quadrature_jacobi_1d.c

一个用来实现偏微分方程中网格的计算库

	  {
	    _points.resize (17);
	    _weights.resize(17);

	    _points[ 0](0)=4.2297654864907678749919877813007e-03L;	_weights[ 0]=1.0748151030768621662834062204936e-02L;
	    _points[ 1](0)=2.2152705311830232294209002101573e-02L;	_weights[ 1]=2.3837762018703244620506074665265e-02L;
	    _points[ 2](0)=5.3856014827184829566760322013645e-02L;	_weights[ 2]=3.4307889795671880028436869439002e-02L;
	    _points[ 3](0)=9.8434936830541362494246924237098e-02L;	_weights[ 3]=4.1143975847068207121110777965721e-02L;
	    _points[ 4](0)=1.5460792826588562987838903880788e-01L;	_weights[ 4]=4.3922618772592577808611328095136e-02L;
	    _points[ 5](0)=2.2075922519215138391363787768336e-01L;	_weights[ 5]=4.2825403927934553301439133345126e-02L;
	    _points[ 6](0)=2.9498586629802348865100598497056e-01L;	_weights[ 6]=3.8555241947102353628223582107170e-02L;
	    _points[ 7](0)=3.7515254164081788200834771392226e-01L;	_weights[ 7]=3.2163570112378639217164962127759e-02L;
	    _points[ 8](0)=4.5895305335301908085933451474375e-01L;	_weights[ 8]=2.4829256111976082802381065145755e-02L;
	    _points[ 9](0)=5.4397667809047570974515217435547e-01L;	_weights[ 9]=1.7638789331050110518481458865839e-02L;
	    _points[10](0)=6.2777753854681427256560538094776e-01L;	_weights[10]=1.1413642238636687747573403275566e-02L;
	    _points[11](0)=7.0794500138508556794362242607309e-01L;	_weights[11]=6.6164197603617147286557116199452e-03L;
	    _points[12](0)=7.8217310308122112810113854015572e-01L;	_weights[12]=3.3465172918198153715474254116460e-03L;
	    _points[13](0)=8.4832708570995060757906353137179e-01L;	_weights[13]=1.4138837589561322316624033902623e-03L;
	    _points[14](0)=9.0450542331432870037906100932836e-01L;	_weights[14]=4.6167405877711308077043506706165e-04L;
	    _points[15](0)=9.4909701659654457024654762835657e-01L;	_weights[15]=9.9356525335473959962406835119113e-05L;
	    _points[16](0)=9.8084389384741256367666372092760e-01L;	_weights[16]=9.1808042001255039722337720228143e-06L;
	
	    return;
	  }

	case THIRTYFOURTH:
	case THIRTYFIFTH:
	  {
	    _points.resize (18);
	    _weights.resize(18);

	    _points[ 0](0)=3.8065822475018763836485343548908e-03L;	_weights[ 0]=9.6823988037660231774964807691529e-03L;
	    _points[ 1](0)=1.9948351047343018666301273550578e-02L;	_weights[ 1]=2.1578772679193827027157750409882e-02L;
	    _points[ 2](0)=4.8549645304224630965525818224597e-02L;	_weights[ 2]=3.1333907671729513327950397913143e-02L;
	    _points[ 3](0)=8.8876259116497388048181392194957e-02L;	_weights[ 3]=3.8075134253447687665457823100366e-02L;
	    _points[ 4](0)=1.3988457083516926493003835526765e-01L;	_weights[ 4]=4.1377182287519565332651504100178e-02L;
	    _points[ 5](0)=2.0025369592363033820671255853211e-01L;	_weights[ 5]=4.1283665809957749414286828772884e-02L;
	    _points[ 6](0)=2.6842018278660208442014712803618e-01L;	_weights[ 6]=3.8262794672349299757849656256339e-02L;
	    _points[ 7](0)=3.4261859780200830045140484446480e-01L;	_weights[ 7]=3.3095976202072497795672769135623e-02L;
	    _points[ 8](0)=4.2092727587031795580391095608392e-01L;	_weights[ 8]=2.6723424368960119486097972811646e-02L;
	    _points[ 9](0)=5.0131810275027358836467598537906e-01L;	_weights[ 9]=2.0078641696369720179443819032712e-02L;
	    _points[10](0)=5.8170905267091792822883758529331e-01L;	_weights[10]=1.3943897653647906425703531920973e-02L;
	    _points[11](0)=6.6001812722531554655212340270381e-01L;	_weights[11]=8.8522782250949774435502470347624e-03L;
	    _points[12](0)=7.3421730813501325031921736140253e-01L;	_weights[12]=5.0502487883546813166841235600508e-03L;
	    _points[13](0)=8.0238514983641747020667379058517e-01L;	_weights[13]=2.5207216384362558022745702364513e-03L;
	    _points[14](0)=8.6275672070005501336081662021610e-01L;	_weights[14]=1.0535502839571923712409403476880e-03L;
	    _points[15](0)=9.1376986411079293616612318979159e-01L;	_weights[15]=3.4109120368765498289598525047321e-04L;
	    _points[16](0)=9.5410789551731665881890309384613e-01L;	_weights[16]=7.2937008664118705328162954331465e-05L;
	    _points[17](0)=9.8274840759428696063307389954630e-01L;	_weights[17]=6.7100861245431215907697266774769e-06L;
	
