qf11to25.cpp

FreeFem++可以生成高质量的有限元网格。可以用于流体力学

#include <stdlib.h>
#include <math.h>
#include <iostream>
#include <fstream>
#include "error.hpp"
#include "AFunction.hpp"
using namespace std;


#include "RNM.hpp"
#include "rgraph.hpp"
#include "fem.hpp"
#include "QuadratureFormular.hpp"
using  namespace Fem2D ; 
/* awk -F[ t=:]* -f tt.awk  coords.txt >QF.cpp

/integration/ { if(ii) {print "};" 
  print "const QuadratureFormular QuadratureFormular_T_" ii "(3," ii " ," N ",P_QuadratureFormular_T_" ii ");"
  print ""
  print ""			 
};ii=$3;N=$5;
 print "static const QuadraturePoint P_QuadratureFormular_T_" $3 "[] = {";}
!/integration/ {print "QuadraturePoint(" $4 "/2," $2"," $3"),"}
END {print "};";
  print "const QuadratureFormular QuadratureFormular_T_" ii "(3," ii " ," N ",P_QuadratureFormular_T_" ii ");"
  print ""
    print ""			 
}
*/
/* 
static const QuadraturePoint P_QuadratureFormular_T_2[] = {
QuadraturePoint(0.6666666666667/2,0.1666666666667,0.6666666666667),
QuadraturePoint(0.6666666666667/2,0.6666666666667,0.1666666666667),
QuadraturePoint(0.6666666666667/2,0.1666666666667,0.1666666666667),
};
const QuadratureFormular QuadratureFormular_T_2(3,2 ,3,P_QuadratureFormular_T_2);


static const QuadraturePoint P_QuadratureFormular_T_4[] = {
QuadraturePoint(0.2199034873106/2,0.0915762135098,0.0915762135098),
QuadraturePoint(0.2199034873106/2,0.8168475729805,0.0915762135098),
QuadraturePoint(0.2199034873106/2,0.0915762135098,0.8168475729805),
QuadraturePoint(0.4467631793560/2,0.1081030181681,0.4459484909160),
QuadraturePoint(0.4467631793560/2,0.4459484909160,0.1081030181681),
QuadraturePoint(0.4467631793560/2,0.4459484909160,0.4459484909160),
};
const QuadratureFormular QuadratureFormular_T_4(3,4 ,6,P_QuadratureFormular_T_4);


static const QuadraturePoint P_QuadratureFormular_T_5[] = {
QuadraturePoint(0.0262712099504/2,0.0000000000000,1.0000000000000),
QuadraturePoint(0.0262716612068/2,1.0000000000000,0.0000000000000),
QuadraturePoint(0.0274163947600/2,0.0000000000000,0.0000000000000),
QuadraturePoint(0.2348383865823/2,0.2673273531185,0.6728199218710),
QuadraturePoint(0.2348412238268/2,0.6728175529461,0.2673288599482),
QuadraturePoint(0.2480251793114/2,0.0649236350054,0.6716530111494),
QuadraturePoint(0.2480304922521/2,0.6716498539042,0.0649251690029),
QuadraturePoint(0.2518604605529/2,0.0654032456800,0.2693789366453),
QuadraturePoint(0.2518660533658/2,0.2693767069140,0.0654054874919),
QuadraturePoint(0.4505789381914/2,0.3386738503896,0.3386799893027),
};
const QuadratureFormular QuadratureFormular_T_5(3,5 ,10,P_QuadratureFormular_T_5);


static const QuadraturePoint P_QuadratureFormular_T_7[] = {
QuadraturePoint(0.0102558174092/2,1.0000000000000,0.0000000000000),
QuadraturePoint(0.0102558174092/2,0.0000000000000,0.0000000000000),
QuadraturePoint(0.0102558174092/2,0.0000000000000,1.0000000000000),
QuadraturePoint(0.1116047046647/2,0.7839656651012,0.0421382841642),
QuadraturePoint(0.1116047046647/2,0.1738960507345,0.7839656651012),
QuadraturePoint(0.1116047046647/2,0.1738960507345,0.0421382841642),
QuadraturePoint(0.1116047046647/2,0.0421382841642,0.1738960507345),
QuadraturePoint(0.1116047046647/2,0.7839656651012,0.1738960507345),
QuadraturePoint(0.1116047046647/2,0.0421382841642,0.7839656651012),
QuadraturePoint(0.1679775595335/2,0.4743880861752,0.4743880861752),
QuadraturePoint(0.1679775595335/2,0.4743880861752,0.0512238276497),
QuadraturePoint(0.1679775595335/2,0.0512238276497,0.4743880861752),
QuadraturePoint(0.2652238803946/2,0.2385615300181,0.5228769399639),
QuadraturePoint(0.2652238803946/2,0.5228769399639,0.2385615300181),
QuadraturePoint(0.2652238803946/2,0.2385615300181,0.2385615300181),
};
const QuadratureFormular QuadratureFormular_T_7(3,7 ,15,P_QuadratureFormular_T_7);


