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|
*DECK ALGPT
SUBROUTINE ALGPT(NGPT,XINF,XSUP,ZGKSI,WGKSI)
*
*-----------------------------------------------------------------------
*
*Purpose:
* returns gauss integration points and weights for integration limits
* specified and to the order specified
*
*Copyright:
* Copyright (C) 1991 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version
*
*Author(s): R. Roy and O. Vagner
*
*Reference:
* integral of F(X)DX , from XINF to XSUP is given by summ from i=1 to
* NGPT of F(ZGKSI(I))*WGKSI(I)
* the points ZGKSI and weights WGKSI are generated according
* to the technique described in Handbook of mathematical functions
* M. Abramowitz and I. Stegun, Dover Publication Inc. (1972);
* all points and weights are taken from A.H. Stroud and D. Secrest,
* gaussian quadrature formulas, Prentice-Hall (1966).
*
*Parameters: input
* NGPT number of gauss points
* XINF lower integration limit
* XSUP upper integration limit
*
*Parameters: output
* ZGKSI integration points
* WGKSI integration weights
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER NGPT
REAL XINF,XSUP,ZGKSI(NGPT),WGKSI(NGPT)
*----
* LOCAL VARIABLES
*----
PARAMETER ( I2= 1, I3= 2, I4= 3, I5= 5, I6= 7, I7=10, I8=13,
> I9=17,I10=21,I11=26,I12=31,I13=37,I14=43,I15=50,
> I16=57,I17=65,I18=73,I19=82,I20=91,I24=101,I28=113,
> I32=127,I64=143,IFN=174)
PARAMETER ( HALF=0.5E0, TWO=2.0E0 )
REAL RZKSI(IFN),RWKSI(IFN),FW,FC
CHARACTER CERROR*4
SAVE RZKSI,RWKSI
C N=2
DATA (RZKSI(I),I=I2,I3-1) / .577350269189626E0/
DATA (RWKSI(I),I=I2,I3-1) / 1.000000000000000E0/
C N=3
DATA (RZKSI(I),I=I3,I4-1) / .774596669241483E0/
DATA (RWKSI(I),I=I3,I4-1) / .555555555555556E0/
C N=4
DATA (RZKSI(I),I=I4,I5-1) / .339981043584856E0,
> .861136311594053E0/
DATA (RWKSI(I),I=I4,I5-1) / .652145154862546E0,
> .347854845137454E0/
C N=5
DATA (RZKSI(I),I=I5,I6-1) / .538469310105683E0,
> .906179845938664E0/
DATA (RWKSI(I),I=I5,I6-1) / .478628670499366E0,
> .236926885056189E0/
C N=6
DATA (RZKSI(I),I=I6,I7-1) / .238619186083197E0,
> .661209386466265E0,
> .932469514203152E0/
DATA (RWKSI(I),I=I6,I7-1) / .467913934572691E0,
> .360761573048139E0,
> .171324492379170E0/
C N=7
DATA (RZKSI(I),I=I7,I8-1) / .405845151377397E0,
> .741531185599394E0,
> .949107912342759E0/
DATA (RWKSI(I),I=I7,I8-1) / .381830050505119E0,
> .279705391489277E0,
> .129484966168870E0/
C N=8
DATA (RZKSI(I),I=I8,I9-1) / .183434642495650E0,
> .525532409916329E0,
> .796666477413627E0,
> .960289856497536E0/
DATA (RWKSI(I),I=I8,I9-1) / .362683783378362E0,
> .313706645877887E0,
> .222381034453374E0,
> .101228536290376E0/
C N=9
DATA (RZKSI(I),I=I9,I10-1) / .324253423403809E0,
> .613371432700590E0,
> .836031107326636E0,
> .968160239507626E0/
DATA (RWKSI(I),I=I9,I10-1) / .312347077040003E0,
> .260610696402935E0,
> .180648160694857E0,
> .081274388361574E0/
C N=10
DATA (RZKSI(I),I=I10,I11-1) / .148874338981631E0,
> .433395394129247E0,
> .679409568299024E0,
> .865063366688985E0,
> .973906528517172E0/
