Line data    Source code

       1             : // The libMesh Finite Element Library.
       2             : // Copyright (C) 2002-2026 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
       3             : 
       4             : // This library is free software; you can redistribute it and/or
       5             : // modify it under the terms of the GNU Lesser General Public
       6             : // License as published by the Free Software Foundation; either
       7             : // version 2.1 of the License, or (at your option) any later version.
       8             : 
       9             : // This library is distributed in the hope that it will be useful,
      10             : // but WITHOUT ANY WARRANTY; without even the implied warranty of
      11             : // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
      12             : // Lesser General Public License for more details.
      13             : 
      14             : // You should have received a copy of the GNU Lesser General Public
      15             : // License along with this library; if not, write to the Free Software
      16             : // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
      17             : 
      18             : 
      19             : 
      20             : // C++ includes
      21             : 
      22             : // Local includes
      23             : #include "libmesh/quadrature_gauss.h"
      24             : 
      25             : namespace libMesh
      26             : {
      27             : 
      28             : 
      29             : 
      30      928058 : void QGauss::init_1D()
      31             : {
      32             :   //----------------------------------------------------------------------
      33             :   // 1D quadrature rules
      34     1208131 :   switch(get_order())
      35             :     {
      36       14686 :     case CONSTANT:
      37             :     case FIRST:
      38             :       {
      39       14686 :         _points.resize (1);
      40       14686 :         _weights.resize(1);
      41             : 
      42       14686 :         _points[0](0)  = 0.;
      43             : 
      44       14686 :         _weights[0]    = 2.;
      45             : 
      46       14686 :         return;
      47             :       }
      48      329428 :     case SECOND:
      49             :     case THIRD:
      50             :       {
      51      329428 :         _points.resize (2);
      52      329428 :         _weights.resize(2);
      53             : 
      54      329428 :         _points[0](0) = -std::sqrt(Real(3))/3;
      55      329428 :         _points[1]    = -_points[0];
      56             : 
      57      329428 :         _weights[0]   = 1.;
      58      329428 :         _weights[1]   = _weights[0];
      59             : 
      60      329428 :         return;
      61             :       }
      62      204229 :     case FOURTH:
      63             :     case FIFTH:
      64             :       {
      65      204229 :         _points.resize (3);
      66      204229 :         _weights.resize(3);
      67             : 
      68      204229 :         _points[ 0](0) = -7.7459666924148337703585307995648e-01_R;
      69      204229 :         _points[ 1](0) = 0.;
      70      204229 :         _points[ 2]    = -_points[0];
      71             : 
      72      204229 :         _weights[ 0]   = Real(5)/9;
      73      204229 :         _weights[ 1]   = Real(8)/9;
      74      204229 :         _weights[ 2]   = _weights[0];
      75             : 
      76      204229 :         return;
      77             :       }
      78      286974 :     case SIXTH:
      79             :     case SEVENTH:
      80             :       {
      81      286974 :         _points.resize (4);
      82      286974 :         _weights.resize(4);
      83             : 
      84      286974 :         _points[ 0](0) = -8.6113631159405257522394648889281e-01_R;
      85      286974 :         _points[ 1](0) = -3.3998104358485626480266575910324e-01_R;
      86      286974 :         _points[ 2]    = -_points[1];
      87      286974 :         _points[ 3]    = -_points[0];
      88             : 
      89      286974 :         _weights[ 0]   = 3.4785484513745385737306394922200e-01_R;
      90      286974 :         _weights[ 1]   = 6.5214515486254614262693605077800e-01_R;
      91      286974 :         _weights[ 2]   = _weights[1];
      92      286974 :         _weights[ 3]   = _weights[0];
      93             : 
      94      286974 :         return;
      95             :       }
      96       52694 :     case EIGHTH:
      97             :     case NINTH:
      98             :       {
      99       52694 :         _points.resize (5);
     100       52694 :         _weights.resize(5);
     101             : 
     102       52694 :         _points[ 0](0) = -9.0617984593866399279762687829939e-01_R;
     103       52694 :         _points[ 1](0) = -5.3846931010568309103631442070021e-01_R;
     104       52694 :         _points[ 2](0) = 0.;
     105       52694 :         _points[ 3]    = -_points[1];
     106       52694 :         _points[ 4]    = -_points[0];
     107             : 
     108       52694 :         _weights[ 0]   = 2.3692688505618908751426404071992e-01_R;
     109       52694 :         _weights[ 1]   = 4.7862867049936646804129151483564e-01_R;
     110       52694 :         _weights[ 2]   = 5.6888888888888888888888888888889e-01_R;
     111       52694 :         _weights[ 3]   = _weights[1];
     112       52694 :         _weights[ 4]   = _weights[0];
     113             : 
     114       52694 :         return;
     115             :       }
     116        9645 :     case TENTH:
     117             :     case ELEVENTH:
     118             :       {
     119        9645 :         _points.resize (6);
     120        9645 :         _weights.resize(6);
     121             : 
     122        9645 :         _points[ 0](0) = -9.3246951420315202781230155449399e-01_R;
