quadrature_jacobi_1d.c

一个用来实现偏微分方程中网格的计算库

	    _points[17](0)=9.6955263708022088547192878623227e-01L;	_weights[17]=8.2788076092398219334600301771448e-04L;
	    _points[18](0)=9.9085180527095568535309483522012e-01L;	_weights[18]=1.4012759417838633744062778723898e-04L;
	
	    return;
	  }

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

	    _points[ 0](0)=3.2761066690500989752646761128711e-03L;	_weights[ 0]=8.3708441762725569742347797346057e-03L;
	    _points[ 1](0)=1.7181218145255713738247704631582e-02L;	_weights[ 1]=1.9034969463701666952317752319364e-02L;
	    _points[ 2](0)=4.1871431117765195244234634143709e-02L;	_weights[ 2]=2.8668237379130596303519483134423e-02L;
	    _points[ 3](0)=7.6800837089621970481870523019947e-02L;	_weights[ 3]=3.6750239836647855880170014918540e-02L;
	    _points[ 4](0)=1.2118986732367606561768615229454e-01L;	_weights[ 4]=4.2890295837978204214146023790200e-02L;
	    _points[ 5](0)=1.7404711263554216522415793419966e-01L;	_weights[ 5]=4.6841691862557827847492882468251e-02L;
	    _points[ 6](0)=2.3419188631359219089445571283230e-01L;	_weights[ 6]=4.8516105059854090810181874268668e-02L;
	    _points[ 7](0)=3.0028067683595016436625841871717e-01L;	_weights[ 7]=4.7985461609943912515256158210751e-02L;
	    _points[ 8](0)=3.7083718058439689644532207953771e-01L;	_weights[ 8]=4.5470588941353475125260875269943e-02L;
	    _points[ 9](0)=4.4428528696301116212882391783598e-01L;	_weights[ 9]=4.1317706816665737825832945172262e-02L;
	    _points[10](0)=5.1898428870357372961841176083024e-01L;	_weights[10]=3.5964919153862747854063187859799e-02L;
	    _points[11](0)=5.9326553348350648796739308654437e-01L;	_weights[11]=2.9901741842629013049082489189589e-02L;
	    _points[12](0)=6.6546969890551364795372958813385e-01L;	_weights[12]=2.3625296173548892813066360441583e-02L;
	    _points[13](0)=7.3398385823565944973202719329584e-01L;	_weights[13]=1.7597066879206016267686128655074e-02L;
	    _points[14](0)=7.9727750833659468770218885137527e-01L;	_weights[14]=1.2204046126680104278798703245791e-02L;
	    _points[15](0)=8.5393675303589045708900439161802e-01L;	_weights[15]=7.7276679300514628735780671415898e-03L;
	    _points[16](0)=9.0269587179345369227634694169967e-01L;	_weights[16]=4.3232191126901531337390520742896e-03L;
	    _points[17](0)=9.4246554236318633869089187742766e-01L;	_weights[17]=2.0114576139640780069071394684122e-03L;
	    _points[18](0)=9.7235694664743691118470187166465e-01L;	_weights[18]=6.8306227608592198451771987553801e-04L;
	    _points[19](0)=9.9169995579293273076654365969470e-01L;	_weights[19]=1.1538190717568529014836276132844e-04L;
	
	    return;
	  }

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

	    _points[ 0](0)=2.9852372832130627418887840757498e-03L;	_weights[ 0]=7.6306059065231890951709176867159e-03L;
	    _points[ 1](0)=1.5662280557573547332895610655678e-02L;	_weights[ 1]=1.7387926076195012545310092581185e-02L;
	    _points[ 2](0)=3.8198288245073553344832819395658e-02L;	_weights[ 2]=2.6287260083203306468723755830943e-02L;
	    _points[ 3](0)=7.0139619062325798139842656763758e-02L;	_weights[ 3]=3.3886790344403175515158905218748e-02L;
	    _points[ 4](0)=1.1083667332036350223762530758616e-01L;	_weights[ 4]=3.9845977571398966444570950002831e-02L;
	    _points[ 5](0)=1.5946112944406525026381380836555e-01L;	_weights[ 5]=4.3935570635150377464859835729052e-02L;
	    _points[ 6](0)=2.1502318535802028508091216764592e-01L;	_weights[ 6]=4.6050270723257502074077985626262e-02L;
	    _points[ 7](0)=2.7639177909378317240968620976306e-01L;	_weights[ 7]=4.6212552611022412660350368837561e-02L;
	    _points[ 8](0)=3.4231763295873079372348132371246e-01L;	_weights[ 8]=4.4566874686154606866984823191992e-02L;
	    _points[ 9](0)=4.1145869156190519892697533612651e-01L;	_weights[ 9]=4.1364760396997617354403702904192e-02L;
	    _points[10](0)=4.8240744461243888053531852185958e-01L;	_weights[10]=3.6942012648499385551903205764287e-02L;
	    _points[11](0)=5.5371958072829359140036561243486e-01L;	_weights[11]=3.1689953050127340376763333466278e-02L;
	    _points[12](0)=6.2394338972128194749630581474409e-01L;	_weights[12]=2.6023046795895555117823162899995e-02L;
	    _points[13](0)=6.9164931501296225721944667896925e-01L;	_weights[13]=2.0345549389821508292035088652126e-02L;
	    _points[14](0)=7.5545905444968698626584997281486e-01L;	_weights[14]=1.5019872613192784763520392446339e-02L;
	    _points[15](0)=8.1407361651269741678894410957934e-01L;	_weights[15]=1.0339209757970312663832726410241e-02L;
	    _points[16](0)=8.6629975897095659707636330435792e-01L;	_weights[16]=6.5065974236456053354067512991831e-03L;
	    _points[17](0)=9.1107426580261577477966643276619e-01L;	_weights[17]=3.6220528697449398652362737797211e-03L;
	    _points[18](0)=9.4748554440639734668609897166113e-01L;	_weights[18]=1.6787560215669155362763365937815e-03L;
	    _points[19](0)=9.7479197566036565307915209128675e-01L;	_weights[19]=5.6849852669976417861179123569953e-04L;
	    _points[20](0)=9.9243549072562147749379027938900e-01L;	_weights[20]=9.5861868529721828979599842865244e-05L;
	
