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*DECK VALU4B
SUBROUTINE VALU4B(IELEM,NUN,LX,LY,X,Y,XXX,YYY,EVECT,ISS,KFLX,
+ IXLG,IYLG,AXY)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Interpolate the flux distribution for DUAL method in 2D.
*
*Copyright:
* Copyright (C) 2002 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. Chambon
*
*Parameters: input
* IELEM finite element order
* =1 : linear Raviart-Thomas
* =2 : parabolic Raviart-Thomas
* =3 : cubic Raviart-Thomas
* =4 : quartic Raviart-Thomas
* NUN number of unknowns
* LX number of elements along the X axis.
* LY number of elements along the Y axis.
* X Cartesian coordinates along the X axis where the flux is
* interpolated.
* Y Cartesian coordinates along the Y axis where the flux is
* interpolated.
* XXX Cartesian coordinates along the X axis.
* YYY Cartesian coordinates along the Y axis.
* EVECT variational coefficients of the flux.
* ISS mixture index assigned to each element.
* KFLX correspondence between local and global numbering.
* IXLG number of interpolated points according to X.
* IYLG number of interpolated points according to Y.
*
*Parameters: output
* AXY interpolated fluxes.
*
*----------------------------------------------------------------------
*
IMPLICIT NONE
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER IELEM,NUN,LX,LY,IXLG,IYLG,ISS(LX*LY),KFLX(LX*LY)
REAL X(IXLG),Y(IYLG),XXX(LX+1),YYY(LY+1),EVECT(NUN),AXY(IXLG,IYLG)
*----
* LOCAL VARIABLES
*----
INTEGER I,J,L,IS,JS,IEL,I1,I2,IE
REAL ORDO,ABSC,COEF(2,5),FLX(5),FLY(5)
REAL U,V
*----
* compute coefficient for legendre polynomials
*----
COEF(:2,:5)=0.0
COEF(1,1)=1.0
COEF(1,2)=2.*3.**0.5
DO IE=1,3
COEF(1,IE+2)=2.0*REAL(2*IE+1)/REAL(IE+1)
1 *(REAL(2*IE+3)/REAL(2*IE+1))**0.5
COEF(2,IE+2)=REAL(IE)/REAL(IE+1)
1 *(REAL(2*IE+3)/REAL(2*IE-1))**0.5
ENDDO
*----
* perform interpolation
*----
DO 105 J=1,IYLG
ORDO=Y(J)
DO 100 I=1,IXLG
ABSC=X(I)
AXY(I,J)=0.0
*
* Find the finite element index containing the interpolation point
IS=0
JS=0
DO 20 L=1,LX
IS=L
IF((ABSC.GE.XXX(L)).AND.(ABSC.LE.XXX(L+1))) GO TO 30
20 CONTINUE
CALL XABORT('VALU4B: WRONG INTERPOLATION(1).')
30 DO 40 L=1,LY
JS=L
IF((ORDO.GE.YYY(L)).AND.(ORDO.LE.YYY(L+1))) GO TO 70
40 CONTINUE
CALL XABORT('VALU4B: WRONG INTERPOLATION(2).')
70 IEL=(JS-1)*LX+IS
*
IF(ISS(IEL).EQ.0) GO TO 100
U=(ABSC-0.5*(XXX(IS)+XXX(IS+1)))/(XXX(IS+1)-XXX(IS))
FLX(1)=COEF(1,1)
FLX(2)=COEF(1,2)*U
V=(ORDO-0.5*(YYY(JS)+YYY(JS+1)))/(YYY(JS+1)-YYY(JS))
FLY(1)=COEF(1,1)
FLY(2)=COEF(1,2)*V
IF(IELEM.GE.2) THEN
DO IE=2,IELEM
FLX(IE+1)=FLX(IE)*U*COEF(1,IE+1)-FLX(IE-1)*COEF(2,IE+1)
FLY(IE+1)=FLY(IE)*V*COEF(1,IE+1)-FLY(IE-1)*COEF(2,IE+1)
ENDDO
ENDIF
DO 92 I2=1,IELEM
DO 91 I1=1,IELEM
L=(I2-1)*(IELEM)+I1
AXY(I,J)=AXY(I,J)+EVECT(KFLX(IEL)+L-1)*FLX(I1)*FLY(I2)
91 CONTINUE
92 CONTINUE
100 CONTINUE
105 CONTINUE
RETURN
END
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