     123        9645 :         _points[ 1](0) = -6.6120938646626451366139959501991e-01_R;
     124        9645 :         _points[ 2](0) = -2.3861918608319690863050172168071e-01_R;
     125        9645 :         _points[ 3]    = -_points[2];
     126        9645 :         _points[ 4]    = -_points[1];
     127        9645 :         _points[ 5]    = -_points[0];
     128             : 
     129        9645 :         _weights[ 0]   = 1.7132449237917034504029614217273e-01_R;
     130        9645 :         _weights[ 1]   = 3.6076157304813860756983351383772e-01_R;
     131        9645 :         _weights[ 2]   = 4.6791393457269104738987034398955e-01_R;
     132        9645 :         _weights[ 3]   = _weights[2];
     133        9645 :         _weights[ 4]   = _weights[1];
     134        9645 :         _weights[ 5]   = _weights[0];
     135             : 
     136        9645 :         return;
     137             :       }
     138         474 :     case TWELFTH:
     139             :     case THIRTEENTH:
     140             :       {
     141         474 :         _points.resize (7);
     142         474 :         _weights.resize(7);
     143             : 
     144         474 :         _points[ 0](0) = -9.4910791234275852452618968404785e-01_R;
     145         474 :         _points[ 1](0) = -7.4153118559939443986386477328079e-01_R;
     146         474 :         _points[ 2](0) = -4.0584515137739716690660641207696e-01_R;
     147         474 :         _points[ 3](0) = 0.;
     148         474 :         _points[ 4]    = -_points[2];
     149         474 :         _points[ 5]    = -_points[1];
     150         474 :         _points[ 6]    = -_points[0];
     151             : 
     152         474 :         _weights[ 0]   = 1.2948496616886969327061143267908e-01_R;
     153         474 :         _weights[ 1]   = 2.7970539148927666790146777142378e-01_R;
     154         474 :         _weights[ 2]   = 3.8183005050511894495036977548898e-01_R;
     155         474 :         _weights[ 3]   = 4.1795918367346938775510204081633e-01_R;
     156         474 :         _weights[ 4]   = _weights[2];
     157         474 :         _weights[ 5]   = _weights[1];
     158         474 :         _weights[ 6]   = _weights[0];
     159             : 
     160         474 :         return;
     161             :       }
     162         317 :     case FOURTEENTH:
     163             :     case FIFTEENTH:
     164             :       {
     165         317 :         _points.resize (8);
     166         317 :         _weights.resize(8);
     167             : 
     168         317 :         _points[ 0](0) = -9.6028985649753623168356086856947e-01_R;
     169         317 :         _points[ 1](0) = -7.9666647741362673959155393647583e-01_R;
     170         317 :         _points[ 2](0) = -5.2553240991632898581773904918925e-01_R;
     171         317 :         _points[ 3](0) = -1.8343464249564980493947614236018e-01_R;
     172         317 :         _points[ 4]    = -_points[3];
     173         317 :         _points[ 5]    = -_points[2];
     174         317 :         _points[ 6]    = -_points[1];
     175         317 :         _points[ 7]    = -_points[0];
     176             : 
     177         317 :         _weights[ 0]   = 1.0122853629037625915253135430996e-01_R;
     178         317 :         _weights[ 1]   = 2.2238103445337447054435599442624e-01_R;
     179         317 :         _weights[ 2]   = 3.1370664587788728733796220198660e-01_R;
     180         317 :         _weights[ 3]   = 3.6268378337836198296515044927720e-01_R;
     181         317 :         _weights[ 4]   = _weights[3];
     182         317 :         _weights[ 5]   = _weights[2];
     183         317 :         _weights[ 6]   = _weights[1];
     184         317 :         _weights[ 7]   = _weights[0];
     185             : 
     186         317 :         return;
     187             :       }
     188         266 :     case SIXTEENTH:
     189             :     case SEVENTEENTH:
     190             :       {
     191         266 :         _points.resize (9);
     192         266 :         _weights.resize(9);
     193             : 
     194         266 :         _points[ 0](0) = -9.6816023950762608983557620290367e-01_R;
     195         266 :         _points[ 1](0) = -8.3603110732663579429942978806973e-01_R;
     196         266 :         _points[ 2](0) = -6.1337143270059039730870203934147e-01_R;
     197         266 :         _points[ 3](0) = -3.2425342340380892903853801464334e-01_R;
     198         266 :         _points[ 4](0) = 0.;
     199         266 :         _points[ 5]    = -_points[3];
     200         266 :         _points[ 6]    = -_points[2];
     201         266 :         _points[ 7]    = -_points[1];
     202         266 :         _points[ 8]    = -_points[0];
     203             : 
     204         266 :         _weights[ 0]   = 8.1274388361574411971892158110524e-02_R;
     205         266 :         _weights[ 1]   = 1.8064816069485740405847203124291e-01_R;
     206         266 :         _weights[ 2]   = 2.6061069640293546231874286941863e-01_R;
     207         266 :         _weights[ 3]   = 3.1234707704000284006863040658444e-01_R;
     208         266 :         _weights[ 4]   = 3.3023935500125976316452506928697e-01_R;
     209         266 :         _weights[ 5]   = _weights[3];
     210         266 :         _weights[ 6]   = _weights[2];
     211         266 :         _weights[ 7]   = _weights[1];
     212         266 :         _weights[ 8]   = _weights[0];
     213             : 
     214         266 :         return;
     215             :       }
     216         150 :     case EIGHTTEENTH:
     217             :     case NINETEENTH:
     218             :       {
     219         150 :         _points.resize (10);
     220         150 :         _weights.resize(10);
     221             : 
     222         150 :         _points[ 0](0) = -9.7390652851717172007796401208445e-01_R;
     223         150 :         _points[ 1](0) = -8.6506336668898451073209668842349e-01_R;