DATA (RWKSI(I),I=I10,I11-1) / .295524224714753E0,
> .269266719309996E0,
> .219086362515982E0,
> .149451349150581E0,
> .066671344308688E0/
C N=11
DATA (RZKSI(I),I=I11,I12-1) /
> .978228658146057E0,.887062599768095E0,
> .730152005574049E0,.519096129206812E0,
> .269543155952345E0/
DATA (RWKSI(I),I=I11,I12-1) /
> .055668567116174E0,.125580369464905E0,
> .186290210927734E0,.233193764591990E0,
> .262804544510247E0/
C N=12
DATA (RZKSI(I),I=I12,I13-1) /
> .125233408511469E0,.367831498998180E0,
> .587317954286617E0,.769902674194305E0,
> .904117256370475E0,.981560634246719E0/
DATA (RWKSI(I),I=I12,I13-1) /
> .249147045813403E0,.233492536538355E0,
> .203167426723066E0,.160078328543346E0,
> .106939325995318E0,.047175336386512E0/
C N=13
DATA (RZKSI(I),I=I13,I14-1) /
> .984183054718588E0,.917598399222978E0,
> .801578090733310E0,.642349339440340E0,
> .448492751036447E0,.230458315955135E0/
DATA (RWKSI(I),I=I13,I14-1) /
> .040484004765316E0,.092121499837728E0,
> .138873510219787E0,.178145980761946E0,
> .207816047536888E0,.226283180262897E0/
C N=14
DATA (RZKSI(I),I=I14,I15-1) /
> .986283808696812E0,.928434883663573E0,
> .827201315069765E0,.687292904811685E0,
> .515248636358154E0,.319112368927890E0,
> .108054948707344E0/
DATA (RWKSI(I),I=I14,I15-1) /
> .035119460331752E0,.080158087159760E0,
> .121518570687903E0,.157203167158193E0,
> .185538397477938E0,.205198463721296E0,
> .215263853463158E0/
C N=15
DATA (RZKSI(I),I=I15,I16-1) /
> .987992518020485E0,.937273392400706E0,
> .848206583410427E0,.724417731360170E0,
> .570972172608539E0,.394151347077563E0,
> .201194093997434E0/
DATA (RWKSI(I),I=I15,I16-1) /
> .030753241996117E0,.070366047488108E0,
> .107159220467172E0,.139570677926154E0,
> .166269205816994E0,.186161000015562E0,
> .198431485327111E0/
C N=16
DATA (RZKSI(I),I=I16,I17-1) /
> .095012509837637E0,.281603550779259E0,
> .458016777657227E0,.617876244402644E0,
> .755404408355003E0,.865631202387832E0,
> .944575023073233E0,.989400934991650E0/
DATA (RWKSI(I),I=I16,I17-1) /
> .189450610455068E0,.182603415044924E0,
> .169156519395003E0,.149595988816577E0,
> .124628971255534E0,.095158511682493E0,
> .062253523938648E0,.027152459411754E0/
C N=17
DATA (RZKSI(I),I=I17,I18-1) /
> .990575475314417E0,.950675521768768E0,
> .880239153726986E0,.781514003896801E0,
> .657671159216691E0,.512690537086477E0,
> .351231763453876E0,.178484181495848E0/
DATA (RWKSI(I),I=I17,I18-1) /
> .024148302868548E0,.055459529373987E0,
> .085036148317179E0,.111883847193404E0,
> .135136368468525E0,.154045761076810E0,
> .168004102156450E0,.176562705366993E0/
C N=18
DATA (RZKSI(I),I=I18,I19-1) /
> .991565168420930E0,.955823949571397E0,
> .892602466497556E0,.803704958972523E0,
> .691687043060353E0,.559770831073947E0,
> .411751161462843E0,.251886225691505E0,
> .084775013041735E0/
DATA (RWKSI(I),I=I18,I19-1) /
> .021616013526483E0,.049714548894970E0,
> .076425730254889E0,.100942044106287E0,
> .122555206711478E0,.140642914670651E0,
> .154684675126265E0,.164276483745833E0,
> .169142382963143E0/
C N=19
