Line data    Source code

       1             : // The libMesh Finite Element Library.
       2             : // Copyright (C) 2002-2025 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     5400757 : void QGauss::init_1D()
      31             : {
      32             :   //----------------------------------------------------------------------
      33             :   // 1D quadrature rules
      34     5679694 :   switch(get_order())
      35             :     {
      36       79883 :     case CONSTANT:
      37             :     case FIRST:
      38             :       {
      39       79883 :         _points.resize (1);
      40       79883 :         _weights.resize(1);
      41             : 
      42       79883 :         _points[0](0)  = 0.;
      43             : 
      44       79883 :         _weights[0]    = 2.;
      45             : 
      46       79883 :         return;
      47             :       }
      48     1620032 :     case SECOND:
      49             :     case THIRD:
      50             :       {
      51     1620032 :         _points.resize (2);
      52     1620032 :         _weights.resize(2);
      53             : 
      54     1620032 :         _points[0](0) = -std::sqrt(Real(3))/3;
      55     1620032 :         _points[1]    = -_points[0];
      56             : 
      57     1620032 :         _weights[0]   = 1.;
      58     1620032 :         _weights[1]   = _weights[0];
      59             : 
      60     1620032 :         return;
      61             :       }
      62     1570084 :     case FOURTH:
      63             :     case FIFTH:
      64             :       {
      65     1570084 :         _points.resize (3);
      66     1570084 :         _weights.resize(3);
      67             : 
      68     1570084 :         _points[ 0](0) = -7.7459666924148337703585307995648e-01_R;
      69     1570084 :         _points[ 1](0) = 0.;
      70     1570084 :         _points[ 2]    = -_points[0];
      71             : 
      72     1570084 :         _weights[ 0]   = Real(5)/9;
      73     1570084 :         _weights[ 1]   = Real(8)/9;
      74     1570084 :         _weights[ 2]   = _weights[0];
      75             : 
      76     1570084 :         return;
      77             :       }
      78     1274897 :     case SIXTH:
      79             :     case SEVENTH:
      80             :       {
      81     1274897 :         _points.resize (4);
      82     1274897 :         _weights.resize(4);
      83             : 
      84     1274897 :         _points[ 0](0) = -8.6113631159405257522394648889281e-01_R;
      85     1274897 :         _points[ 1](0) = -3.3998104358485626480266575910324e-01_R;
      86     1274897 :         _points[ 2]    = -_points[1];
      87     1274897 :         _points[ 3]    = -_points[0];
      88             : 
      89     1274897 :         _weights[ 0]   = 3.4785484513745385737306394922200e-01_R;
      90     1274897 :         _weights[ 1]   = 6.5214515486254614262693605077800e-01_R;
      91     1274897 :         _weights[ 2]   = _weights[1];
      92     1274897 :         _weights[ 3]   = _weights[0];
      93             : 
      94     1274897 :         return;
      95             :       }
      96      452616 :     case EIGHTH:
      97             :     case NINTH:
      98             :       {
      99      452616 :         _points.resize (5);
     100      452616 :         _weights.resize(5);
     101             : 
     102      452616 :         _points[ 0](0) = -9.0617984593866399279762687829939e-01_R;
     103      452616 :         _points[ 1](0) = -5.3846931010568309103631442070021e-01_R;
     104      452616 :         _points[ 2](0) = 0.;
     105      452616 :         _points[ 3]    = -_points[1];
     106      452616 :         _points[ 4]    = -_points[0];
     107             : 
     108      452616 :         _weights[ 0]   = 2.3692688505618908751426404071992e-01_R;
     109      452616 :         _weights[ 1]   = 4.7862867049936646804129151483564e-01_R;
     110      452616 :         _weights[ 2]   = 5.6888888888888888888888888888889e-01_R;
     111      452616 :         _weights[ 3]   = _weights[1];
     112      452616 :         _weights[ 4]   = _weights[0];
     113             : 
     114      452616 :         return;
     115             :       }
     116       82750 :     case TENTH:
     117             :     case ELEVENTH:
     118             :       {
     119       82750 :         _points.resize (6);
     120       82750 :         _weights.resize(6);
     121             : 
     122       82750 :         _points[ 0](0) = -9.3246951420315202781230155449399e-01_R;
     123       82750 :         _points[ 1](0) = -6.6120938646626451366139959501991e-01_R;
     124       82750 :         _points[ 2](0) = -2.3861918608319690863050172168071e-01_R;
     125       82750 :         _points[ 3]    = -_points[2];
     126       82750 :         _points[ 4]    = -_points[1];
     127       82750 :         _points[ 5]    = -_points[0];
     128             : 
     129       82750 :         _weights[ 0]   = 1.7132449237917034504029614217273e-01_R;
     130       82750 :         _weights[ 1]   = 3.6076157304813860756983351383772e-01_R;
     131       82750 :         _weights[ 2]   = 4.6791393457269104738987034398955e-01_R;
     132       82750 :         _weights[ 3]   = _weights[2];
     133       82750 :         _weights[ 4]   = _weights[1];
     134       82750 :         _weights[ 5]   = _weights[0];
     135             : 
     136       82750 :         return;
     137             :       }
     138        2947 :     case TWELFTH:
     139             :     case THIRTEENTH:
     140             :       {
     141        2947 :         _points.resize (7);
     142        2947 :         _weights.resize(7);
     143             : 
