025326e-01L; 00575 _points[ 1](0) = -9.6020815213483003085277884068765e-01L; 00576 _points[ 2](0) = -9.0315590361481790164266092853231e-01L; 00577 _points[ 3](0) = -8.2271465653714282497892248671271e-01L; 00578 _points[ 4](0) = -7.2096617733522937861709586082378e-01L; 00579 _points[ 5](0) = -6.0054530466168102346963816494624e-01L; 00580 _points[ 6](0) = -4.6457074137596094571726714810410e-01L; 00581 _points[ 7](0) = -3.1656409996362983199011732884984e-01L; 00582 _points[ 8](0) = -1.6035864564022537586809611574074e-01L; 00583 _points[ 9](0) = 0.; 00584 _points[10] = -_points[8]; 00585 _points[11] = -_points[7]; 00586 _points[12] = -_points[6]; 00587 _points[13] = -_points[5]; 00588 _points[14] = -_points[4]; 00589 _points[15] = -_points[3]; 00590 _points[16] = -_points[2]; 00591 _points[17] = -_points[1]; 00592 _points[18] = -_points[0]; 00593 00594 _weights[ 0] = 1.9461788229726477036312041464438e-02L; 00595 _weights[ 1] = 4.4814226765699600332838157401994e-02L; 00596 _weights[ 2] = 6.9044542737641226580708258006013e-02L; 00597 _weights[ 3] = 9.1490021622449999464462094123840e-02L; 00598 _weights[ 4] = 1.1156664554733399471602390168177e-01L; 00599 _weights[ 5] = 1.2875396253933622767551578485688e-01L; 00600 _weights[ 6] = 1.4260670217360661177574610944190e-01L; 00601 _weights[ 7] = 1.5276604206585966677885540089766e-01L; 00602 _weights[ 8] = 1.5896884339395434764995643946505e-01L; 00603 _weights[ 9] = 1.6105444984878369597916362532092e-01L; 00604 _weights[10] = _weights[8]; 00605 _weights[11] = _weights[7]; 00606 _weights[12] = _weights[6]; 00607 _weights[13] = _weights[5]; 00608 _weights[14] = _weights[4]; 00609 _weights[15] = _weights[3]; 00610 _weights[16] = _weights[2]; 00611 _weights[17] = _weights[1]; 00612 _weights[18] = _weights[0]; 00613 00614 return; 00615 } 00616 00617 case THIRTYEIGHTH: 00618 case THIRTYNINTH: 00619 { 00620 _points.resize (20); 00621 _weights.resize(20); 00622 00623 _points[ 0](0) = -9.9312859918509492478612238847132e-01L; 00624 _points[ 1](0) = -9.6397192727791379126766613119728e-01L; 00625 _points[ 2](0) = -9.1223442825132590586775244120330e-01L; 00626 _points[ 3](0) = -8.3911697182221882339452906170152e-01L; 00627 _points[ 4](0) = -7.4633190646015079261430507035564e-01L; 00628 _points[ 5](0) = -6.3605368072651502545283669622629e-01L; 00629 _points[ 6](0) = -5.1086700195082709800436405095525e-01L; 00630 _points[ 7](0) = -3.7370608871541956067254817702493e-01L; 00631 _points[ 8](0) = -2.2778585114164507808049619536857e-01L; 00632 _points[ 9](0) = -7.6526521133497333754640409398838e-02L; 00633 _points[10] = -_points[9]; 00634 _points[11] = -_points[8]; 00635 _points[12] = -_points[7]; 00636 _points[13] = -_points[6]; 00637 _points[14] = -_points[5]; 00638 _points[15] = -_points[4]; 00639 _points[16] = -_points[3]; 00640 _points[17] = -_points[2]; 00641 _points[18] = -_points[1]; 00642 _points[19] = -_points[0]; 00643 00644 _weights[ 0] = 1.7614007139152118311861962351853e-02L; 00645 _weights[ 1] = 4.0601429800386941331039952274932e-02L; 00646 _weights[ 2] = 6.2672048334109063569506535187042e-02L; 00647 _weights[ 3] = 8.3276741576704748724758143222046e-02L; 00648 _weights[ 4] = 1.0193011981724043503675013548035e-01L; 00649 _weights[ 5] = 1.1819453196151841731237737771138e-01L; 00650 _weights[ 6] = 1.3168863844917662689849449974816e-01L; 00651 _weights[ 7] = 1.4209610931838205132929832506716e-01L; 00652 _weights[ 8] = 1.4917298647260374678782873700197e-01L; 00653 _weights[ 9] = 1.5275338713072585069808433195510e-01L; 00654 _weights[10] = _weights[9]; 00655 _weights[11] = _weights[8]; 00656 _weights[12] = _weights[7]; 00657 _weights[13] = _weights[6]; 00658 _weights[14] = _weights[5]; 00659 _weights[15] = _weights[4]; 00660 _weights[16] = _weights[3]; 00661 _weights[17] = _weights[2]; 00662 _weights[18] = _weights[1]; 00663 _weights[19] = _weights[0]; 00664 00665 return; 00666 } 00667 00668 case FORTIETH: 00669 case FORTYFIRST: 00670 { 00671 _points.resize (21); 00672 _weights.resize(21); 00673 00674 _points[ 0](0) = -9.9375217062038950026024203593794e-01L; 00675 _points[ 1](0) = -9.6722683856630629431662221490770e-01L; 00676 _points[ 2](0) = -9.2009933415040082879018713371497e-01L; 00677 _points[ 3](0) = -8.5336336458331728364725063858757e-01L; 