quadrature_gauss_1d.c

一个用来实现偏微分方程中网格的计算库

	_points[ 0](0) = -9.8799251802048542848956571858661e-01L;
	_points[ 1](0) = -9.3727339240070590430775894771021e-01L;
	_points[ 2](0) = -8.4820658341042721620064832077422e-01L;
	_points[ 3](0) = -7.2441773136017004741618605461394e-01L;
	_points[ 4](0) = -5.7097217260853884753722673725391e-01L;
	_points[ 5](0) = -3.9415134707756336989720737098105e-01L;
	_points[ 6](0) = -2.0119409399743452230062830339460e-01L;
	_points[ 7](0) = 0.;
	_points[ 8]    = -_points[6];
	_points[ 9]    = -_points[5];
	_points[10]    = -_points[4];
	_points[11]    = -_points[3];
	_points[12]    = -_points[2];
	_points[13]    = -_points[1];
	_points[14]    = -_points[0];

	_weights[ 0]   = 3.0753241996117268354628393577204e-02L;
	_weights[ 1]   = 7.0366047488108124709267416450667e-02L;
	_weights[ 2]   = 1.0715922046717193501186954668587e-01L;
	_weights[ 3]   = 1.3957067792615431444780479451103e-01L;
	_weights[ 4]   = 1.6626920581699393355320086048121e-01L;
	_weights[ 5]   = 1.8616100001556221102680056186642e-01L;
	_weights[ 6]   = 1.9843148532711157645611832644384e-01L;
	_weights[ 7]   = 2.0257824192556127288062019996752e-01L;
	_weights[ 8]   = _weights[6];
	_weights[ 9]   = _weights[5];
	_weights[10]   = _weights[4];
	_weights[11]   = _weights[3];
	_weights[12]   = _weights[2];
	_weights[13]   = _weights[1];
	_weights[14]   = _weights[0];

	return;
      }

    case THIRTIETH:
    case THIRTYFIRST:
      {
	_points.resize (16);
	_weights.resize(16);

	_points[ 0](0) = -9.8940093499164993259615417345033e-01L;
	_points[ 1](0) = -9.4457502307323257607798841553461e-01L;
	_points[ 2](0) = -8.6563120238783174388046789771239e-01L;
	_points[ 3](0) = -7.5540440835500303389510119484744e-01L;
	_points[ 4](0) = -6.1787624440264374844667176404879e-01L;
	_points[ 5](0) = -4.5801677765722738634241944298358e-01L;
	_points[ 6](0) = -2.8160355077925891323046050146050e-01L;
	_points[ 7](0) = -9.5012509837637440185319335424958e-02L;
	_points[ 8]    = -_points[7];
	_points[ 9]    = -_points[6];
	_points[10]    = -_points[5];
	_points[11]    = -_points[4];
	_points[12]    = -_points[3];
	_points[13]    = -_points[2];
	_points[14]    = -_points[1];
	_points[15]    = -_points[0];

	_weights[ 0]   = 2.7152459411754094851780572456018e-02L;
	_weights[ 1]   = 6.2253523938647892862843836994378e-02L;
	_weights[ 2]   = 9.5158511682492784809925107602246e-02L;
	_weights[ 3]   = 1.2462897125553387205247628219202e-01L;
	_weights[ 4]   = 1.4959598881657673208150173054748e-01L;
	_weights[ 5]   = 1.6915651939500253818931207903033e-01L;
	_weights[ 6]   = 1.8260341504492358886676366796922e-01L;
	_weights[ 7]   = 1.8945061045506849628539672320828e-01L;
	_weights[ 8]   = _weights[7];
	_weights[ 9]   = _weights[6];
	_weights[10]   = _weights[5];
	_weights[11]   = _weights[4];
	_weights[12]   = _weights[3];
	_weights[13]   = _weights[2];
	_weights[14]   = _weights[1];
	_weights[15]   = _weights[0];

	return;
      }

    case THIRTYSECOND:
    case THIRTYTHIRD:
      {
	_points.resize (17);
	_weights.resize(17);