     144        2947 :         _points[ 0](0) = -9.4910791234275852452618968404785e-01_R;
     145        2947 :         _points[ 1](0) = -7.4153118559939443986386477328079e-01_R;
     146        2947 :         _points[ 2](0) = -4.0584515137739716690660641207696e-01_R;
     147        2947 :         _points[ 3](0) = 0.;
     148        2947 :         _points[ 4]    = -_points[2];
     149        2947 :         _points[ 5]    = -_points[1];
     150        2947 :         _points[ 6]    = -_points[0];
     151             : 
     152        2947 :         _weights[ 0]   = 1.2948496616886969327061143267908e-01_R;
     153        2947 :         _weights[ 1]   = 2.7970539148927666790146777142378e-01_R;
     154        2947 :         _weights[ 2]   = 3.8183005050511894495036977548898e-01_R;
     155        2947 :         _weights[ 3]   = 4.1795918367346938775510204081633e-01_R;
     156        2947 :         _weights[ 4]   = _weights[2];
     157        2947 :         _weights[ 5]   = _weights[1];
     158        2947 :         _weights[ 6]   = _weights[0];
     159             : 
     160        2947 :         return;
     161             :       }
     162        2130 :     case FOURTEENTH:
     163             :     case FIFTEENTH:
     164             :       {
     165        2130 :         _points.resize (8);
     166        2130 :         _weights.resize(8);
     167             : 
     168        2130 :         _points[ 0](0) = -9.6028985649753623168356086856947e-01_R;
     169        2130 :         _points[ 1](0) = -7.9666647741362673959155393647583e-01_R;
     170        2130 :         _points[ 2](0) = -5.2553240991632898581773904918925e-01_R;
     171        2130 :         _points[ 3](0) = -1.8343464249564980493947614236018e-01_R;
     172        2130 :         _points[ 4]    = -_points[3];
     173        2130 :         _points[ 5]    = -_points[2];
     174        2130 :         _points[ 6]    = -_points[1];
     175        2130 :         _points[ 7]    = -_points[0];
     176             : 
     177        2130 :         _weights[ 0]   = 1.0122853629037625915253135430996e-01_R;
     178        2130 :         _weights[ 1]   = 2.2238103445337447054435599442624e-01_R;
     179        2130 :         _weights[ 2]   = 3.1370664587788728733796220198660e-01_R;
     180        2130 :         _weights[ 3]   = 3.6268378337836198296515044927720e-01_R;
     181        2130 :         _weights[ 4]   = _weights[3];
     182        2130 :         _weights[ 5]   = _weights[2];
     183        2130 :         _weights[ 6]   = _weights[1];
     184        2130 :         _weights[ 7]   = _weights[0];
     185             : 
     186        2130 :         return;
     187             :       }
     188        1708 :     case SIXTEENTH:
     189             :     case SEVENTEENTH:
     190             :       {
     191        1708 :         _points.resize (9);
     192        1708 :         _weights.resize(9);
     193             : 
     194        1708 :         _points[ 0](0) = -9.6816023950762608983557620290367e-01_R;
     195        1708 :         _points[ 1](0) = -8.3603110732663579429942978806973e-01_R;
     196        1708 :         _points[ 2](0) = -6.1337143270059039730870203934147e-01_R;
     197        1708 :         _points[ 3](0) = -3.2425342340380892903853801464334e-01_R;
     198        1708 :         _points[ 4](0) = 0.;
     199        1708 :         _points[ 5]    = -_points[3];
     200        1708 :         _points[ 6]    = -_points[2];
     201        1708 :         _points[ 7]    = -_points[1];
     202        1708 :         _points[ 8]    = -_points[0];
     203             : 
     204        1708 :         _weights[ 0]   = 8.1274388361574411971892158110524e-02_R;
     205        1708 :         _weights[ 1]   = 1.8064816069485740405847203124291e-01_R;
     206        1708 :         _weights[ 2]   = 2.6061069640293546231874286941863e-01_R;
     207        1708 :         _weights[ 3]   = 3.1234707704000284006863040658444e-01_R;
     208        1708 :         _weights[ 4]   = 3.3023935500125976316452506928697e-01_R;
     209        1708 :         _weights[ 5]   = _weights[3];
     210        1708 :         _weights[ 6]   = _weights[2];
     211        1708 :         _weights[ 7]   = _weights[1];
     212        1708 :         _weights[ 8]   = _weights[0];
     213             : 
     214        1708 :         return;
     215             :       }
     216        1155 :     case EIGHTTEENTH:
     217             :     case NINETEENTH:
     218             :       {
     219        1155 :         _points.resize (10);
     220        1155 :         _weights.resize(10);
     221             : 
     222        1155 :         _points[ 0](0) = -9.7390652851717172007796401208445e-01_R;
     223        1155 :         _points[ 1](0) = -8.6506336668898451073209668842349e-01_R;
     224        1155 :         _points[ 2](0) = -6.7940956829902440623432736511487e-01_R;
     225        1155 :         _points[ 3](0) = -4.3339539412924719079926594316578e-01_R;
     226        1155 :         _points[ 4](0) = -1.4887433898163121088482600112972e-01_R;
     227        1155 :         _points[ 5]    = -_points[4];
     228        1155 :         _points[ 6]    = -_points[3];
     229        1155 :         _points[ 7]    = -_points[2];
     230        1155 :         _points[ 8]    = -_points[1];
     231        1155 :         _points[ 9]    = -_points[0];
     232             : 
     233        1155 :         _weights[ 0]   = 6.6671344308688137593568809893332e-02_R;
     234        1155 :         _weights[ 1]   = 1.4945134915058059314577633965770e-01_R;
     235        1155 :         _weights[ 2]   = 2.1908636251598204399553493422816e-01_R;
     236        1155 :         _weights[ 3]   = 2.6926671930999635509122692156947e-01_R;
     237        1155 :         _weights[ 4]   = 2.9552422471475287017389299465134e-01_R;