static const QuadraturePoint P_QuadratureFormular_T_9[] = {
QuadraturePoint(0.0519871420646/2,0.0451890097844,0.0451890097844),
QuadraturePoint(0.0519871420646/2,0.0451890097844,0.9096219804312),
QuadraturePoint(0.0519871420646/2,0.9096219804312,0.0451890097844),
QuadraturePoint(0.0707034101784/2,0.7475124727339,0.0304243617288),
QuadraturePoint(0.0707034101784/2,0.2220631655373,0.0304243617288),
QuadraturePoint(0.0707034101784/2,0.7475124727339,0.2220631655373),
QuadraturePoint(0.0707034101784/2,0.2220631655373,0.7475124727339),
QuadraturePoint(0.0707034101784/2,0.0304243617288,0.7475124727339),
QuadraturePoint(0.0707034101784/2,0.0304243617288,0.2220631655373),
QuadraturePoint(0.0909390760952/2,0.1369912012649,0.2182900709714),
QuadraturePoint(0.0909390760952/2,0.6447187277637,0.2182900709714),
QuadraturePoint(0.0909390760952/2,0.1369912012649,0.6447187277637),
QuadraturePoint(0.0909390760952/2,0.2182900709714,0.6447187277637),
QuadraturePoint(0.0909390760952/2,0.2182900709714,0.1369912012649),
QuadraturePoint(0.0909390760952/2,0.6447187277637,0.1369912012649),
QuadraturePoint(0.1032344051380/2,0.0369603304334,0.4815198347833),
QuadraturePoint(0.1032344051380/2,0.4815198347833,0.0369603304334),
QuadraturePoint(0.1032344051380/2,0.4815198347833,0.4815198347833),
QuadraturePoint(0.1881601469167/2,0.4036039798179,0.1927920403641),
QuadraturePoint(0.1881601469167/2,0.4036039798179,0.4036039798179),
QuadraturePoint(0.1881601469167/2,0.1927920403641,0.4036039798179),
};
const QuadratureFormular QuadratureFormular_T_9(3,9 ,21,P_QuadratureFormular_T_9);
*/

static  QuadraturePoint P_QuadratureFormular_T_11[] = {
QuadraturePoint(0.0114082494033/2,0.0000000000000,0.9451704450174),
QuadraturePoint(0.0114082494033/2,0.9451704450173,0.0000000000000),
QuadraturePoint(0.0132691285720/2,0.9289002405719,0.0685505797224),
QuadraturePoint(0.0132691285720/2,0.0685505797224,0.9289002405717),
QuadraturePoint(0.0155865773350/2,0.0243268355615,0.0243268355616),
QuadraturePoint(0.0408274780428/2,0.1279662835335,0.0277838749488),
QuadraturePoint(0.0408274780429/2,0.0277838749488,0.1279662835337),
QuadraturePoint(0.0579849665116/2,0.0287083428360,0.7498347588657),
QuadraturePoint(0.0579849665116/2,0.7498347588656,0.0287083428360),
QuadraturePoint(0.0601385247663/2,0.7228007909707,0.2497602062385),
QuadraturePoint(0.0601385247663/2,0.2497602062386,0.7228007909707),
QuadraturePoint(0.0625273888433/2,0.0865562992839,0.8325513856997),
QuadraturePoint(0.0625273888433/2,0.8325513856998,0.0865562992839),
QuadraturePoint(0.0639684321504/2,0.3061619157672,0.0303526617491),
QuadraturePoint(0.0639684321504/2,0.0303526617491,0.3061619157675),
QuadraturePoint(0.0661325872161/2,0.4868610595047,0.4868610595047),
QuadraturePoint(0.0668503236820/2,0.6657904293017,0.1765456154219),
QuadraturePoint(0.0668503236821/2,0.1765456154221,0.6657904293016),
QuadraturePoint(0.0686904305977/2,0.0293121007360,0.5295657488669),
QuadraturePoint(0.0686904305977/2,0.5295657488667,0.0293121007360),
QuadraturePoint(0.1002717543859/2,0.1444673824391,0.1444673824391),
QuadraturePoint(0.1143136784099/2,0.3299740111411,0.5361815729050),
QuadraturePoint(0.1143136784099/2,0.5361815729052,0.3299740111409),
QuadraturePoint(0.1223648146752/2,0.5511507516862,0.1437790861923),
QuadraturePoint(0.1223648146752/2,0.1437790861923,0.5511507516862),
QuadraturePoint(0.1394422334178/2,0.3348066587327,0.1529619437161),
QuadraturePoint(0.1394422334178/2,0.1529619437161,0.3348066587327),
QuadraturePoint(0.1744377829182/2,0.3430183498147,0.3430183498147),
};
const QuadratureFormular QuadratureFormular_T_11(11 ,28,P_QuadratureFormular_T_11);