	    return;
	  }

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

	    _points[ 0](0)=2.7314460088842296840089704503200e-03L;	_weights[ 0]=6.9842561136978136538216549700282e-03L;
	    _points[ 1](0)=1.4335933483699706185308039285053e-02L;	_weights[ 1]=1.5944053454778496864565929126309e-02L;
	    _points[ 2](0)=3.4986328351216449387218814071085e-02L;	_weights[ 2]=2.4184236671890499758870393233781e-02L;
	    _points[ 3](0)=6.4302641132158882531275071395686e-02L;	_weights[ 3]=3.1327596999375227892408958559682e-02L;
	    _points[ 4](0)=1.0173934345216392401258226593794e-01L;	_weights[ 4]=3.7077054093202864483217335909271e-02L;
	    _points[ 5](0)=1.4659920015766541692656584266952e-01L;	_weights[ 5]=4.1222404906411452577079119693783e-02L;
	    _points[ 6](0)=1.9804660411818261484660504028001e-01L;	_weights[ 6]=4.3651203786303462995293138094828e-02L;
	    _points[ 7](0)=2.5512320697168696957682873507625e-01L;	_weights[ 7]=4.4353370900419806188626977124445e-02L;
	    _points[ 8](0)=3.1676578871044727183421117602379e-01L;	_weights[ 8]=4.3418750145417827908334525766667e-02L;
	    _points[ 9](0)=3.8182606925675020305095127628112e-01L;	_weights[ 9]=4.1027795781940901638265438618895e-02L;
	    _points[10](0)=4.4909210098681733251387195042393e-01L;	_weights[10]=3.7436116466930019239662981188891e-02L;
	    _points[11](0)=5.1731084595099112005136286684174e-01L;	_weights[11]=3.2954058785385534039887856528676e-02L;
	    _points[12](0)=5.8521151795129912975524533467408e-01L;	_weights[12]=2.7922870823442631249079662456458e-02L;
	    _points[13](0)=6.5152925489581447403580682231185e-01L;	_weights[13]=2.2689228598160995380212860776143e-02L;
	    _points[14](0)=7.1502868047476240261215783933800e-01L;	_weights[14]=1.7580017560152292742735027157072e-02L;
	    _points[15](0)=7.7452691606482263532020273841099e-01L;	_weights[15]=1.2879230281365339696348205046681e-02L;
	    _points[16](0)=8.2891561362172651235400549854277e-01L;	_weights[16]=8.8086724401109070881737532508054e-03L;
	    _points[17](0)=8.7718159746542002099358323827803e-01L;	_weights[17]=5.5138751021276410109163746634529e-03L;
	    _points[18](0)=9.1842572498984926327926994425432e-01L;	_weights[18]=3.0562141131504037344643025112362e-03L;
	    _points[19](0)=9.5187959322971991452332541323047e-01L;	_weights[19]=1.4117668531394242829582650189559e-03L;
	    _points[20](0)=9.7691966323712886717816657113704e-01L;	_weights[20]=4.7692790565900675904839748933142e-04L;
	    _points[21](0)=9.9307748504434821490300210664154e-01L;	_weights[21]=8.0298216937450816028842814607537e-05L;
	
	    return;
	  }
      
	default:
	  {
	    std::cerr << "Quadrature rule " << _order
		      << " not supported!" << std::endl;
	      
	    libmesh_error();
	  }
	} // end switch(_order + 2*p)

      libmesh_error();
    } // end if ((_alpha == 1) && (_beta == 0))


  
  else if ((_alpha == 2) && (_beta == 0))
    {
      
      switch(_order + 2*p)
	{
	case CONSTANT:
	case FIRST:
	  {
	    _points.resize (1);
	    _weights.resize(1);
	
