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SUBROUTINE BRESS1(ITRIAL,XX,DIFF,SIGR,SIGT,A11)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Assembly of leakage system matrices for the nodal expansion method.
*
*Copyright:
* Copyright (C) 2021 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): A. Hebert
*
*Parameters: input
* ITRIAL type of base (=1: polynomial; =2: hyperbolic)
* XX mesh width.
* SIGR macroscopic removal cross section.
* SIGT macroscopic cross section.
*
*Parameters: output
* A11 nodal matrix.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER ITRIAL
REAL XX,DIFF,SIGR,SIGT,A11(4,4)
*----
* WEIGHT RESIDUAL EQUATIONS
*----
A11(:4,:4)=0.0
DX2=XX**2
ETA=XX*SQRT(SIGR/DIFF)
A11(1,1)=SIGT/12.0
A11(2,2)=SIGT/20.0
IF(ITRIAL == 1) THEN
A11(1,3)=-SIGT/120.0-DIFF/(2.0*DX2)
A11(2,4)=-SIGT/700.0-DIFF/(5.0*DX2)
ELSE IF(ITRIAL == 2) THEN
ALP1=ETA*COSH(ETA/2.0)-2.0*SINH(ETA/2.0)
ALP2=((12.0+ETA**2)*SINH(ETA/2.0)-6.0*ETA*COSH(ETA/2.0))/ETA
A11(1,3)=SIGT*ALP1/(ETA**2)-DIFF*ALP1/DX2
A11(2,4)=SIGT*ALP2/(ETA**2)-DIFF*ALP2/DX2
ENDIF
! LEFT CURRENT CONDITION
A11(3,1)=-DIFF/XX
A11(3,2)=3.0*DIFF/XX
IF(ITRIAL == 1) THEN
A11(3,3)=-DIFF/(2.0*XX)
A11(3,4)=DIFF/(5.0*XX)
ELSE IF(ITRIAL == 2) THEN
A11(3,3)=-(DIFF/XX)*ETA*COSH(ETA/2.0)
A11(3,4)=(DIFF/XX)*ETA*SINH(ETA/2.0)
ENDIF
! RIGHT CURRENT CONDITION
A11(4,1)=-DIFF/XX
A11(4,2)=-3.0*DIFF/XX
IF(ITRIAL == 1) THEN
A11(4,3)=-DIFF/(2.0*XX)
A11(4,4)=-DIFF/(5.0*XX)
ELSE IF(ITRIAL == 2) THEN
A11(4,3)=-(DIFF/XX)*ETA*COSH(ETA/2.0)
A11(4,4)=-(DIFF/XX)*ETA*SINH(ETA/2.0)
ENDIF
RETURN
END
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