DATA (RZKSI(I),I=I19,I20-1) /
> .992406843843584E0,.960208152134830E0,
> .903155903614818E0,.822714656537143E0,
> .720966177335229E0,.600545304661681E0,
> .464570741375961E0,.316564099963630E0,
> .160358645640225E0/
DATA (RWKSI(I),I=I19,I20-1) /
> .019461788229726E0,.044814226765700E0,
> .069044542737641E0,.091490021622450E0,
> .111566645547334E0,.128753962539336E0,
> .142606702173607E0,.152766042065860E0,
> .158968843393954E0/
C N=20
DATA (RZKSI(I),I=I20,I24-1) /
> .076526521133497E0,.227785851141645E0,
> .373706088715420E0,.510867001950827E0,
> .636053680726515E0,.746331906460151E0,
> .839116971822219E0,.912234428251326E0,
> .963971927277914E0,.993128599185095E0/
DATA (RWKSI(I),I=I20,I24-1) /
> .152753387130726E0,.149172986472604E0,
> .142096109318382E0,.131688638449177E0,
> .118194531961518E0,.101930119817240E0,
> .083276741576705E0,.062672048334109E0,
> .040601429800387E0,.017614007139152E0/
C N=24
DATA (RZKSI(I),I=I24,I28-1) /
> .995187219997021E0,.974728555971309E0,
> .938274552002733E0,.886415527004401E0,
> .820001985973903E0,.740124191578554E0,
> .648093651936975E0,.545421471388839E0,
> .433793507626045E0,.315042679696163E0,
> .191118867473616E0,.064056892862605E0/
DATA (RWKSI(I),I=I24,I28-1) /
> .012341229799987E0,.028531388628934E0,
> .044277438817420E0,.059298584915437E0,
> .073346481411080E0,.086190161531953E0,
> .097618652104114E0,.107444270115966E0,
> .115505668053726E0,.121670472927803E0,
> .125837456346828E0,.127938195346752E0/
C N=28
DATA (RZKSI(I),I=I28,I32-1) /
> .996442497573954E0,.981303165370873E0,
> .954259280628938E0,.915633026392132E0,
> .865892522574395E0,.805641370917179E0,
> .735610878013632E0,.656651094038865E0,
> .569720471811402E0,.475874224955118E0,
> .376251516089079E0,.272061627635178E0,
> .164569282133380E0,.055079289884034E0/
DATA (RWKSI(I),I=I28,I32-1) /
> .009124282593094E0,.021132112592771E0,
> .032901427782304E0,.044272934759004E0,
> .055107345675717E0,.065272923966999E0,
> .074646214234569E0,.083113417228901E0,
> .090571744393033E0,.096930657997930E0,
> .102112967578061E0,.106055765922846E0,
> .108711192258294E0,.110047013016475E0/
C N=32
DATA (RZKSI(I),I=I32,I64-1) /
> .048307665687738E0,.144471961582796E0,
> .239287362252137E0,.331868602282128E0,
> .421351276130635E0,.506899908932229E0,
> .587715757240762E0,.663044266930215E0,
> .732182118740290E0,.794483795967942E0,
> .849367613732570E0,.896321155766052E0,
> .934906075937740E0,.964762255587506E0,
> .985611511545268E0,.997263861849482E0/
DATA (RWKSI(I),I=I32,I64-1) /
> .096540088514728E0,.095638720079275E0,
> .093844399080805E0,.091173878695764E0,
> .087652093004404E0,.083311924226947E0,
> .078193895787070E0,.072345794108849E0,
> .065822222776362E0,.058684093478536E0,
> .050998059262376E0,.042835898022227E0,
> .034273862913021E0,.025392065309262E0,
> .016274394730906E0,.007018610009470E0/
C N=64
DATA (RZKSI(I),I=I64,IFN) /
> .024350292663424E0,.072993121787799E0,.121462819296121E0,
> .169644420423993E0,.217423643740007E0,.264687162208767E0,