     238        1155 :         _weights[ 5]   = _weights[4];
     239        1155 :         _weights[ 6]   = _weights[3];
     240        1155 :         _weights[ 7]   = _weights[2];
     241        1155 :         _weights[ 8]   = _weights[1];
     242        1155 :         _weights[ 9]   = _weights[0];
     243             : 
     244        1155 :         return;
     245             :       }
     246             : 
     247         639 :     case TWENTIETH:
     248             :     case TWENTYFIRST:
     249             :       {
     250         639 :         _points.resize (11);
     251         639 :         _weights.resize(11);
     252             : 
     253         639 :         _points[ 0](0) = -9.7822865814605699280393800112286e-01_R;
     254         639 :         _points[ 1](0) = -8.8706259976809529907515776930393e-01_R;
     255         639 :         _points[ 2](0) = -7.3015200557404932409341625203115e-01_R;
     256         639 :         _points[ 3](0) = -5.1909612920681181592572566945861e-01_R;
     257         639 :         _points[ 4](0) = -2.6954315595234497233153198540086e-01_R;
     258         639 :         _points[ 5](0) = 0.;
     259         639 :         _points[ 6]    = -_points[4];
     260         639 :         _points[ 7]    = -_points[3];
     261         639 :         _points[ 8]    = -_points[2];
     262         639 :         _points[ 9]    = -_points[1];
     263         639 :         _points[10]    = -_points[0];
     264             : 
     265         639 :         _weights[ 0]   = 5.5668567116173666482753720442549e-02_R;
     266         639 :         _weights[ 1]   = 1.2558036946490462463469429922394e-01_R;
     267         639 :         _weights[ 2]   = 1.8629021092773425142609764143166e-01_R;
     268         639 :         _weights[ 3]   = 2.3319376459199047991852370484318e-01_R;
     269         639 :         _weights[ 4]   = 2.6280454451024666218068886989051e-01_R;
     270         639 :         _weights[ 5]   = 2.7292508677790063071448352833634e-01_R;
     271         639 :         _weights[ 6]   = _weights[4];
     272         639 :         _weights[ 7]   = _weights[3];
     273         639 :         _weights[ 8]   = _weights[2];
     274         639 :         _weights[ 9]   = _weights[1];
     275         639 :         _weights[10]   = _weights[0];
     276             : 
     277         639 :         return;
     278             :       }
     279             : 
     280      310496 :     case TWENTYSECOND:
     281             :     case TWENTYTHIRD:
     282             :       {
     283      310496 :         _points.resize (12);
     284      310496 :         _weights.resize(12);
     285             : 
     286      310496 :         _points[ 0](0) = -9.8156063424671925069054909014928e-01_R;
     287      310496 :         _points[ 1](0) = -9.0411725637047485667846586611910e-01_R;
     288      310496 :         _points[ 2](0) = -7.6990267419430468703689383321282e-01_R;
     289      310496 :         _points[ 3](0) = -5.8731795428661744729670241894053e-01_R;
     290      310496 :         _points[ 4](0) = -3.6783149899818019375269153664372e-01_R;
     291      310496 :         _points[ 5](0) = -1.2523340851146891547244136946385e-01_R;
     292      310496 :         _points[ 6]    = -_points[5];
     293      310496 :         _points[ 7]    = -_points[4];
     294      310496 :         _points[ 8]    = -_points[3];
     295      310496 :         _points[ 9]    = -_points[2];
     296      310496 :         _points[10]    = -_points[1];
     297      310496 :         _points[11]    = -_points[0];
     298             : 
     299      310496 :         _weights[ 0]   = 4.7175336386511827194615961485017e-02_R;
     300      310496 :         _weights[ 1]   = 1.0693932599531843096025471819400e-01_R;
     301      310496 :         _weights[ 2]   = 1.6007832854334622633465252954336e-01_R;
     302      310496 :         _weights[ 3]   = 2.0316742672306592174906445580980e-01_R;
     303      310496 :         _weights[ 4]   = 2.3349253653835480876084989892483e-01_R;
     304      310496 :         _weights[ 5]   = 2.4914704581340278500056243604295e-01_R;
     305      310496 :         _weights[ 6]   = _weights[5];
     306      310496 :         _weights[ 7]   = _weights[4];
     307      310496 :         _weights[ 8]   = _weights[3];
     308      310496 :         _weights[ 9]   = _weights[2];
     309      310496 :         _weights[10]   = _weights[1];
     310      310496 :         _weights[11]   = _weights[0];
     311             : 
     312      310496 :         return;
     313             :       }
     314             : 
     315         142 :     case TWENTYFOURTH:
     316             :     case TWENTYFIFTH:
     317             :       {
     318         142 :         _points.resize (13);
     319         142 :         _weights.resize(13);
     320             : 
     321         142 :         _points[ 0](0) = -9.8418305471858814947282944880711e-01_R;
     322         142 :         _points[ 1](0) = -9.1759839922297796520654783650072e-01_R;
     323         142 :         _points[ 2](0) = -8.0157809073330991279420648958286e-01_R;
     324         142 :         _points[ 3](0) = -6.4234933944034022064398460699552e-01_R;
     325         142 :         _points[ 4](0) = -4.4849275103644685287791285212764e-01_R;
     326         142 :         _points[ 5](0) = -2.3045831595513479406552812109799e-01_R;
     327         142 :         _points[ 6](0) = 0.;
     328         142 :         _points[ 7]    = -_points[5];
     329         142 :         _points[ 8]    = -_points[4];
     330         142 :         _points[ 9]    = -_points[3];
     331         142 :         _points[10]    = -_points[2];
     332         142 :         _points[11]    = -_points[1];
     333         142 :         _points[12]    = -_points[0];