	    return;
	  }

	case THIRTYSIXTH:
	case THIRTYSEVENTH:
	  {
	    _points.resize (19);
	    _weights.resize(19);

	    _points[ 0](0)=3.4438904038624902806940509331722e-03L;	_weights[ 0]=8.7672970568792323661393261305840e-03L;
	    _points[ 1](0)=1.8056978337900562863030093954343e-02L;	_weights[ 1]=1.9620856340232434512901283777202e-02L;
	    _points[ 2](0)=4.3987395090842734455198832773659e-02L;	_weights[ 2]=2.8708149778704086122791006941433e-02L;
	    _points[ 3](0)=8.0633276366661415469721776663016e-02L;	_weights[ 3]=3.5278117199476000434599584597235e-02L;
	    _points[ 4](0)=1.2713640986156026953002535083969e-01L;	_weights[ 4]=3.8922386222261737550985848811514e-02L;
	    _points[ 5](0)=1.8240698366909185313069695387128e-01L;	_weights[ 5]=3.9598248214880677015066061570123e-02L;
	    _points[ 6](0)=2.4514956909516857055249217701821e-01L;	_weights[ 6]=3.7607500520347543950912173611332e-02L;
	    _points[ 7](0)=3.1389356741821822415240859865307e-01L;	_weights[ 7]=3.3525068070610283960905700567460e-02L;
	    _points[ 8](0)=3.8702770276933220341545290751683e-01L;	_weights[ 8]=2.8091607936102907649141378579235e-02L;
	    _points[ 9](0)=4.6283779855202027820220487054694e-01L;	_weights[ 9]=2.2090563149823990465333672755377e-02L;
	    _points[10](0)=5.3954696279208808766943066332998e-01L;	_weights[10]=1.6231815321996325630177612472423e-02L;
	    _points[11](0)=6.1535724480454716546694016358337e-01L;	_weights[11]=1.1061440629037007897211784796273e-02L;
	    _points[12](0)=6.8849179091409498918986551203802e-01L;	_weights[12]=6.9108110779321981973514541466546e-03L;
	    _points[13](0)=7.5723651917329793549736932794667e-01L;	_weights[13]=3.8897848125530902102984958782958e-03L;
	    _points[14](0)=8.1998035706323733537954006841029e-01L;	_weights[14]=1.9197884726923132048372710905667e-03L;
	    _points[15](0)=8.7525316298382668006594890887609e-01L;	_weights[15]=7.9504432544855937325482850317179e-04L;
	    _points[16](0)=9.2176068172914004889937421632274e-01L;	_weights[16]=2.5553085889097125647555166013802e-04L;
	    _points[17](0)=9.5841690242340714510347790926694e-01L;	_weights[17]=5.4342643132004416773622274012570e-05L;
	    _points[18](0)=9.8438280655170201067612761745569e-01L;	_weights[18]=4.9807023319691181766751703037610e-06L;
	
	    return;
	  }

	case THIRTYEIGHTH:
	case THIRTYNINTH:
	  {
	    _points.resize (20);
	    _weights.resize(20);