     224         150 :         _points[ 2](0) = -6.7940956829902440623432736511487e-01_R;
     225         150 :         _points[ 3](0) = -4.3339539412924719079926594316578e-01_R;
     226         150 :         _points[ 4](0) = -1.4887433898163121088482600112972e-01_R;
     227         150 :         _points[ 5]    = -_points[4];
     228         150 :         _points[ 6]    = -_points[3];
     229         150 :         _points[ 7]    = -_points[2];
     230         150 :         _points[ 8]    = -_points[1];
     231         150 :         _points[ 9]    = -_points[0];
     232             : 
     233         150 :         _weights[ 0]   = 6.6671344308688137593568809893332e-02_R;
     234         150 :         _weights[ 1]   = 1.4945134915058059314577633965770e-01_R;
     235         150 :         _weights[ 2]   = 2.1908636251598204399553493422816e-01_R;
     236         150 :         _weights[ 3]   = 2.6926671930999635509122692156947e-01_R;
     237         150 :         _weights[ 4]   = 2.9552422471475287017389299465134e-01_R;
     238         150 :         _weights[ 5]   = _weights[4];
     239         150 :         _weights[ 6]   = _weights[3];
     240         150 :         _weights[ 7]   = _weights[2];
     241         150 :         _weights[ 8]   = _weights[1];
     242         150 :         _weights[ 9]   = _weights[0];
     243             : 
     244         150 :         return;
     245             :       }
     246             : 
     247          63 :     case TWENTIETH:
     248             :     case TWENTYFIRST:
     249             :       {
     250          63 :         _points.resize (11);
     251          63 :         _weights.resize(11);
     252             : 
     253          63 :         _points[ 0](0) = -9.7822865814605699280393800112286e-01_R;
     254          63 :         _points[ 1](0) = -8.8706259976809529907515776930393e-01_R;
     255          63 :         _points[ 2](0) = -7.3015200557404932409341625203115e-01_R;
     256          63 :         _points[ 3](0) = -5.1909612920681181592572566945861e-01_R;
     257          63 :         _points[ 4](0) = -2.6954315595234497233153198540086e-01_R;
     258          63 :         _points[ 5](0) = 0.;
     259          63 :         _points[ 6]    = -_points[4];
     260          63 :         _points[ 7]    = -_points[3];
     261          63 :         _points[ 8]    = -_points[2];
     262          63 :         _points[ 9]    = -_points[1];
     263          63 :         _points[10]    = -_points[0];
     264             : 
     265          63 :         _weights[ 0]   = 5.5668567116173666482753720442549e-02_R;
     266          63 :         _weights[ 1]   = 1.2558036946490462463469429922394e-01_R;
     267          63 :         _weights[ 2]   = 1.8629021092773425142609764143166e-01_R;
     268          63 :         _weights[ 3]   = 2.3319376459199047991852370484318e-01_R;
     269          63 :         _weights[ 4]   = 2.6280454451024666218068886989051e-01_R;
     270          63 :         _weights[ 5]   = 2.7292508677790063071448352833634e-01_R;
     271          63 :         _weights[ 6]   = _weights[4];
     272          63 :         _weights[ 7]   = _weights[3];
     273          63 :         _weights[ 8]   = _weights[2];
     274          63 :         _weights[ 9]   = _weights[1];
     275          63 :         _weights[10]   = _weights[0];
     276             : 
     277          63 :         return;
     278             :       }
     279             : 
     280       28992 :     case TWENTYSECOND:
     281             :     case TWENTYTHIRD:
     282             :       {
     283       28992 :         _points.resize (12);
     284       28992 :         _weights.resize(12);
     285             : 
     286       28992 :         _points[ 0](0) = -9.8156063424671925069054909014928e-01_R;
     287       28992 :         _points[ 1](0) = -9.0411725637047485667846586611910e-01_R;
     288       28992 :         _points[ 2](0) = -7.6990267419430468703689383321282e-01_R;
     289       28992 :         _points[ 3](0) = -5.8731795428661744729670241894053e-01_R;
     290       28992 :         _points[ 4](0) = -3.6783149899818019375269153664372e-01_R;
     291       28992 :         _points[ 5](0) = -1.2523340851146891547244136946385e-01_R;
     292       28992 :         _points[ 6]    = -_points[5];
     293       28992 :         _points[ 7]    = -_points[4];
     294       28992 :         _points[ 8]    = -_points[3];
     295       28992 :         _points[ 9]    = -_points[2];
     296       28992 :         _points[10]    = -_points[1];
     297       28992 :         _points[11]    = -_points[0];
     298             : 
     299       28992 :         _weights[ 0]   = 4.7175336386511827194615961485017e-02_R;
     300       28992 :         _weights[ 1]   = 1.0693932599531843096025471819400e-01_R;
     301       28992 :         _weights[ 2]   = 1.6007832854334622633465252954336e-01_R;
     302       28992 :         _weights[ 3]   = 2.0316742672306592174906445580980e-01_R;
     303       28992 :         _weights[ 4]   = 2.3349253653835480876084989892483e-01_R;
     304       28992 :         _weights[ 5]   = 2.4914704581340278500056243604295e-01_R;
     305       28992 :         _weights[ 6]   = _weights[5];
     306       28992 :         _weights[ 7]   = _weights[4];
     307       28992 :         _weights[ 8]   = _weights[3];
     308       28992 :         _weights[ 9]   = _weights[2];
     309       28992 :         _weights[10]   = _weights[1];
     310       28992 :         _weights[11]   = _weights[0];
     311             : 
     312       28992 :         return;
     313             :       }
     314             : 
     315          14 :     case TWENTYFOURTH:
     316             :     case TWENTYFIFTH:
     317             :       {
     318          14 :         _points.resize (13);
     319          14 :         _weights.resize(13);
     320             : 
     321          14 :         _points[ 0](0) = -9.8418305471858814947282944880711e-01_R;