     334             : 
     335         142 :         _weights[ 0]   = 4.0484004765315879520021592200986e-02_R;
     336         142 :         _weights[ 1]   = 9.2121499837728447914421775953797e-02_R;
     337         142 :         _weights[ 2]   = 1.3887351021978723846360177686887e-01_R;
     338         142 :         _weights[ 3]   = 1.7814598076194573828004669199610e-01_R;
     339         142 :         _weights[ 4]   = 2.0781604753688850231252321930605e-01_R;
     340         142 :         _weights[ 5]   = 2.2628318026289723841209018603978e-01_R;
     341         142 :         _weights[ 6]   = 2.3255155323087391019458951526884e-01_R;
     342         142 :         _weights[ 7]   = _weights[5];
     343         142 :         _weights[ 8]   = _weights[4];
     344         142 :         _weights[ 9]   = _weights[3];
     345         142 :         _weights[10]   = _weights[2];
     346         142 :         _weights[11]   = _weights[1];
     347         142 :         _weights[12]   = _weights[0];
     348             : 
     349         142 :         return;
     350             :       }
     351             : 
     352         142 :     case TWENTYSIXTH:
     353             :     case TWENTYSEVENTH:
     354             :       {
     355         142 :         _points.resize (14);
     356         142 :         _weights.resize(14);
     357             : 
     358         142 :         _points[ 0](0) = -9.8628380869681233884159726670405e-01_R;
     359         142 :         _points[ 1](0) = -9.2843488366357351733639113937787e-01_R;
     360         142 :         _points[ 2](0) = -8.2720131506976499318979474265039e-01_R;
     361         142 :         _points[ 3](0) = -6.8729290481168547014801980301933e-01_R;
     362         142 :         _points[ 4](0) = -5.1524863635815409196529071855119e-01_R;
     363         142 :         _points[ 5](0) = -3.1911236892788976043567182416848e-01_R;
     364         142 :         _points[ 6](0) = -1.0805494870734366206624465021983e-01_R;
     365         142 :         _points[ 7]    = -_points[6];
     366         142 :         _points[ 8]    = -_points[5];
     367         142 :         _points[ 9]    = -_points[4];
     368         142 :         _points[10]    = -_points[3];
     369         142 :         _points[11]    = -_points[2];
     370         142 :         _points[12]    = -_points[1];
     371         142 :         _points[13]    = -_points[0];
     372             : 
     373         142 :         _weights[ 0]   = 3.5119460331751863031832876138192e-02_R;
     374         142 :         _weights[ 1]   = 8.0158087159760209805633277062854e-02_R;
     375         142 :         _weights[ 2]   = 1.2151857068790318468941480907248e-01_R;
     376         142 :         _weights[ 3]   = 1.5720316715819353456960193862384e-01_R;
     377         142 :         _weights[ 4]   = 1.8553839747793781374171659012516e-01_R;
     378         142 :         _weights[ 5]   = 2.0519846372129560396592406566122e-01_R;
     379         142 :         _weights[ 6]   = 2.1526385346315779019587644331626e-01_R;
     380         142 :         _weights[ 7]   = _weights[6];
     381         142 :         _weights[ 8]   = _weights[5];
     382         142 :         _weights[ 9]   = _weights[4];
     383         142 :         _weights[10]   = _weights[3];
     384         142 :         _weights[11]   = _weights[2];
     385         142 :         _weights[12]   = _weights[1];
     386         142 :         _weights[13]   = _weights[0];
     387             : 
     388         142 :         return;
     389             :       }
     390             : 
     391         142 :     case TWENTYEIGHTH:
     392             :     case TWENTYNINTH:
     393             :       {
     394         142 :         _points.resize (15);
     395         142 :         _weights.resize(15);
     396             : 
     397         142 :         _points[ 0](0) = -9.8799251802048542848956571858661e-01_R;
     398         142 :         _points[ 1](0) = -9.3727339240070590430775894771021e-01_R;
     399         142 :         _points[ 2](0) = -8.4820658341042721620064832077422e-01_R;
     400         142 :         _points[ 3](0) = -7.2441773136017004741618605461394e-01_R;
     401         142 :         _points[ 4](0) = -5.7097217260853884753722673725391e-01_R;
     402         142 :         _points[ 5](0) = -3.9415134707756336989720737098105e-01_R;
     403         142 :         _points[ 6](0) = -2.0119409399743452230062830339460e-01_R;
     404         142 :         _points[ 7](0) = 0.;
     405         142 :         _points[ 8]    = -_points[6];
     406         142 :         _points[ 9]    = -_points[5];
     407         142 :         _points[10]    = -_points[4];
     408         142 :         _points[11]    = -_points[3];
     409         142 :         _points[12]    = -_points[2];
     410         142 :         _points[13]    = -_points[1];
     411         142 :         _points[14]    = -_points[0];
     412             : 
     413         142 :         _weights[ 0]   = 3.0753241996117268354628393577204e-02_R;
     414         142 :         _weights[ 1]   = 7.0366047488108124709267416450667e-02_R;
     415         142 :         _weights[ 2]   = 1.0715922046717193501186954668587e-01_R;
     416         142 :         _weights[ 3]   = 1.3957067792615431444780479451103e-01_R;
     417         142 :         _weights[ 4]   = 1.6626920581699393355320086048121e-01_R;
     418         142 :         _weights[ 5]   = 1.8616100001556221102680056186642e-01_R;
     419         142 :         _weights[ 6]   = 1.9843148532711157645611832644384e-01_R;
     420         142 :         _weights[ 7]   = 2.0257824192556127288062019996752e-01_R;
     421         142 :         _weights[ 8]   = _weights[6];
     422         142 :         _weights[ 9]   = _weights[5];