	    _points[ 0](0)=3.1306837407435895621501417495463e-03L;	_weights[ 0]=7.9757927362766516852273101574255e-03L;
	    _points[ 1](0)=1.6422088133987832902541614256258e-02L;	_weights[ 1]=1.7913752325738559101773958866323e-02L;
	    _points[ 2](0)=4.0036900461906780996320149828793e-02L;	_weights[ 2]=2.6382564429125584794513408474046e-02L;
	    _points[ 3](0)=7.3477191785285283057566545285874e-02L;	_weights[ 3]=3.2734644317573148047479656498988e-02L;
	    _points[ 4](0)=1.1603090765548680494669743156748e-01L;	_weights[ 4]=3.6587916553227064986609295576925e-02L;
	    _points[ 5](0)=1.6679125348100943001298070145849e-01L;	_weights[ 5]=3.7847390376922340715354694449373e-02L;
	    _points[ 6](0)=2.2467641938430503840938196483210e-01L;	_weights[ 6]=3.6697420472018132713254249570653e-02L;
	    _points[ 7](0)=2.8845271218127238477194070665240e-01L;	_weights[ 7]=3.3556431453475493479002714822739e-02L;
	    _points[ 8](0)=3.5676087010245310564705506663326e-01L;	_weights[ 8]=2.9002404745589285169916357261403e-02L;
	    _points[ 9](0)=4.2814504093325668461542503477245e-01L;	_weights[ 9]=2.3682290414246053980866450266495e-02L;
	    _points[10](0)=5.0108381548284855137062465413693e-01L;	_weights[10]=1.8220503418268691551843315309759e-02L;
	    _points[11](0)=5.7402265818282687172751219665371e-01L;	_weights[11]=1.3140919256661651742108133720781e-02L;
	    _points[12](0)=6.4540704577736756661732083476397e-01L;	_weights[12]=8.8135560782433553289252731679767e-03L;
	    _points[13](0)=7.1371561101528768074208343535393e-01L;	_weights[13]=5.4320908061230274500120111426487e-03L;
	    _points[14](0)=7.7749259203548675355112594583658e-01L;	_weights[14]=3.0224891709073793749184859780611e-03L;
	    _points[15](0)=8.3537891463156172517151839471341e-01L;	_weights[15]=1.4774444419714858062838576456553e-03L;
	    _points[16](0)=8.8614130291454714368728293036495e-01L;	_weights[16]=6.0704570426725825415272373108771e-04L;
	    _points[17](0)=9.2869901491875054534509783716727e-01L;	_weights[17]=1.9388830961751181076983851525948e-04L;
	    _points[18](0)=9.6214871215049818970916080642292e-01L;	_weights[18]=4.1039102087320205549074040898061e-05L;
	    _points[19](0)=9.8579578884064184668002313135922e-01L;	_weights[19]=3.7492209933371347725241368372638e-06L;
	
	    return;
	  }


	case FORTIETH:
	case FORTYFIRST:
	  {
	    _points.resize (21);
	    _weights.resize(21);

	    _points[ 0](0)=2.8583506000918943222556277168267e-03L;	_weights[ 0]=7.2866317313744308995629793584932e-03L;
	    _points[ 1](0)=1.4999364972075522340357135916023e-02L;	_weights[ 1]=1.6417061144242818824757454238052e-02L;
	    _points[ 2](0)=3.6593863281140122626545055282186e-02L;	_weights[ 2]=2.4316074956305588348553255406534e-02L;
	    _points[ 3](0)=6.7226441667938638526563947674675e-02L;	_weights[ 3]=3.0423854654878694196479542521305e-02L;
	    _points[ 4](0)=1.0630147973769311755044868847393e-01L;	_weights[ 4]=3.4388553550627421941340376509459e-02L;
	    _points[ 5](0)=1.5305857495571921224970195300963e-01L;	_weights[ 5]=3.6085277384893044986268336555960e-02L;
	    _points[ 6](0)=2.0658770608253356867698033417515e-01L;	_weights[ 6]=3.5615944774693119613624648820995e-02L;
	    _points[ 7](0)=2.6584701401081590981089215154372e-01L;	_weights[ 7]=3.3281046762833346236473134492600e-02L;
	    _points[ 8](0)=3.2968309899010272373734914205452e-01L;	_weights[ 8]=2.9528072702082493907799384765866e-02L;
	    _points[ 9](0)=3.9685347698561900950394342909483e-01L;	_weights[ 9]=2.4885083875255978309567929915161e-02L;
	    _points[10](0)=4.6605076663517464847296649003812e-01L;	_weights[10]=1.9889780066352815019424534213776e-02L;
	    _points[11](0)=5.3592813869303216093268951839176e-01L;	_weights[11]=1.5024528041917190276613254752701e-02L;
	    _points[12](0)=6.0512553397610192844810985230774e-01L;	_weights[12]=1.0666270365508680718786852036243e-02L;
	    _points[13](0)=6.7229614098692961628997049948121e-01L;	_weights[13]=7.0573209743621604363614669672455e-03L;
	    _points[14](0)=7.3613262059728734846410297670221e-01L;	_weights[14]=4.2993100642134152210363702100934e-03L;
	    _points[15](0)=7.9539257374613146232498650332774e-01L;	_weights[15]=2.3686215346115318974092271035074e-03L;
	    _points[16](0)=8.4892277353768883984401746895126e-01L;	_weights[16]=1.1482414207164748272703814817286e-03L;
	    _points[17](0)=8.9568174292546676052820257429765e-01L;	_weights[17]=4.6857361253397420043294612589344e-04L;
	    _points[18](0)=9.3476043640122994798279429359660e-01L;	_weights[18]=1.4884999898655056859287865070751e-04L;
	    _points[19](0)=9.6540160736574245809294907904429e-01L;	_weights[19]=3.1377233396792732027953172274463e-05L;
	    _points[20](0)=9.8702556657875783654690055164718e-01L;	_weights[20]=2.8584835468101709504260347382715e-06L;
	