	_points[ 0](0) = -9.9057547531441733567543401994067e-01L;
	_points[ 1](0) = -9.5067552176876776122271695789580e-01L;
	_points[ 2](0) = -8.8023915372698590212295569448816e-01L;
	_points[ 3](0) = -7.8151400389680140692523005552048e-01L;
	_points[ 4](0) = -6.5767115921669076585030221664300e-01L;
	_points[ 5](0) = -5.1269053708647696788624656862955e-01L;
	_points[ 6](0) = -3.5123176345387631529718551709535e-01L;
	_points[ 7](0) = -1.7848418149584785585067749365407e-01L;
	_points[ 8](0) = 0.;
	_points[ 9]    = -_points[7];
	_points[10]    = -_points[6];
	_points[11]    = -_points[5];
	_points[12]    = -_points[4];
	_points[13]    = -_points[3];
	_points[14]    = -_points[2];
	_points[15]    = -_points[1];
	_points[16]    = -_points[0];

	_weights[ 0]   = 2.4148302868547931960110026287565e-02L;
	_weights[ 1]   = 5.5459529373987201129440165358245e-02L;
	_weights[ 2]   = 8.5036148317179180883535370191062e-02L;
	_weights[ 3]   = 1.1188384719340397109478838562636e-01L;
	_weights[ 4]   = 1.3513636846852547328631998170235e-01L;
	_weights[ 5]   = 1.5404576107681028808143159480196e-01L;
	_weights[ 6]   = 1.6800410215645004450997066378832e-01L;
	_weights[ 7]   = 1.7656270536699264632527099011320e-01L;
	_weights[ 8]   = 1.7944647035620652545826564426189e-01L;
	_weights[ 9]   = _weights[7];
	_weights[10]   = _weights[6];
	_weights[11]   = _weights[5];
	_weights[12]   = _weights[4];
	_weights[13]   = _weights[3];
	_weights[14]   = _weights[2];
	_weights[15]   = _weights[1];
	_weights[16]   = _weights[0];

	return;
      }

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

	_points[ 0](0) = -9.9156516842093094673001600470615e-01L;
	_points[ 1](0) = -9.5582394957139775518119589292978e-01L;
	_points[ 2](0) = -8.9260246649755573920606059112715e-01L;
	_points[ 3](0) = -8.0370495897252311568241745501459e-01L;
	_points[ 4](0) = -6.9168704306035320787489108128885e-01L;
	_points[ 5](0) = -5.5977083107394753460787154852533e-01L;
	_points[ 6](0) = -4.1175116146284264603593179383305e-01L;
	_points[ 7](0) = -2.5188622569150550958897285487791e-01L;
	_points[ 8](0) = -8.4775013041735301242261852935784e-02L;
	_points[ 9]    = -_points[8];
	_points[10]    = -_points[7];
	_points[11]    = -_points[6];
	_points[12]    = -_points[5];
	_points[13]    = -_points[4];
	_points[14]    = -_points[3];
	_points[15]    = -_points[2];
	_points[16]    = -_points[1];
	_points[17]    = -_points[0];

	_weights[ 0]   = 2.1616013526483310313342710266452e-02L;
	_weights[ 1]   = 4.9714548894969796453334946202639e-02L;
	_weights[ 2]   = 7.6425730254889056529129677616637e-02L;
	_weights[ 3]   = 1.0094204410628716556281398492483e-01L;
	_weights[ 4]   = 1.2255520671147846018451912680020e-01L;
	_weights[ 5]   = 1.4064291467065065120473130375195e-01L;
	_weights[ 6]   = 1.5468467512626524492541800383637e-01L;
	_weights[ 7]   = 1.6427648374583272298605377646593e-01L;
	_weights[ 8]   = 1.6914238296314359184065647013499e-01L;
	_weights[ 9]   = _weights[8];
	_weights[10]   = _weights[7];
	_weights[11]   = _weights[6];
	_weights[12]   = _weights[5];
	_weights[13]   = _weights[4];
	_weights[14]   = _weights[3];
	_weights[15]   = _weights[2];
	_weights[16]   = _weights[1];
	_weights[17]   = _weights[0];

	return;
      }

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

	_points[ 0](0) = -9.9240684384358440318901767025326e-01L;
	_points[ 1](0) = -9.6020815213483003085277884068765e-01L;
	_points[ 2](0) = -9.0315590361481790164266092853231e-01L;
	_points[ 3](0) = -8.2271465653714282497892248671271e-01L;
	_points[ 4](0) = -7.2096617733522937861709586082378e-01L;
	_points[ 5](0) = -6.0054530466168102346963816494624e-01L;
	_points[ 6](0) = -4.6457074137596094571726714810410e-01L;
	_points[ 7](0) = -3.1656409996362983199011732884984e-01L;
	_points[ 8](0) = -1.6035864564022537586809611574074e-01L;
	_points[ 9](0) = 0.;
	_points[10]    = -_points[8];
	_points[11]    = -_points[7];
	_points[12]    = -_points[6];
	_points[13]    = -_points[5];
	_points[14]    = -_points[4];
	_points[15]    = -_points[3];
	_points[16]    = -_points[2];
	_points[17]    = -_points[1];
	_points[18]    = -_points[0];