     423         142 :         _weights[10]   = _weights[4];
     424         142 :         _weights[11]   = _weights[3];
     425         142 :         _weights[12]   = _weights[2];
     426         142 :         _weights[13]   = _weights[1];
     427         142 :         _weights[14]   = _weights[0];
     428             : 
     429         142 :         return;
     430             :       }
     431             : 
     432         142 :     case THIRTIETH:
     433             :     case THIRTYFIRST:
     434             :       {
     435         142 :         _points.resize (16);
     436         142 :         _weights.resize(16);
     437             : 
     438         142 :         _points[ 0](0) = -9.8940093499164993259615417345033e-01_R;
     439         142 :         _points[ 1](0) = -9.4457502307323257607798841553461e-01_R;
     440         142 :         _points[ 2](0) = -8.6563120238783174388046789771239e-01_R;
     441         142 :         _points[ 3](0) = -7.5540440835500303389510119484744e-01_R;
     442         142 :         _points[ 4](0) = -6.1787624440264374844667176404879e-01_R;
     443         142 :         _points[ 5](0) = -4.5801677765722738634241944298358e-01_R;
     444         142 :         _points[ 6](0) = -2.8160355077925891323046050146050e-01_R;
     445         142 :         _points[ 7](0) = -9.5012509837637440185319335424958e-02_R;
     446         142 :         _points[ 8]    = -_points[7];
     447         142 :         _points[ 9]    = -_points[6];
     448         142 :         _points[10]    = -_points[5];
     449         142 :         _points[11]    = -_points[4];
     450         142 :         _points[12]    = -_points[3];
     451         142 :         _points[13]    = -_points[2];
     452         142 :         _points[14]    = -_points[1];
     453         142 :         _points[15]    = -_points[0];
     454             : 
     455         142 :         _weights[ 0]   = 2.7152459411754094851780572456018e-02_R;
     456         142 :         _weights[ 1]   = 6.2253523938647892862843836994378e-02_R;
     457         142 :         _weights[ 2]   = 9.5158511682492784809925107602246e-02_R;
     458         142 :         _weights[ 3]   = 1.2462897125553387205247628219202e-01_R;
     459         142 :         _weights[ 4]   = 1.4959598881657673208150173054748e-01_R;
     460         142 :         _weights[ 5]   = 1.6915651939500253818931207903033e-01_R;
     461         142 :         _weights[ 6]   = 1.8260341504492358886676366796922e-01_R;
     462         142 :         _weights[ 7]   = 1.8945061045506849628539672320828e-01_R;
     463         142 :         _weights[ 8]   = _weights[7];
     464         142 :         _weights[ 9]   = _weights[6];
     465         142 :         _weights[10]   = _weights[5];
     466         142 :         _weights[11]   = _weights[4];
     467         142 :         _weights[12]   = _weights[3];
     468         142 :         _weights[13]   = _weights[2];
     469         142 :         _weights[14]   = _weights[1];
     470         142 :         _weights[15]   = _weights[0];
     471             : 
     472         142 :         return;
     473             :       }
     474             : 
     475         142 :     case THIRTYSECOND:
     476             :     case THIRTYTHIRD:
     477             :       {
     478         142 :         _points.resize (17);
     479         142 :         _weights.resize(17);
     480             : 
     481         142 :         _points[ 0](0) = -9.9057547531441733567543401994067e-01_R;
     482         142 :         _points[ 1](0) = -9.5067552176876776122271695789580e-01_R;
     483         142 :         _points[ 2](0) = -8.8023915372698590212295569448816e-01_R;
     484         142 :         _points[ 3](0) = -7.8151400389680140692523005552048e-01_R;
     485         142 :         _points[ 4](0) = -6.5767115921669076585030221664300e-01_R;
     486         142 :         _points[ 5](0) = -5.1269053708647696788624656862955e-01_R;
     487         142 :         _points[ 6](0) = -3.5123176345387631529718551709535e-01_R;
     488         142 :         _points[ 7](0) = -1.7848418149584785585067749365407e-01_R;
     489         142 :         _points[ 8](0) = 0.;
     490         142 :         _points[ 9]    = -_points[7];
     491         142 :         _points[10]    = -_points[6];
     492         142 :         _points[11]    = -_points[5];
     493         142 :         _points[12]    = -_points[4];
     494         142 :         _points[13]    = -_points[3];
     495         142 :         _points[14]    = -_points[2];
     496         142 :         _points[15]    = -_points[1];
     497         142 :         _points[16]    = -_points[0];
     498             : 
     499         142 :         _weights[ 0]   = 2.4148302868547931960110026287565e-02_R;
     500         142 :         _weights[ 1]   = 5.5459529373987201129440165358245e-02_R;
     501         142 :         _weights[ 2]   = 8.5036148317179180883535370191062e-02_R;
     502         142 :         _weights[ 3]   = 1.1188384719340397109478838562636e-01_R;
     503         142 :         _weights[ 4]   = 1.3513636846852547328631998170235e-01_R;
     504         142 :         _weights[ 5]   = 1.5404576107681028808143159480196e-01_R;
     505         142 :         _weights[ 6]   = 1.6800410215645004450997066378832e-01_R;
     506         142 :         _weights[ 7]   = 1.7656270536699264632527099011320e-01_R;
     507         142 :         _weights[ 8]   = 1.7944647035620652545826564426189e-01_R;
     508         142 :         _weights[ 9]   = _weights[7];
     509         142 :         _weights[10]   = _weights[6];
     510         142 :         _weights[11]   = _weights[5];
     511         142 :         _weights[12]   = _weights[4];
     512         142 :         _weights[13]   = _weights[3];