static  QuadraturePoint P_QuadratureFormular_T_13[] = {
QuadraturePoint(0.0166240998757/2,0.0242935351590,0.9493059293846),
QuadraturePoint(0.0166811699778/2,0.0265193427722,0.0242695130640),
QuadraturePoint(0.0166830569067/2,0.9492126023551,0.0265067966437),
QuadraturePoint(0.0175680870083/2,0.0033775763749,0.4767316412363),
QuadraturePoint(0.0184474661845/2,0.4757672298101,0.5198921829102),
QuadraturePoint(0.0197942410188/2,0.5190783193471,0.0055912706202),
QuadraturePoint(0.0203540395855/2,0.8616839745321,0.0133996048618),
QuadraturePoint(0.0206852863940/2,0.1249209759926,0.8613054321334),
QuadraturePoint(0.0208271366086/2,0.0138565453861,0.1247733717358),
QuadraturePoint(0.0317819778279/2,0.0211887064222,0.8438438351223),
QuadraturePoint(0.0320472035241/2,0.8432296787219,0.1354563645830),
QuadraturePoint(0.0320607681146/2,0.1354231797865,0.0213482820656),
QuadraturePoint(0.0430765959183/2,0.3088853510679,0.0221919663014),
QuadraturePoint(0.0438473415339/2,0.6685057595169,0.3089012879389),
QuadraturePoint(0.0439209672733/2,0.0226545012557,0.6691709943321),
QuadraturePoint(0.0479951923691/2,0.2808515408772,0.6924718155106),
QuadraturePoint(0.0483806260733/2,0.6922446749051,0.0268723345026),
QuadraturePoint(0.0484867423375/2,0.0268617447119,0.2810093973222),
QuadraturePoint(0.0556964488024/2,0.1141778485470,0.7973581413586),
QuadraturePoint(0.0561026364356/2,0.7974807922061,0.0879806508791),
QuadraturePoint(0.0565190123693/2,0.0892807293894,0.1145020561128),
QuadraturePoint(0.0689289890670/2,0.1052487892455,0.6686904119922),
QuadraturePoint(0.0717213336089/2,0.6663022280740,0.2275051631832),
QuadraturePoint(0.0727453920976/2,0.2307803737547,0.1054572561221),
QuadraturePoint(0.0788807336737/2,0.1705059157540,0.5174064398658),
QuadraturePoint(0.0810114345512/2,0.5086593973043,0.3170523855209),
QuadraturePoint(0.0825725299055/2,0.3141823862281,0.1810706361659),
QuadraturePoint(0.0842044567330/2,0.4617460817864,0.4678594539804),
QuadraturePoint(0.0843585533305/2,0.0693087496081,0.4622856042085),
QuadraturePoint(0.0851969868488/2,0.4651955259268,0.0724357805669),
QuadraturePoint(0.0902845328052/2,0.2578625857893,0.6131395039177),
QuadraturePoint(0.0914283143485/2,0.6112627766779,0.1300360834609),
QuadraturePoint(0.0916279065409/2,0.1305182135934,0.2581713828884),
QuadraturePoint(0.1025573374896/2,0.4281437991828,0.2362005969817),
QuadraturePoint(0.1033159661413/2,0.3356995783730,0.4311026308588),
QuadraturePoint(0.1035854367193/2,0.2305424298836,0.3456013949376),
};
const QuadratureFormular QuadratureFormular_T_13(13 ,36,P_QuadratureFormular_T_13);


static  QuadraturePoint P_QuadratureFormular_T_14[] = {
QuadraturePoint(0.0010616711990/2,0.0000000000000,1.0000000000000),
QuadraturePoint(0.0010616711990/2,1.0000000000000,0.0000000000000),
QuadraturePoint(0.0010616711990/2,0.0000000000000,0.0000000000000),
QuadraturePoint(0.0131460236101/2,0.0573330873026,0.0151382269814),
QuadraturePoint(0.0131460236101/2,0.0573330873026,0.9275286857160),
QuadraturePoint(0.0131460236101/2,0.9275286857160,0.0573330873026),
QuadraturePoint(0.0131460236101/2,0.0151382269814,0.0573330873026),
QuadraturePoint(0.0131460236101/2,0.9275286857160,0.0151382269814),
QuadraturePoint(0.0131460236101/2,0.0151382269814,0.9275286857160),
QuadraturePoint(0.0242881926949/2,0.8159625040711,0.1659719969565),
QuadraturePoint(0.0242881926949/2,0.8159625040711,0.0180654989724),
QuadraturePoint(0.0242881926949/2,0.1659719969565,0.8159625040711),
QuadraturePoint(0.0242881926949/2,0.0180654989724,0.8159625040711),
QuadraturePoint(0.0242881926949/2,0.1659719969565,0.0180654989724),
QuadraturePoint(0.0242881926949/2,0.0180654989724,0.1659719969565),
QuadraturePoint(0.0316799866332/2,0.3165475556378,0.0186886898773),