     322          14 :         _points[ 1](0) = -9.1759839922297796520654783650072e-01_R;
     323          14 :         _points[ 2](0) = -8.0157809073330991279420648958286e-01_R;
     324          14 :         _points[ 3](0) = -6.4234933944034022064398460699552e-01_R;
     325          14 :         _points[ 4](0) = -4.4849275103644685287791285212764e-01_R;
     326          14 :         _points[ 5](0) = -2.3045831595513479406552812109799e-01_R;
     327          14 :         _points[ 6](0) = 0.;
     328          14 :         _points[ 7]    = -_points[5];
     329          14 :         _points[ 8]    = -_points[4];
     330          14 :         _points[ 9]    = -_points[3];
     331          14 :         _points[10]    = -_points[2];
     332          14 :         _points[11]    = -_points[1];
     333          14 :         _points[12]    = -_points[0];
     334             : 
     335          14 :         _weights[ 0]   = 4.0484004765315879520021592200986e-02_R;
     336          14 :         _weights[ 1]   = 9.2121499837728447914421775953797e-02_R;
     337          14 :         _weights[ 2]   = 1.3887351021978723846360177686887e-01_R;
     338          14 :         _weights[ 3]   = 1.7814598076194573828004669199610e-01_R;
     339          14 :         _weights[ 4]   = 2.0781604753688850231252321930605e-01_R;
     340          14 :         _weights[ 5]   = 2.2628318026289723841209018603978e-01_R;
     341          14 :         _weights[ 6]   = 2.3255155323087391019458951526884e-01_R;
     342          14 :         _weights[ 7]   = _weights[5];
     343          14 :         _weights[ 8]   = _weights[4];
     344          14 :         _weights[ 9]   = _weights[3];
     345          14 :         _weights[10]   = _weights[2];
     346          14 :         _weights[11]   = _weights[1];
     347          14 :         _weights[12]   = _weights[0];
     348             : 
     349          14 :         return;
     350             :       }
     351             : 
     352          14 :     case TWENTYSIXTH:
     353             :     case TWENTYSEVENTH:
     354             :       {
     355          14 :         _points.resize (14);
     356          14 :         _weights.resize(14);
     357             : 
     358          14 :         _points[ 0](0) = -9.8628380869681233884159726670405e-01_R;
     359          14 :         _points[ 1](0) = -9.2843488366357351733639113937787e-01_R;
     360          14 :         _points[ 2](0) = -8.2720131506976499318979474265039e-01_R;
     361          14 :         _points[ 3](0) = -6.8729290481168547014801980301933e-01_R;
     362          14 :         _points[ 4](0) = -5.1524863635815409196529071855119e-01_R;
     363          14 :         _points[ 5](0) = -3.1911236892788976043567182416848e-01_R;
     364          14 :         _points[ 6](0) = -1.0805494870734366206624465021983e-01_R;
     365          14 :         _points[ 7]    = -_points[6];
     366          14 :         _points[ 8]    = -_points[5];
     367          14 :         _points[ 9]    = -_points[4];
     368          14 :         _points[10]    = -_points[3];
     369          14 :         _points[11]    = -_points[2];
     370          14 :         _points[12]    = -_points[1];
     371          14 :         _points[13]    = -_points[0];
     372             : 
     373          14 :         _weights[ 0]   = 3.5119460331751863031832876138192e-02_R;
     374          14 :         _weights[ 1]   = 8.0158087159760209805633277062854e-02_R;
     375          14 :         _weights[ 2]   = 1.2151857068790318468941480907248e-01_R;
     376          14 :         _weights[ 3]   = 1.5720316715819353456960193862384e-01_R;
     377          14 :         _weights[ 4]   = 1.8553839747793781374171659012516e-01_R;
     378          14 :         _weights[ 5]   = 2.0519846372129560396592406566122e-01_R;
     379          14 :         _weights[ 6]   = 2.1526385346315779019587644331626e-01_R;
     380          14 :         _weights[ 7]   = _weights[6];
     381          14 :         _weights[ 8]   = _weights[5];
     382          14 :         _weights[ 9]   = _weights[4];
     383          14 :         _weights[10]   = _weights[3];
     384          14 :         _weights[11]   = _weights[2];
     385          14 :         _weights[12]   = _weights[1];
     386          14 :         _weights[13]   = _weights[0];
     387             : 
     388          14 :         return;
     389             :       }
     390             : 
     391          14 :     case TWENTYEIGHTH:
     392             :     case TWENTYNINTH:
     393             :       {
     394          14 :         _points.resize (15);
     395          14 :         _weights.resize(15);
     396             : 
     397          14 :         _points[ 0](0) = -9.8799251802048542848956571858661e-01_R;
     398          14 :         _points[ 1](0) = -9.3727339240070590430775894771021e-01_R;
     399          14 :         _points[ 2](0) = -8.4820658341042721620064832077422e-01_R;
     400          14 :         _points[ 3](0) = -7.2441773136017004741618605461394e-01_R;
     401          14 :         _points[ 4](0) = -5.7097217260853884753722673725391e-01_R;
     402          14 :         _points[ 5](0) = -3.9415134707756336989720737098105e-01_R;
     403          14 :         _points[ 6](0) = -2.0119409399743452230062830339460e-01_R;
     404          14 :         _points[ 7](0) = 0.;
     405          14 :         _points[ 8]    = -_points[6];
     406          14 :         _points[ 9]    = -_points[5];
     407          14 :         _points[10]    = -_points[4];
     408          14 :         _points[11]    = -_points[3];
     409          14 :         _points[12]    = -_points[2];
     410          14 :         _points[13]    = -_points[1];
     411          14 :         _points[14]    = -_points[0];
     412             : 
     413          14 :         _weights[ 0]   = 3.0753241996117268354628393577204e-02_R;