	_weights[ 0]   = 1.9461788229726477036312041464438e-02L;
	_weights[ 1]   = 4.4814226765699600332838157401994e-02L;
	_weights[ 2]   = 6.9044542737641226580708258006013e-02L;
	_weights[ 3]   = 9.1490021622449999464462094123840e-02L;
	_weights[ 4]   = 1.1156664554733399471602390168177e-01L;
	_weights[ 5]   = 1.2875396253933622767551578485688e-01L;
	_weights[ 6]   = 1.4260670217360661177574610944190e-01L;
	_weights[ 7]   = 1.5276604206585966677885540089766e-01L;
	_weights[ 8]   = 1.5896884339395434764995643946505e-01L;
	_weights[ 9]   = 1.6105444984878369597916362532092e-01L;
	_weights[10]   = _weights[8];
	_weights[11]   = _weights[7];
	_weights[12]   = _weights[6];
	_weights[13]   = _weights[5];
	_weights[14]   = _weights[4];
	_weights[15]   = _weights[3];
	_weights[16]   = _weights[2];
	_weights[17]   = _weights[1];
	_weights[18]   = _weights[0];

	return;
      }

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

	_points[ 0](0) = -9.9312859918509492478612238847132e-01L;
	_points[ 1](0) = -9.6397192727791379126766613119728e-01L;
	_points[ 2](0) = -9.1223442825132590586775244120330e-01L;
	_points[ 3](0) = -8.3911697182221882339452906170152e-01L;
	_points[ 4](0) = -7.4633190646015079261430507035564e-01L;
	_points[ 5](0) = -6.3605368072651502545283669622629e-01L;
	_points[ 6](0) = -5.1086700195082709800436405095525e-01L;
	_points[ 7](0) = -3.7370608871541956067254817702493e-01L;
	_points[ 8](0) = -2.2778585114164507808049619536857e-01L;
	_points[ 9](0) = -7.6526521133497333754640409398838e-02L;
	_points[10]    = -_points[9];
	_points[11]    = -_points[8];
	_points[12]    = -_points[7];
	_points[13]    = -_points[6];
	_points[14]    = -_points[5];
	_points[15]    = -_points[4];
	_points[16]    = -_points[3];
	_points[17]    = -_points[2];
	_points[18]    = -_points[1];
	_points[19]    = -_points[0];

	_weights[ 0]   = 1.7614007139152118311861962351853e-02L;
	_weights[ 1]   = 4.0601429800386941331039952274932e-02L;
	_weights[ 2]   = 6.2672048334109063569506535187042e-02L;
	_weights[ 3]   = 8.3276741576704748724758143222046e-02L;
	_weights[ 4]   = 1.0193011981724043503675013548035e-01L;
	_weights[ 5]   = 1.1819453196151841731237737771138e-01L;
	_weights[ 6]   = 1.3168863844917662689849449974816e-01L;
	_weights[ 7]   = 1.4209610931838205132929832506716e-01L;
	_weights[ 8]   = 1.4917298647260374678782873700197e-01L;
	_weights[ 9]   = 1.5275338713072585069808433195510e-01L;
	_weights[10]   = _weights[9];
	_weights[11]   = _weights[8];
	_weights[12]   = _weights[7];
	_weights[13]   = _weights[6];
	_weights[14]   = _weights[5];
	_weights[15]   = _weights[4];
	_weights[16]   = _weights[3];
	_weights[17]   = _weights[2];
	_weights[18]   = _weights[1];
	_weights[19]   = _weights[0];

	return;
      }

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

	_points[ 0](0) = -9.9375217062038950026024203593794e-01L;
	_points[ 1](0) = -9.6722683856630629431662221490770e-01L;
	_points[ 2](0) = -9.2009933415040082879018713371497e-01L;
	_points[ 3](0) = -8.5336336458331728364725063858757e-01L;
	_points[ 4](0) = -7.6843996347567790861587785130623e-01L;
	_points[ 5](0) = -6.6713880419741231930596666999034e-01L;
	_points[ 6](0) = -5.5161883588721980705901879672431e-01L;
	_points[ 7](0) = -4.2434212020743878357366888854379e-01L;
	_points[ 8](0) = -2.8802131680240109660079251606460e-01L;
	_points[ 9](0) = -1.4556185416089509093703098233869e-01L;
	_points[10](0) = 0.;
	_points[11]    = -_points[9];
	_points[12]    = -_points[8];
	_points[13]    = -_points[7];
	_points[14]    = -_points[6];
	_points[15]    = -_points[5];
	_points[16]    = -_points[4];
	_points[17]    = -_points[3];
	_points[18]    = -_points[2];
	_points[19]    = -_points[1];
	_points[20]    = -_points[0];