     513         142 :         _weights[14]   = _weights[2];
     514         142 :         _weights[15]   = _weights[1];
     515         142 :         _weights[16]   = _weights[0];
     516             : 
     517         142 :         return;
     518             :       }
     519             : 
     520         142 :     case THIRTYFOURTH:
     521             :     case THIRTYFIFTH:
     522             :       {
     523         142 :         _points.resize (18);
     524         142 :         _weights.resize(18);
     525             : 
     526         142 :         _points[ 0](0) = -9.9156516842093094673001600470615e-01_R;
     527         142 :         _points[ 1](0) = -9.5582394957139775518119589292978e-01_R;
     528         142 :         _points[ 2](0) = -8.9260246649755573920606059112715e-01_R;
     529         142 :         _points[ 3](0) = -8.0370495897252311568241745501459e-01_R;
     530         142 :         _points[ 4](0) = -6.9168704306035320787489108128885e-01_R;
     531         142 :         _points[ 5](0) = -5.5977083107394753460787154852533e-01_R;
     532         142 :         _points[ 6](0) = -4.1175116146284264603593179383305e-01_R;
     533         142 :         _points[ 7](0) = -2.5188622569150550958897285487791e-01_R;
     534         142 :         _points[ 8](0) = -8.4775013041735301242261852935784e-02_R;
     535         142 :         _points[ 9]    = -_points[8];
     536         142 :         _points[10]    = -_points[7];
     537         142 :         _points[11]    = -_points[6];
     538         142 :         _points[12]    = -_points[5];
     539         142 :         _points[13]    = -_points[4];
     540         142 :         _points[14]    = -_points[3];
     541         142 :         _points[15]    = -_points[2];
     542         142 :         _points[16]    = -_points[1];
     543         142 :         _points[17]    = -_points[0];
     544             : 
     545         142 :         _weights[ 0]   = 2.1616013526483310313342710266452e-02_R;
     546         142 :         _weights[ 1]   = 4.9714548894969796453334946202639e-02_R;
     547         142 :         _weights[ 2]   = 7.6425730254889056529129677616637e-02_R;
     548         142 :         _weights[ 3]   = 1.0094204410628716556281398492483e-01_R;
     549         142 :         _weights[ 4]   = 1.2255520671147846018451912680020e-01_R;
     550         142 :         _weights[ 5]   = 1.4064291467065065120473130375195e-01_R;
     551         142 :         _weights[ 6]   = 1.5468467512626524492541800383637e-01_R;
     552         142 :         _weights[ 7]   = 1.6427648374583272298605377646593e-01_R;
     553         142 :         _weights[ 8]   = 1.6914238296314359184065647013499e-01_R;
     554         142 :         _weights[ 9]   = _weights[8];
     555         142 :         _weights[10]   = _weights[7];
     556         142 :         _weights[11]   = _weights[6];
     557         142 :         _weights[12]   = _weights[5];
     558         142 :         _weights[13]   = _weights[4];
     559         142 :         _weights[14]   = _weights[3];
     560         142 :         _weights[15]   = _weights[2];
     561         142 :         _weights[16]   = _weights[1];
     562         142 :         _weights[17]   = _weights[0];
     563             : 
     564         142 :         return;
     565             :       }
     566             : 
     567         142 :     case THIRTYSIXTH:
     568             :     case THIRTYSEVENTH:
     569             :       {
     570         142 :         _points.resize (19);
     571         142 :         _weights.resize(19);
     572             : 
     573         142 :         _points[ 0](0) = -9.9240684384358440318901767025326e-01_R;
     574         142 :         _points[ 1](0) = -9.6020815213483003085277884068765e-01_R;
     575         142 :         _points[ 2](0) = -9.0315590361481790164266092853231e-01_R;
     576         142 :         _points[ 3](0) = -8.2271465653714282497892248671271e-01_R;
     577         142 :         _points[ 4](0) = -7.2096617733522937861709586082378e-01_R;
     578         142 :         _points[ 5](0) = -6.0054530466168102346963816494624e-01_R;
     579         142 :         _points[ 6](0) = -4.6457074137596094571726714810410e-01_R;
     580         142 :         _points[ 7](0) = -3.1656409996362983199011732884984e-01_R;
     581         142 :         _points[ 8](0) = -1.6035864564022537586809611574074e-01_R;
     582         142 :         _points[ 9](0) = 0.;
     583         142 :         _points[10]    = -_points[8];
     584         142 :         _points[11]    = -_points[7];
     585         142 :         _points[12]    = -_points[6];
     586         142 :         _points[13]    = -_points[5];
     587         142 :         _points[14]    = -_points[4];
     588         142 :         _points[15]    = -_points[3];
     589         142 :         _points[16]    = -_points[2];
     590         142 :         _points[17]    = -_points[1];
     591         142 :         _points[18]    = -_points[0];
     592             : 
     593         142 :         _weights[ 0]   = 1.9461788229726477036312041464438e-02_R;
     594         142 :         _weights[ 1]   = 4.4814226765699600332838157401994e-02_R;
     595         142 :         _weights[ 2]   = 6.9044542737641226580708258006013e-02_R;
     596         142 :         _weights[ 3]   = 9.1490021622449999464462094123840e-02_R;
     597         142 :         _weights[ 4]   = 1.1156664554733399471602390168177e-01_R;
     598         142 :         _weights[ 5]   = 1.2875396253933622767551578485688e-01_R;
     599         142 :         _weights[ 6]   = 1.4260670217360661177574610944190e-01_R;
     600         142 :         _weights[ 7]   = 1.5276604206585966677885540089766e-01_R;
     601         142 :         _weights[ 8]   = 1.5896884339395434764995643946505e-01_R;