     414          14 :         _weights[ 1]   = 7.0366047488108124709267416450667e-02_R;
     415          14 :         _weights[ 2]   = 1.0715922046717193501186954668587e-01_R;
     416          14 :         _weights[ 3]   = 1.3957067792615431444780479451103e-01_R;
     417          14 :         _weights[ 4]   = 1.6626920581699393355320086048121e-01_R;
     418          14 :         _weights[ 5]   = 1.8616100001556221102680056186642e-01_R;
     419          14 :         _weights[ 6]   = 1.9843148532711157645611832644384e-01_R;
     420          14 :         _weights[ 7]   = 2.0257824192556127288062019996752e-01_R;
     421          14 :         _weights[ 8]   = _weights[6];
     422          14 :         _weights[ 9]   = _weights[5];
     423          14 :         _weights[10]   = _weights[4];
     424          14 :         _weights[11]   = _weights[3];
     425          14 :         _weights[12]   = _weights[2];
     426          14 :         _weights[13]   = _weights[1];
     427          14 :         _weights[14]   = _weights[0];
     428             : 
     429          14 :         return;
     430             :       }
     431             : 
     432          14 :     case THIRTIETH:
     433             :     case THIRTYFIRST:
     434             :       {
     435          14 :         _points.resize (16);
     436          14 :         _weights.resize(16);
     437             : 
     438          14 :         _points[ 0](0) = -9.8940093499164993259615417345033e-01_R;
     439          14 :         _points[ 1](0) = -9.4457502307323257607798841553461e-01_R;
     440          14 :         _points[ 2](0) = -8.6563120238783174388046789771239e-01_R;
     441          14 :         _points[ 3](0) = -7.5540440835500303389510119484744e-01_R;
     442          14 :         _points[ 4](0) = -6.1787624440264374844667176404879e-01_R;
     443          14 :         _points[ 5](0) = -4.5801677765722738634241944298358e-01_R;
     444          14 :         _points[ 6](0) = -2.8160355077925891323046050146050e-01_R;
     445          14 :         _points[ 7](0) = -9.5012509837637440185319335424958e-02_R;
     446          14 :         _points[ 8]    = -_points[7];
     447          14 :         _points[ 9]    = -_points[6];
     448          14 :         _points[10]    = -_points[5];
     449          14 :         _points[11]    = -_points[4];
     450          14 :         _points[12]    = -_points[3];
     451          14 :         _points[13]    = -_points[2];
     452          14 :         _points[14]    = -_points[1];
     453          14 :         _points[15]    = -_points[0];
     454             : 
     455          14 :         _weights[ 0]   = 2.7152459411754094851780572456018e-02_R;
     456          14 :         _weights[ 1]   = 6.2253523938647892862843836994378e-02_R;
     457          14 :         _weights[ 2]   = 9.5158511682492784809925107602246e-02_R;
     458          14 :         _weights[ 3]   = 1.2462897125553387205247628219202e-01_R;
     459          14 :         _weights[ 4]   = 1.4959598881657673208150173054748e-01_R;
     460          14 :         _weights[ 5]   = 1.6915651939500253818931207903033e-01_R;
     461          14 :         _weights[ 6]   = 1.8260341504492358886676366796922e-01_R;
     462          14 :         _weights[ 7]   = 1.8945061045506849628539672320828e-01_R;
     463          14 :         _weights[ 8]   = _weights[7];
     464          14 :         _weights[ 9]   = _weights[6];
     465          14 :         _weights[10]   = _weights[5];
     466          14 :         _weights[11]   = _weights[4];
     467          14 :         _weights[12]   = _weights[3];
     468          14 :         _weights[13]   = _weights[2];
     469          14 :         _weights[14]   = _weights[1];
     470          14 :         _weights[15]   = _weights[0];
     471             : 
     472          14 :         return;
     473             :       }
     474             : 
     475          14 :     case THIRTYSECOND:
     476             :     case THIRTYTHIRD:
     477             :       {
     478          14 :         _points.resize (17);
     479          14 :         _weights.resize(17);
     480             : 
     481          14 :         _points[ 0](0) = -9.9057547531441733567543401994067e-01_R;
     482          14 :         _points[ 1](0) = -9.5067552176876776122271695789580e-01_R;
     483          14 :         _points[ 2](0) = -8.8023915372698590212295569448816e-01_R;
     484          14 :         _points[ 3](0) = -7.8151400389680140692523005552048e-01_R;
     485          14 :         _points[ 4](0) = -6.5767115921669076585030221664300e-01_R;
     486          14 :         _points[ 5](0) = -5.1269053708647696788624656862955e-01_R;
     487          14 :         _points[ 6](0) = -3.5123176345387631529718551709535e-01_R;
     488          14 :         _points[ 7](0) = -1.7848418149584785585067749365407e-01_R;
     489          14 :         _points[ 8](0) = 0.;
     490          14 :         _points[ 9]    = -_points[7];
     491          14 :         _points[10]    = -_points[6];
     492          14 :         _points[11]    = -_points[5];
     493          14 :         _points[12]    = -_points[4];
     494          14 :         _points[13]    = -_points[3];
     495          14 :         _points[14]    = -_points[2];
     496          14 :         _points[15]    = -_points[1];
     497          14 :         _points[16]    = -_points[0];
     498             : 
     499          14 :         _weights[ 0]   = 2.4148302868547931960110026287565e-02_R;
     500          14 :         _weights[ 1]   = 5.5459529373987201129440165358245e-02_R;
     501          14 :         _weights[ 2]   = 8.5036148317179180883535370191062e-02_R;
     502          14 :         _weights[ 3]   = 1.1188384719340397109478838562636e-01_R;
     503          14 :         _weights[ 4]   = 1.3513636846852547328631998170235e-01_R;
     504          14 :         _weights[ 5]   = 1.5404576107681028808143159480196e-01_R;