	_weights[ 0]   = 1.6017228257774333324224616858471e-02L;
	_weights[ 1]   = 3.6953789770852493799950668299330e-02L;
	_weights[ 2]   = 5.7134425426857208283635826472448e-02L;
	_weights[ 3]   = 7.6100113628379302017051653300183e-02L;
	_weights[ 4]   = 9.3444423456033861553289741113932e-02L;
	_weights[ 5]   = 1.0879729916714837766347457807011e-01L;
	_weights[ 6]   = 1.2183141605372853419536717712572e-01L;
	_weights[ 7]   = 1.3226893863333746178105257449678e-01L;
	_weights[ 8]   = 1.3988739479107315472213342386758e-01L;
	_weights[ 9]   = 1.4452440398997005906382716655375e-01L;
	_weights[10]   = 1.4608113364969042719198514768337e-01L;
	_weights[11]   = _weights[9];
	_weights[12]   = _weights[8];
	_weights[13]   = _weights[7];
	_weights[14]   = _weights[6];
	_weights[15]   = _weights[5];
	_weights[16]   = _weights[4];
	_weights[17]   = _weights[3];
	_weights[18]   = _weights[2];
	_weights[19]   = _weights[1];
	_weights[20]   = _weights[0];

	return;
      }

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

	_points[ 0](0) = -9.9429458548239929207303142116130e-01L;
	_points[ 1](0) = -9.7006049783542872712395098676527e-01L;
	_points[ 2](0) = -9.2695677218717400052069293925905e-01L;
	_points[ 3](0) = -8.6581257772030013653642563701938e-01L;
	_points[ 4](0) = -7.8781680597920816200427795540835e-01L;
	_points[ 5](0) = -6.9448726318668278005068983576226e-01L;
	_points[ 6](0) = -5.8764040350691159295887692763865e-01L;
	_points[ 7](0) = -4.6935583798675702640633071096641e-01L;
	_points[ 8](0) = -3.4193582089208422515814742042738e-01L;
	_points[ 9](0) = -2.0786042668822128547884653391955e-01L;
	_points[10](0) = -6.9739273319722221213841796118628e-02L;
	_points[11]    = -_points[10];
	_points[12]    = -_points[9];
	_points[13]    = -_points[8];
	_points[14]    = -_points[7];
	_points[15]    = -_points[6];
	_points[16]    = -_points[5];
	_points[17]    = -_points[4];
	_points[18]    = -_points[3];
	_points[19]    = -_points[2];
	_points[20]    = -_points[1];
	_points[21]    = -_points[0];

	_weights[ 0]   = 1.4627995298272200684991098047185e-02L;
	_weights[ 1]   = 3.3774901584814154793302246865913e-02L;
	_weights[ 2]   = 5.2293335152683285940312051273211e-02L;
	_weights[ 3]   = 6.9796468424520488094961418930218e-02L;
	_weights[ 4]   = 8.5941606217067727414443681372703e-02L;
	_weights[ 5]   = 1.0041414444288096493207883783054e-01L;
	_weights[ 6]   = 1.1293229608053921839340060742175e-01L;
	_weights[ 7]   = 1.2325237681051242428556098615481e-01L;
	_weights[ 8]   = 1.3117350478706237073296499253031e-01L;
	_weights[ 9]   = 1.3654149834601517135257383123152e-01L;
	_weights[10]   = 1.3925187285563199337541024834181e-01L;
	_weights[11]   = _weights[10];
	_weights[12]   = _weights[9];
	_weights[13]   = _weights[8];
	_weights[14]   = _weights[7];
	_weights[15]   = _weights[6];
	_weights[16]   = _weights[5];
	_weights[17]   = _weights[4];
	_weights[18]   = _weights[3];
	_weights[19]   = _weights[2];
	_weights[20]   = _weights[1];
	_weights[21]   = _weights[0];

	return;
      }


    default:
      {
	std::cerr << "Quadrature rule " << _order
		  << " not supported!" << std::endl;
	      
	libmesh_error();
      }
    }



  return;
}