	    return;
	  }

	case FORTYSECOND:
	case FORTYTHIRD:
	  {
	    _points.resize (22);
	    _weights.resize(22);

	    _points[ 0](0)=2.6200747203711594248593674552649e-03L;	_weights[ 0]=6.6829315239216368796332393406135e-03L;
	    _points[ 1](0)=1.3753657987385804025756750709059e-02L;	_weights[ 1]=1.5098062421623821319493004238262e-02L;
	    _points[ 2](0)=3.3575226848026692714308191640158e-02L;	_weights[ 2]=2.2473713734526648003280648297671e-02L;
	    _points[ 3](0)=6.1735561623069601690826574395308e-02L;	_weights[ 3]=2.8324458025288763364233486167273e-02L;
	    _points[ 4](0)=9.7732696675368642458479884996723e-02L;	_weights[ 4]=3.2329473952869436965326587507885e-02L;
	    _points[ 5](0)=1.4092439775695158519450619775816e-01L;	_weights[ 5]=3.4348599664417779736425965942178e-02L;
	    _points[ 6](0)=1.9053995518421662849913969152881e-01L;	_weights[ 6]=3.4426309828130701949676126316990e-02L;
	    _points[ 7](0)=2.4569399962450332222446519900435e-01L;	_weights[ 7]=3.2774586900497126738748991342107e-02L;
	    _points[ 8](0)=3.0540231844259902315260853518244e-01L;	_weights[ 8]=2.9737336628427308246400548097974e-02L;
	    _points[ 9](0)=3.6859942495594128250321664201293e-01L;	_weights[ 9]=2.5741821234796918381507016798653e-02L;
	    _points[10](0)=4.3415757484015513750820121247106e-01L;	_weights[10]=2.1244167813524304464862872202199e-02L;
	    _points[11](0)=5.0090689264793505011775015892772e-01L;	_weights[11]=1.6676482379699419616981906191727e-02L;
	    _points[12](0)=5.6765625027260978702177266771788e-01L;	_weights[12]=1.2402453510959574984251948178874e-02L;
	    _points[13](0)=6.3321452557266284279166256182373e-01L;	_weights[13]=8.6866984738749141556196547655377e-03L;
	    _points[14](0)=6.9641186298595172661126707689713e-01L;	_weights[14]=5.6807683849250404394970034550940e-03L;
	    _points[15](0)=7.5612055917893487122928793527786e-01L;	_weights[15]=3.4260685209698087638377353482425e-03L;
	    _points[16](0)=8.1127520683922050787811864631196e-01L;	_weights[16]=1.8713879532585689543042377871244e-03L;
	    _points[17](0)=8.6089175276286621730656128908876e-01L;	_weights[17]=9.0066625279251987400261357834378e-04L;
	    _points[18](0)=9.0408517849775272066170136431884e-01L;	_weights[18]=3.6536328467284676654467859219800e-04L;
	    _points[19](0)=9.4008566921081846961603077466108e-01L;	_weights[19]=1.1551470917602499323205530447797e-04L;
	    _points[20](0)=9.6825388381656365288164210087944e-01L;	_weights[20]=2.4263177919766775694554800111547e-05L;
	    _points[21](0)=9.8810245999087788318348935085438e-01L;	_weights[21]=2.2049570604019597784590797971169e-06L;
	
	    return;
	  }

      
	default:
	  {
	    std::cerr << "Quadrature rule " << _order
		      << " not supported!" << std::endl;
	      
	    libmesh_error();
	  }
	} // end switch(_order + 2*p)

      libmesh_error();
    } // end else if ((_alpha == 2) && (_beta == 0))

  else
    {
      std::cerr << "Unsupported combination of (alpha,beta) = ("
		<< _alpha
		<< ","
		<< _beta
		<< ") requested in Jacobi-Gauss quadrature rule."
		<< std::endl;
    }

  
  return;
}