     505          14 :         _weights[ 6]   = 1.6800410215645004450997066378832e-01_R;
     506          14 :         _weights[ 7]   = 1.7656270536699264632527099011320e-01_R;
     507          14 :         _weights[ 8]   = 1.7944647035620652545826564426189e-01_R;
     508          14 :         _weights[ 9]   = _weights[7];
     509          14 :         _weights[10]   = _weights[6];
     510          14 :         _weights[11]   = _weights[5];
     511          14 :         _weights[12]   = _weights[4];
     512          14 :         _weights[13]   = _weights[3];
     513          14 :         _weights[14]   = _weights[2];
     514          14 :         _weights[15]   = _weights[1];
     515          14 :         _weights[16]   = _weights[0];
     516             : 
     517          14 :         return;
     518             :       }
     519             : 
     520          14 :     case THIRTYFOURTH:
     521             :     case THIRTYFIFTH:
     522             :       {
     523          14 :         _points.resize (18);
     524          14 :         _weights.resize(18);
     525             : 
     526          14 :         _points[ 0](0) = -9.9156516842093094673001600470615e-01_R;
     527          14 :         _points[ 1](0) = -9.5582394957139775518119589292978e-01_R;
     528          14 :         _points[ 2](0) = -8.9260246649755573920606059112715e-01_R;
     529          14 :         _points[ 3](0) = -8.0370495897252311568241745501459e-01_R;
     530          14 :         _points[ 4](0) = -6.9168704306035320787489108128885e-01_R;
     531          14 :         _points[ 5](0) = -5.5977083107394753460787154852533e-01_R;
     532          14 :         _points[ 6](0) = -4.1175116146284264603593179383305e-01_R;
     533          14 :         _points[ 7](0) = -2.5188622569150550958897285487791e-01_R;
     534          14 :         _points[ 8](0) = -8.4775013041735301242261852935784e-02_R;
     535          14 :         _points[ 9]    = -_points[8];
     536          14 :         _points[10]    = -_points[7];
     537          14 :         _points[11]    = -_points[6];
     538          14 :         _points[12]    = -_points[5];
     539          14 :         _points[13]    = -_points[4];
     540          14 :         _points[14]    = -_points[3];
     541          14 :         _points[15]    = -_points[2];
     542          14 :         _points[16]    = -_points[1];
     543          14 :         _points[17]    = -_points[0];
     544             : 
     545          14 :         _weights[ 0]   = 2.1616013526483310313342710266452e-02_R;
     546          14 :         _weights[ 1]   = 4.9714548894969796453334946202639e-02_R;
     547          14 :         _weights[ 2]   = 7.6425730254889056529129677616637e-02_R;
     548          14 :         _weights[ 3]   = 1.0094204410628716556281398492483e-01_R;
     549          14 :         _weights[ 4]   = 1.2255520671147846018451912680020e-01_R;
     550          14 :         _weights[ 5]   = 1.4064291467065065120473130375195e-01_R;
     551          14 :         _weights[ 6]   = 1.5468467512626524492541800383637e-01_R;
     552          14 :         _weights[ 7]   = 1.6427648374583272298605377646593e-01_R;
     553          14 :         _weights[ 8]   = 1.6914238296314359184065647013499e-01_R;
     554          14 :         _weights[ 9]   = _weights[8];
     555          14 :         _weights[10]   = _weights[7];
     556          14 :         _weights[11]   = _weights[6];
     557          14 :         _weights[12]   = _weights[5];
     558          14 :         _weights[13]   = _weights[4];
     559          14 :         _weights[14]   = _weights[3];
     560          14 :         _weights[15]   = _weights[2];
     561          14 :         _weights[16]   = _weights[1];
     562          14 :         _weights[17]   = _weights[0];
     563             : 
     564          14 :         return;
     565             :       }
     566             : 
     567          14 :     case THIRTYSIXTH:
     568             :     case THIRTYSEVENTH:
     569             :       {
     570          14 :         _points.resize (19);
     571          14 :         _weights.resize(19);
     572             : 
     573          14 :         _points[ 0](0) = -9.9240684384358440318901767025326e-01_R;
     574          14 :         _points[ 1](0) = -9.6020815213483003085277884068765e-01_R;
     575          14 :         _points[ 2](0) = -9.0315590361481790164266092853231e-01_R;
     576          14 :         _points[ 3](0) = -8.2271465653714282497892248671271e-01_R;
     577          14 :         _points[ 4](0) = -7.2096617733522937861709586082378e-01_R;
     578          14 :         _points[ 5](0) = -6.0054530466168102346963816494624e-01_R;
     579          14 :         _points[ 6](0) = -4.6457074137596094571726714810410e-01_R;
     580          14 :         _points[ 7](0) = -3.1656409996362983199011732884984e-01_R;
     581          14 :         _points[ 8](0) = -1.6035864564022537586809611574074e-01_R;
     582          14 :         _points[ 9](0) = 0.;
     583          14 :         _points[10]    = -_points[8];
     584          14 :         _points[11]    = -_points[7];
     585          14 :         _points[12]    = -_points[6];
     586          14 :         _points[13]    = -_points[5];
     587          14 :         _points[14]    = -_points[4];
     588          14 :         _points[15]    = -_points[3];
     589          14 :         _points[16]    = -_points[2];
     590          14 :         _points[17]    = -_points[1];
     591          14 :         _points[18]    = -_points[0];
     592             : 
     593          14 :         _weights[ 0]   = 1.9461788229726477036312041464438e-02_R;
     594          14 :         _weights[ 1]   = 4.4814226765699600332838157401994e-02_R;
     595          14 :         _weights[ 2]   = 6.9044542737641226580708258006013e-02_R;
     596          14 :         _weights[ 3]   = 9.1490021622449999464462094123840e-02_R;
     597          14 :         _weights[ 4]   = 1.1156664554733399471602390168177e-01_R;