     602         142 :         _weights[ 9]   = 1.6105444984878369597916362532092e-01_R;
     603         142 :         _weights[10]   = _weights[8];
     604         142 :         _weights[11]   = _weights[7];
     605         142 :         _weights[12]   = _weights[6];
     606         142 :         _weights[13]   = _weights[5];
     607         142 :         _weights[14]   = _weights[4];
     608         142 :         _weights[15]   = _weights[3];
     609         142 :         _weights[16]   = _weights[2];
     610         142 :         _weights[17]   = _weights[1];
     611         142 :         _weights[18]   = _weights[0];
     612             : 
     613         142 :         return;
     614             :       }
     615             : 
     616         142 :     case THIRTYEIGHTH:
     617             :     case THIRTYNINTH:
     618             :       {
     619         142 :         _points.resize (20);
     620         142 :         _weights.resize(20);
     621             : 
     622         142 :         _points[ 0](0) = -9.9312859918509492478612238847132e-01_R;
     623         142 :         _points[ 1](0) = -9.6397192727791379126766613119728e-01_R;
     624         142 :         _points[ 2](0) = -9.1223442825132590586775244120330e-01_R;
     625         142 :         _points[ 3](0) = -8.3911697182221882339452906170152e-01_R;
     626         142 :         _points[ 4](0) = -7.4633190646015079261430507035564e-01_R;
     627         142 :         _points[ 5](0) = -6.3605368072651502545283669622629e-01_R;
     628         142 :         _points[ 6](0) = -5.1086700195082709800436405095525e-01_R;
     629         142 :         _points[ 7](0) = -3.7370608871541956067254817702493e-01_R;
     630         142 :         _points[ 8](0) = -2.2778585114164507808049619536857e-01_R;
     631         142 :         _points[ 9](0) = -7.6526521133497333754640409398838e-02_R;
     632         142 :         _points[10]    = -_points[9];
     633         142 :         _points[11]    = -_points[8];
     634         142 :         _points[12]    = -_points[7];
     635         142 :         _points[13]    = -_points[6];
     636         142 :         _points[14]    = -_points[5];
     637         142 :         _points[15]    = -_points[4];
     638         142 :         _points[16]    = -_points[3];
     639         142 :         _points[17]    = -_points[2];
     640         142 :         _points[18]    = -_points[1];
     641         142 :         _points[19]    = -_points[0];
     642             : 
     643         142 :         _weights[ 0]   = 1.7614007139152118311861962351853e-02_R;
     644         142 :         _weights[ 1]   = 4.0601429800386941331039952274932e-02_R;
     645         142 :         _weights[ 2]   = 6.2672048334109063569506535187042e-02_R;
     646         142 :         _weights[ 3]   = 8.3276741576704748724758143222046e-02_R;
     647         142 :         _weights[ 4]   = 1.0193011981724043503675013548035e-01_R;
     648         142 :         _weights[ 5]   = 1.1819453196151841731237737771138e-01_R;
     649         142 :         _weights[ 6]   = 1.3168863844917662689849449974816e-01_R;
     650         142 :         _weights[ 7]   = 1.4209610931838205132929832506716e-01_R;
     651         142 :         _weights[ 8]   = 1.4917298647260374678782873700197e-01_R;
     652         142 :         _weights[ 9]   = 1.5275338713072585069808433195510e-01_R;
     653         142 :         _weights[10]   = _weights[9];
     654         142 :         _weights[11]   = _weights[8];
     655         142 :         _weights[12]   = _weights[7];
     656         142 :         _weights[13]   = _weights[6];
     657         142 :         _weights[14]   = _weights[5];
     658         142 :         _weights[15]   = _weights[4];
     659         142 :         _weights[16]   = _weights[3];
     660         142 :         _weights[17]   = _weights[2];
     661         142 :         _weights[18]   = _weights[1];
     662         142 :         _weights[19]   = _weights[0];
     663             : 
     664         142 :         return;
     665             :       }
     666             : 
     667         142 :     case FORTIETH:
     668             :     case FORTYFIRST:
     669             :       {
     670         142 :         _points.resize (21);
     671         142 :         _weights.resize(21);
     672             : 
     673         142 :         _points[ 0](0) = -9.9375217062038950026024203593794e-01_R;
     674         142 :         _points[ 1](0) = -9.6722683856630629431662221490770e-01_R;
     675         142 :         _points[ 2](0) = -9.2009933415040082879018713371497e-01_R;
     676         142 :         _points[ 3](0) = -8.5336336458331728364725063858757e-01_R;
     677         142 :         _points[ 4](0) = -7.6843996347567790861587785130623e-01_R;
     678         142 :         _points[ 5](0) = -6.6713880419741231930596666999034e-01_R;
     679         142 :         _points[ 6](0) = -5.5161883588721980705901879672431e-01_R;
     680         142 :         _points[ 7](0) = -4.2434212020743878357366888854379e-01_R;
     681         142 :         _points[ 8](0) = -2.8802131680240109660079251606460e-01_R;
     682         142 :         _points[ 9](0) = -1.4556185416089509093703098233869e-01_R;
     683         142 :         _points[10](0) = 0.;
     684         142 :         _points[11]    = -_points[9];
     685         142 :         _points[12]    = -_points[8];
     686         142 :         _points[13]    = -_points[7];
     687         142 :         _points[14]    = -_points[6];
     688         142 :         _points[15]    = -_points[5];
     689         142 :         _points[16]    = -_points[4];
     690         142 :         _points[17]    = -_points[3];
     691         142 :         _points[18]    = -_points[2];