	    _points[0](0)  = 0.25;
	
	    _weights[0]    = 1./3.;
	
	    return;
	  }
	case SECOND:
	case THIRD:
	  {
	    _points.resize (2);
	    _weights.resize(2);
	    
	    _points[ 0](0)=1.2251482265544137786674043037115e-01L;	_weights[ 0]=2.3254745125350790274997694884235e-01L;
	    _points[ 1](0)=5.4415184401122528879992623629551e-01L;	_weights[ 1]=1.0078588207982543058335638449099e-01L;

	    return;
	  }
	case FOURTH:
	case FIFTH:
	  {
	    _points.resize (3);
	    _weights.resize(3);
	      
	    _points[ 0](0)=7.2994024073149732155837979012003e-02L;	_weights[ 0]=1.5713636106488661331834482221327e-01L;
	    _points[ 1](0)=3.4700376603835188472176354340395e-01L;	_weights[ 1]=1.4624626925986602200351202036424e-01L;
	    _points[ 2](0)=7.0500220988849838312239847758405e-01L;	_weights[ 2]=2.9950703008580698011476490755827e-02L;

	    return;
	  }
	case SIXTH:
	case SEVENTH:
	  {
	    _points.resize (4);
	    _weights.resize(4);
	      
	    _points[ 0](0)=4.8500549446997329297067257098986e-02L;	_weights[ 0]=1.1088841561127798368323131746895e-01L;
	    _points[ 1](0)=2.3860073755186230505898141272470e-01L;	_weights[ 1]=1.4345878979921420904832801427594e-01L;
	    _points[ 2](0)=5.1704729510436750234057336938307e-01L;	_weights[ 2]=6.8633887172923075317376345041811e-02L;
	    _points[ 3](0)=7.9585141789677286330337796079324e-01L;	_weights[ 3]=1.0352240749918065284397656546639e-02L;

	    return;
	  }
	case EIGHTH:
	case NINTH:
	  {
	    _points.resize (5);
	    _weights.resize(5);
	      
	    _points[ 0](0)=3.4578939918215091524457428631527e-02L;	_weights[ 0]=8.1764784285770917904880732922352e-02L;
	    _points[ 1](0)=1.7348032077169572310459241798618e-01L;	_weights[ 1]=1.2619896189991148802883293516467e-01L;
	    _points[ 2](0)=3.8988638706551932824089541038499e-01L;	_weights[ 2]=8.9200161221590000186254493070384e-02L;
	    _points[ 3](0)=6.3433347263088677234716388892062e-01L;	_weights[ 3]=3.2055600722961919254748930556633e-02L;
	    _points[ 4](0)=8.5105421294701641811622418741001e-01L;	_weights[ 4]=4.1138252030990079586162416192983e-03L;

	    return;
	  }
	case TENTH:
	case ELEVENTH:
	  {
	
	    _points.resize (6);
	    _weights.resize(6);
	      
	    _points[ 0](0)=2.5904555093667192754643606997235e-02L;	_weights[ 0]=6.2538702726580937878526556468332e-02L;
	    _points[ 1](0)=1.3156394165798513398691085074097e-01L;	_weights[ 1]=1.0737649973678063260575568234795e-01L;
	    _points[ 2](0)=3.0243691802289123274990557791855e-01L;	_weights[ 2]=9.4577186748541203568292051720052e-02L;
	    _points[ 3](0)=5.0903641316475208401103990516772e-01L;	_weights[ 3]=5.1289571129616210220129325076919e-02L;
	    _points[ 4](0)=7.1568112731171391876766262459361e-01L;	_weights[ 4]=1.5720297184945051327851262130020e-02L;
	    _points[ 5](0)=8.8680561617756186630126600601049e-01L;	_weights[ 5]=1.8310758068692977327784555900562e-03L;

	    return;
	  }
	case TWELFTH:
	case THIRTEENTH:
	  {
	    _points.resize (7);
	    _weights.resize(7);
	      
	    _points[ 0](0)=2.0132773773400507230501687117472e-02L;	_weights[ 0]=4.9276501776438120823429129084905e-02L;
	    _points[ 1](0)=1.0308902914804901475222678600595e-01L;	_weights[ 1]=9.0698824612686144536967479972374e-02L;
	    _points[ 2](0)=2.4055412604805753665369914150100e-01L;	_weights[ 2]=9.1733803279795254111416595896867e-02L;