     598          14 :         _weights[ 5]   = 1.2875396253933622767551578485688e-01_R;
     599          14 :         _weights[ 6]   = 1.4260670217360661177574610944190e-01_R;
     600          14 :         _weights[ 7]   = 1.5276604206585966677885540089766e-01_R;
     601          14 :         _weights[ 8]   = 1.5896884339395434764995643946505e-01_R;
     602          14 :         _weights[ 9]   = 1.6105444984878369597916362532092e-01_R;
     603          14 :         _weights[10]   = _weights[8];
     604          14 :         _weights[11]   = _weights[7];
     605          14 :         _weights[12]   = _weights[6];
     606          14 :         _weights[13]   = _weights[5];
     607          14 :         _weights[14]   = _weights[4];
     608          14 :         _weights[15]   = _weights[3];
     609          14 :         _weights[16]   = _weights[2];
     610          14 :         _weights[17]   = _weights[1];
     611          14 :         _weights[18]   = _weights[0];
     612             : 
     613          14 :         return;
     614             :       }
     615             : 
     616          14 :     case THIRTYEIGHTH:
     617             :     case THIRTYNINTH:
     618             :       {
     619          14 :         _points.resize (20);
     620          14 :         _weights.resize(20);
     621             : 
     622          14 :         _points[ 0](0) = -9.9312859918509492478612238847132e-01_R;
     623          14 :         _points[ 1](0) = -9.6397192727791379126766613119728e-01_R;
     624          14 :         _points[ 2](0) = -9.1223442825132590586775244120330e-01_R;
     625          14 :         _points[ 3](0) = -8.3911697182221882339452906170152e-01_R;
     626          14 :         _points[ 4](0) = -7.4633190646015079261430507035564e-01_R;
     627          14 :         _points[ 5](0) = -6.3605368072651502545283669622629e-01_R;
     628          14 :         _points[ 6](0) = -5.1086700195082709800436405095525e-01_R;
     629          14 :         _points[ 7](0) = -3.7370608871541956067254817702493e-01_R;
     630          14 :         _points[ 8](0) = -2.2778585114164507808049619536857e-01_R;
     631          14 :         _points[ 9](0) = -7.6526521133497333754640409398838e-02_R;
     632          14 :         _points[10]    = -_points[9];
     633          14 :         _points[11]    = -_points[8];
     634          14 :         _points[12]    = -_points[7];
     635          14 :         _points[13]    = -_points[6];
     636          14 :         _points[14]    = -_points[5];
     637          14 :         _points[15]    = -_points[4];
     638          14 :         _points[16]    = -_points[3];
     639          14 :         _points[17]    = -_points[2];
     640          14 :         _points[18]    = -_points[1];
     641          14 :         _points[19]    = -_points[0];
     642             : 
     643          14 :         _weights[ 0]   = 1.7614007139152118311861962351853e-02_R;
     644          14 :         _weights[ 1]   = 4.0601429800386941331039952274932e-02_R;
     645          14 :         _weights[ 2]   = 6.2672048334109063569506535187042e-02_R;
     646          14 :         _weights[ 3]   = 8.3276741576704748724758143222046e-02_R;
     647          14 :         _weights[ 4]   = 1.0193011981724043503675013548035e-01_R;
     648          14 :         _weights[ 5]   = 1.1819453196151841731237737771138e-01_R;
     649          14 :         _weights[ 6]   = 1.3168863844917662689849449974816e-01_R;
     650          14 :         _weights[ 7]   = 1.4209610931838205132929832506716e-01_R;
     651          14 :         _weights[ 8]   = 1.4917298647260374678782873700197e-01_R;
     652          14 :         _weights[ 9]   = 1.5275338713072585069808433195510e-01_R;
     653          14 :         _weights[10]   = _weights[9];
     654          14 :         _weights[11]   = _weights[8];
     655          14 :         _weights[12]   = _weights[7];
     656          14 :         _weights[13]   = _weights[6];
     657          14 :         _weights[14]   = _weights[5];
     658          14 :         _weights[15]   = _weights[4];
     659          14 :         _weights[16]   = _weights[3];
     660          14 :         _weights[17]   = _weights[2];
     661          14 :         _weights[18]   = _weights[1];
     662          14 :         _weights[19]   = _weights[0];
     663             : 
     664          14 :         return;
     665             :       }
     666             : 
     667          14 :     case FORTIETH:
     668             :     case FORTYFIRST:
     669             :       {
     670          14 :         _points.resize (21);
     671          14 :         _weights.resize(21);
     672             : 
     673          14 :         _points[ 0](0) = -9.9375217062038950026024203593794e-01_R;
     674          14 :         _points[ 1](0) = -9.6722683856630629431662221490770e-01_R;
     675          14 :         _points[ 2](0) = -9.2009933415040082879018713371497e-01_R;
     676          14 :         _points[ 3](0) = -8.5336336458331728364725063858757e-01_R;
     677          14 :         _points[ 4](0) = -7.6843996347567790861587785130623e-01_R;
     678          14 :         _points[ 5](0) = -6.6713880419741231930596666999034e-01_R;
     679          14 :         _points[ 6](0) = -5.5161883588721980705901879672431e-01_R;
     680          14 :         _points[ 7](0) = -4.2434212020743878357366888854379e-01_R;
     681          14 :         _points[ 8](0) = -2.8802131680240109660079251606460e-01_R;
     682          14 :         _points[ 9](0) = -1.4556185416089509093703098233869e-01_R;
     683          14 :         _points[10](0) = 0.;
     684          14 :         _points[11]    = -_points[9];
     685          14 :         _points[12]    = -_points[8];
     686          14 :         _points[13]    = -_points[7];
     687          14 :         _points[14]    = -_points[6];
     688          14 :         _points[15]    = -_points[5];