     692         142 :         _points[19]    = -_points[1];
     693         142 :         _points[20]    = -_points[0];
     694             : 
     695         142 :         _weights[ 0]   = 1.6017228257774333324224616858471e-02_R;
     696         142 :         _weights[ 1]   = 3.6953789770852493799950668299330e-02_R;
     697         142 :         _weights[ 2]   = 5.7134425426857208283635826472448e-02_R;
     698         142 :         _weights[ 3]   = 7.6100113628379302017051653300183e-02_R;
     699         142 :         _weights[ 4]   = 9.3444423456033861553289741113932e-02_R;
     700         142 :         _weights[ 5]   = 1.0879729916714837766347457807011e-01_R;
     701         142 :         _weights[ 6]   = 1.2183141605372853419536717712572e-01_R;
     702         142 :         _weights[ 7]   = 1.3226893863333746178105257449678e-01_R;
     703         142 :         _weights[ 8]   = 1.3988739479107315472213342386758e-01_R;
     704         142 :         _weights[ 9]   = 1.4452440398997005906382716655375e-01_R;
     705         142 :         _weights[10]   = 1.4608113364969042719198514768337e-01_R;
     706         142 :         _weights[11]   = _weights[9];
     707         142 :         _weights[12]   = _weights[8];
     708         142 :         _weights[13]   = _weights[7];
     709         142 :         _weights[14]   = _weights[6];
     710         142 :         _weights[15]   = _weights[5];
     711         142 :         _weights[16]   = _weights[4];
     712         142 :         _weights[17]   = _weights[3];
     713         142 :         _weights[18]   = _weights[2];
     714         142 :         _weights[19]   = _weights[1];
     715         142 :         _weights[20]   = _weights[0];
     716             : 
     717         142 :         return;
     718             :       }
     719             : 
     720         142 :     case FORTYSECOND:
     721             :     case FORTYTHIRD:
     722             :       {
     723         142 :         _points.resize (22);
     724         142 :         _weights.resize(22);
     725             : 
     726         142 :         _points[ 0](0) = -9.9429458548239929207303142116130e-01_R;
     727         142 :         _points[ 1](0) = -9.7006049783542872712395098676527e-01_R;
     728         142 :         _points[ 2](0) = -9.2695677218717400052069293925905e-01_R;
     729         142 :         _points[ 3](0) = -8.6581257772030013653642563701938e-01_R;
     730         142 :         _points[ 4](0) = -7.8781680597920816200427795540835e-01_R;
     731         142 :         _points[ 5](0) = -6.9448726318668278005068983576226e-01_R;
     732         142 :         _points[ 6](0) = -5.8764040350691159295887692763865e-01_R;
     733         142 :         _points[ 7](0) = -4.6935583798675702640633071096641e-01_R;
     734         142 :         _points[ 8](0) = -3.4193582089208422515814742042738e-01_R;
     735         142 :         _points[ 9](0) = -2.0786042668822128547884653391955e-01_R;
     736         142 :         _points[10](0) = -6.9739273319722221213841796118628e-02_R;
     737         142 :         _points[11]    = -_points[10];
     738         142 :         _points[12]    = -_points[9];
     739         142 :         _points[13]    = -_points[8];
     740         142 :         _points[14]    = -_points[7];
     741         142 :         _points[15]    = -_points[6];
     742         142 :         _points[16]    = -_points[5];
     743         142 :         _points[17]    = -_points[4];
     744         142 :         _points[18]    = -_points[3];
     745         142 :         _points[19]    = -_points[2];
     746         142 :         _points[20]    = -_points[1];
     747         142 :         _points[21]    = -_points[0];
     748             : 
     749         142 :         _weights[ 0]   = 1.4627995298272200684991098047185e-02_R;
     750         142 :         _weights[ 1]   = 3.3774901584814154793302246865913e-02_R;
     751         142 :         _weights[ 2]   = 5.2293335152683285940312051273211e-02_R;
     752         142 :         _weights[ 3]   = 6.9796468424520488094961418930218e-02_R;
     753         142 :         _weights[ 4]   = 8.5941606217067727414443681372703e-02_R;
     754         142 :         _weights[ 5]   = 1.0041414444288096493207883783054e-01_R;
     755         142 :         _weights[ 6]   = 1.1293229608053921839340060742175e-01_R;
     756         142 :         _weights[ 7]   = 1.2325237681051242428556098615481e-01_R;
     757         142 :         _weights[ 8]   = 1.3117350478706237073296499253031e-01_R;
     758         142 :         _weights[ 9]   = 1.3654149834601517135257383123152e-01_R;
     759         142 :         _weights[10]   = 1.3925187285563199337541024834181e-01_R;
     760         142 :         _weights[11]   = _weights[10];
     761         142 :         _weights[12]   = _weights[9];
     762         142 :         _weights[13]   = _weights[8];
     763         142 :         _weights[14]   = _weights[7];
     764         142 :         _weights[15]   = _weights[6];
     765         142 :         _weights[16]   = _weights[5];
     766         142 :         _weights[17]   = _weights[4];
     767         142 :         _weights[18]   = _weights[3];
     768         142 :         _weights[19]   = _weights[2];
     769         142 :         _weights[20]   = _weights[1];
     770         142 :         _weights[21]   = _weights[0];
     771             : 
     772         142 :         return;
     773             :       }
     774             : 
     775             : 
     776           0 :     default:
     777           0 :       libmesh_error_msg("Quadrature rule " << _order << " not supported!");
     778             :     }
     779             : }
     780             : 
     781             : } // namespace libMesh