> .311322871990211E0,.357220158337668E0,.402270157963992E0,
> .446366017253464E0,.489403145707053E0,.531279464019894E0,
> .571895646202634E0,.611155355172393E0,.648965471254657E0,
> .685236313054233E0,.719881850171611E0,.752819907260532E0,
> .783972358943341E0,.813265315122798E0,.840629296252580E0,
> .865999398154093E0,.889315445995114E0,.910522137078503E0,
> .929569172131940E0,.946411374858403E0,.961008799652054E0,
> .973326827789911E0,.983336253884626E0,.991013371476744E0,
> .996340116771955E0,.999305041735772E0/
DATA (RWKSI(I),I=I64,IFN) /
> .048690957009140E0,.048575467441503E0,.048344762234803E0,
> .047999388596458E0,.047540165714830E0,.046968182816210E0,
> .046284796581314E0,.045491627927418E0,.044590558163757E0,
> .043583724529323E0,.042473515123654E0,.041262563242624E0,
> .039953741132720E0,.038550153178616E0,.037055128540240E0,
> .035472213256882E0,.033805161837142E0,.032057928354852E0,
> .030234657072402E0,.028339672614259E0,.026377469715055E0,
> .024352702568711E0,.022270173808383E0,.020134823153530E0,
> .017951715775697E0,.015726030476025E0,.013463047896719E0,
> .011168139460131E0,.008846759826364E0,.006504457968978E0,
> .004147033260562E0,.001783280721696E0/
*
IDEP=0
IFIN=0
FW=HALF*(XSUP-XINF)
FC=HALF*(XSUP+XINF)
IF( NGPT.EQ. 1 ) THEN
ZGKSI(1)=FC
WGKSI(1)=TWO*FW
RETURN
ELSE IF( NGPT.EQ. 2 ) THEN
IDEP=I2
IFIN=I3-1
ELSE IF( NGPT.EQ. 3 ) THEN
IDEP=I3
IFIN=I4-1
ELSE IF( NGPT.EQ. 4 ) THEN
IDEP=I4
IFIN=I5-1
ELSE IF( NGPT.EQ. 5 ) THEN
IDEP=I5
IFIN=I6-1
ELSE IF( NGPT.EQ. 6 ) THEN
IDEP=I6
IFIN=I7-1
ELSE IF( NGPT.EQ. 7 ) THEN
IDEP=I7
IFIN=I8-1
ELSE IF( NGPT.EQ. 8 ) THEN
IDEP=I8
IFIN=I9-1
ELSE IF( NGPT.EQ. 9 ) THEN
IDEP=I9
IFIN=I10-1
ELSE IF( NGPT.EQ.10 ) THEN
IDEP=I10
IFIN=I11-1
ELSE IF( NGPT.EQ.11 ) THEN
IDEP=I11
IFIN=I12-1
ELSE IF( NGPT.EQ.12 ) THEN
IDEP=I12
IFIN=I13-1
ELSE IF( NGPT.EQ.13 ) THEN
IDEP=I13
IFIN=I14-1
ELSE IF(NGPT.EQ.14 ) THEN
IDEP=I14
IFIN=I15-1
ELSE IF(NGPT.EQ.15 ) THEN
IDEP=I15
IFIN=I16-1
ELSE IF(NGPT.EQ.16 ) THEN
IDEP=I16
IFIN=I17-1
ELSE IF(NGPT.EQ.17 ) THEN
IDEP=I17
IFIN=I18-1
ELSE IF(NGPT.EQ.18 ) THEN
IDEP=I18
IFIN=I19-1
ELSE IF(NGPT.EQ.19 ) THEN
IDEP=I19
IFIN=I20-1
ELSE IF( NGPT.EQ.20 ) THEN
IDEP=I20
IFIN=I24-1
ELSE IF( NGPT.EQ.24 ) THEN
IDEP=I24
IFIN=I28-1
ELSE IF( NGPT.EQ.28 ) THEN
IDEP=I28
IFIN=I32-1
ELSE IF( NGPT.EQ.32 ) THEN
IDEP=I32
IFIN=I64-1
ELSE IF( NGPT.EQ.64 ) THEN
IDEP=I64
IFIN=IFN
ELSE
WRITE(CERROR,'(I4)') NGPT
CALL XABORT('ALGPT:INVALID NBR.OF GAUSS PTS.='//CERROR//' ***
> 1 TO 20,24,28,32,64 PTS. ARE PERMITTED')
ENDIF
C------
C INITIALIZE ZGKSI AND WGKSI STARTING FROM BOTTOM WITH NEGATIVE
C AND FINISHING WITH POSITIVE
C------
IUP=1
IDN=NGPT
DO 100 I=IFIN,IDEP,-1
ZGKSI(IUP)=-FW*RZKSI(I)+FC
WGKSI(IUP)=FW*RWKSI(I)
ZGKSI(IDN)=FW*RZKSI(I)+FC
WGKSI(IDN)=FW*RWKSI(I)
IUP=IUP+1
IDN=IDN-1
100 CONTINUE
C------
C FOR ODD NGPT, CENTRAL POINT IS 0.0 AND WEIGHT IS (2.0-TOTAL WEIGHT)
C------
IF(IUP.EQ.IDN) THEN
ZGKSI(IUP)=FC
DO 110 I=1,IUP-1
FW=FW-WGKSI(I)
110 CONTINUE
WGKSI(IUP)=TWO*FW
ENDIF
RETURN
END
|