     689          14 :         _points[16]    = -_points[4];
     690          14 :         _points[17]    = -_points[3];
     691          14 :         _points[18]    = -_points[2];
     692          14 :         _points[19]    = -_points[1];
     693          14 :         _points[20]    = -_points[0];
     694             : 
     695          14 :         _weights[ 0]   = 1.6017228257774333324224616858471e-02_R;
     696          14 :         _weights[ 1]   = 3.6953789770852493799950668299330e-02_R;
     697          14 :         _weights[ 2]   = 5.7134425426857208283635826472448e-02_R;
     698          14 :         _weights[ 3]   = 7.6100113628379302017051653300183e-02_R;
     699          14 :         _weights[ 4]   = 9.3444423456033861553289741113932e-02_R;
     700          14 :         _weights[ 5]   = 1.0879729916714837766347457807011e-01_R;
     701          14 :         _weights[ 6]   = 1.2183141605372853419536717712572e-01_R;
     702          14 :         _weights[ 7]   = 1.3226893863333746178105257449678e-01_R;
     703          14 :         _weights[ 8]   = 1.3988739479107315472213342386758e-01_R;
     704          14 :         _weights[ 9]   = 1.4452440398997005906382716655375e-01_R;
     705          14 :         _weights[10]   = 1.4608113364969042719198514768337e-01_R;
     706          14 :         _weights[11]   = _weights[9];
     707          14 :         _weights[12]   = _weights[8];
     708          14 :         _weights[13]   = _weights[7];
     709          14 :         _weights[14]   = _weights[6];
     710          14 :         _weights[15]   = _weights[5];
     711          14 :         _weights[16]   = _weights[4];
     712          14 :         _weights[17]   = _weights[3];
     713          14 :         _weights[18]   = _weights[2];
     714          14 :         _weights[19]   = _weights[1];
     715          14 :         _weights[20]   = _weights[0];
     716             : 
     717          14 :         return;
     718             :       }
     719             : 
     720          14 :     case FORTYSECOND:
     721             :     case FORTYTHIRD:
     722             :       {
     723          14 :         _points.resize (22);
     724          14 :         _weights.resize(22);
     725             : 
     726          14 :         _points[ 0](0) = -9.9429458548239929207303142116130e-01_R;
     727          14 :         _points[ 1](0) = -9.7006049783542872712395098676527e-01_R;
     728          14 :         _points[ 2](0) = -9.2695677218717400052069293925905e-01_R;
     729          14 :         _points[ 3](0) = -8.6581257772030013653642563701938e-01_R;
     730          14 :         _points[ 4](0) = -7.8781680597920816200427795540835e-01_R;
     731          14 :         _points[ 5](0) = -6.9448726318668278005068983576226e-01_R;
     732          14 :         _points[ 6](0) = -5.8764040350691159295887692763865e-01_R;
     733          14 :         _points[ 7](0) = -4.6935583798675702640633071096641e-01_R;
     734          14 :         _points[ 8](0) = -3.4193582089208422515814742042738e-01_R;
     735          14 :         _points[ 9](0) = -2.0786042668822128547884653391955e-01_R;
     736          14 :         _points[10](0) = -6.9739273319722221213841796118628e-02_R;
     737          14 :         _points[11]    = -_points[10];
     738          14 :         _points[12]    = -_points[9];
     739          14 :         _points[13]    = -_points[8];
     740          14 :         _points[14]    = -_points[7];
     741          14 :         _points[15]    = -_points[6];
     742          14 :         _points[16]    = -_points[5];
     743          14 :         _points[17]    = -_points[4];
     744          14 :         _points[18]    = -_points[3];
     745          14 :         _points[19]    = -_points[2];
     746          14 :         _points[20]    = -_points[1];
     747          14 :         _points[21]    = -_points[0];
     748             : 
     749          14 :         _weights[ 0]   = 1.4627995298272200684991098047185e-02_R;
     750          14 :         _weights[ 1]   = 3.3774901584814154793302246865913e-02_R;
     751          14 :         _weights[ 2]   = 5.2293335152683285940312051273211e-02_R;
     752          14 :         _weights[ 3]   = 6.9796468424520488094961418930218e-02_R;
     753          14 :         _weights[ 4]   = 8.5941606217067727414443681372703e-02_R;
     754          14 :         _weights[ 5]   = 1.0041414444288096493207883783054e-01_R;
     755          14 :         _weights[ 6]   = 1.1293229608053921839340060742175e-01_R;
     756          14 :         _weights[ 7]   = 1.2325237681051242428556098615481e-01_R;
     757          14 :         _weights[ 8]   = 1.3117350478706237073296499253031e-01_R;
     758          14 :         _weights[ 9]   = 1.3654149834601517135257383123152e-01_R;
     759          14 :         _weights[10]   = 1.3925187285563199337541024834181e-01_R;
     760          14 :         _weights[11]   = _weights[10];
     761          14 :         _weights[12]   = _weights[9];
     762          14 :         _weights[13]   = _weights[8];
     763          14 :         _weights[14]   = _weights[7];
     764          14 :         _weights[15]   = _weights[6];
     765          14 :         _weights[16]   = _weights[5];
     766          14 :         _weights[17]   = _weights[4];
     767          14 :         _weights[18]   = _weights[3];
     768          14 :         _weights[19]   = _weights[2];
     769          14 :         _weights[20]   = _weights[1];
     770          14 :         _weights[21]   = _weights[0];
     771             : 
     772          14 :         return;
     773             :       }
     774             : 
     775             : 
     776           0 :     default:
     777           0 :       libmesh_error_msg("Quadrature rule " << _order << " not supported!");
     778             :     }
     779             : }
     780             : 
     781             : } // namespace libMesh