00678 _points[ 4](0) = -7.6843996347567790861587785130623e-01L; 00679 _points[ 5](0) = -6.6713880419741231930596666999034e-01L; 00680 _points[ 6](0) = -5.5161883588721980705901879672431e-01L; 00681 _points[ 7](0) = -4.2434212020743878357366888854379e-01L; 00682 _points[ 8](0) = -2.8802131680240109660079251606460e-01L; 00683 _points[ 9](0) = -1.4556185416089509093703098233869e-01L; 00684 _points[10](0) = 0.; 00685 _points[11] = -_points[9]; 00686 _points[12] = -_points[8]; 00687 _points[13] = -_points[7]; 00688 _points[14] = -_points[6]; 00689 _points[15] = -_points[5]; 00690 _points[16] = -_points[4]; 00691 _points[17] = -_points[3]; 00692 _points[18] = -_points[2]; 00693 _points[19] = -_points[1]; 00694 _points[20] = -_points[0]; 00695 00696 _weights[ 0] = 1.6017228257774333324224616858471e-02L; 00697 _weights[ 1] = 3.6953789770852493799950668299330e-02L; 00698 _weights[ 2] = 5.7134425426857208283635826472448e-02L; 00699 _weights[ 3] = 7.6100113628379302017051653300183e-02L; 00700 _weights[ 4] = 9.3444423456033861553289741113932e-02L; 00701 _weights[ 5] = 1.0879729916714837766347457807011e-01L; 00702 _weights[ 6] = 1.2183141605372853419536717712572e-01L; 00703 _weights[ 7] = 1.3226893863333746178105257449678e-01L; 00704 _weights[ 8] = 1.3988739479107315472213342386758e-01L; 00705 _weights[ 9] = 1.4452440398997005906382716655375e-01L; 00706 _weights[10] = 1.4608113364969042719198514768337e-01L; 00707 _weights[11] = _weights[9]; 00708 _weights[12] = _weights[8]; 00709 _weights[13] = _weights[7]; 00710 _weights[14] = _weights[6]; 00711 _weights[15] = _weights[5]; 00712 _weights[16] = _weights[4]; 00713 _weights[17] = _weights[3]; 00714 _weights[18] = _weights[2]; 00715 _weights[19] = _weights[1]; 00716 _weights[20] = _weights[0]; 00717 00718 return; 00719 } 00720 00721 case FORTYSECOND: 00722 case FORTYTHIRD: 00723 { 00724 _points.resize (22); 00725 _weights.resize(22); 00726 00727 _points[ 0](0) = -9.9429458548239929207303142116130e-01L; 00728 _points[ 1](0) = -9.7006049783542872712395098676527e-01L; 00729 _points[ 2](0) = -9.2695677218717400052069293925905e-01L; 00730 _points[ 3](0) = -8.6581257772030013653642563701938e-01L; 00731 _points[ 4](0) = -7.8781680597920816200427795540835e-01L; 00732 _points[ 5](0) = -6.9448726318668278005068983576226e-01L; 00733 _points[ 6](0) = -5.8764040350691159295887692763865e-01L; 00734 _points[ 7](0) = -4.6935583798675702640633071096641e-01L; 00735 _points[ 8](0) = -3.4193582089208422515814742042738e-01L; 00736 _points[ 9](0) = -2.0786042668822128547884653391955e-01L; 00737 _points[10](0) = -6.9739273319722221213841796118628e-02L; 00738 _points[11] = -_points[10]; 00739 _points[12] = -_points[9]; 00740 _points[13] = -_points[8]; 00741 _points[14] = -_points[7]; 00742 _points[15] = -_points[6]; 00743 _points[16] = -_points[5]; 00744 _points[17] = -_points[4]; 00745 _points[18] = -_points[3]; 00746 _points[19] = -_points[2]; 00747 _points[20] = -_points[1]; 00748 _points[21] = -_points[0]; 00749 00750 _weights[ 0] = 1.4627995298272200684991098047185e-02L; 00751 _weights[ 1] = 3.3774901584814154793302246865913e-02L; 00752 _weights[ 2] = 5.2293335152683285940312051273211e-02L; 00753 _weights[ 3] = 6.9796468424520488094961418930218e-02L; 00754 _weights[ 4] = 8.5941606217067727414443681372703e-02L; 00755 _weights[ 5] = 1.0041414444288096493207883783054e-01L; 00756 _weights[ 6] = 1.1293229608053921839340060742175e-01L; 00757 _weights[ 7] = 1.2325237681051242428556098615481e-01L; 00758 _weights[ 8] = 1.3117350478706237073296499253031e-01L; 00759 _weights[ 9] = 1.3654149834601517135257383123152e-01L; 00760 _weights[10] = 1.3925187285563199337541024834181e-01L; 00761 _weights[11] = _weights[10]; 00762 _weights[12] = _weights[9]; 00763 _weights[13] = _weights[8]; 00764 _weights[14] = _weights[7]; 00765 _weights[15] = _weights[6]; 00766 _weights[16] = _weights[5]; 00767 _weights[17] = _weights[4]; 00768 _weights[18] = _weights[3]; 00769 _weights[19] = _weights[2]; 00770 _weights[20] = _weights[1]; 00771 _weights[21] = _weights[0]; 00772 00773 return; 00774 } 00775 00776 00777 default: 00778 libmesh_error_msg("Quadrature rule " << _order << " not supported!"); 00779 } 00780 } 00781 00782 } // namespace libMesh
generated by
