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quadrature.F
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MODULE QUADRATURETRI
USE SIZES
IMPLICIT NONE
!C INTEGER, parameter:: SZ = 8
INTEGER, private:: pcub, ncubs
REAL(SZ), private, pointer:: cub2d(:,:)
REAL(SZ), private, allocatable:: brscub2d(:,:)
REAL(SZ), private, allocatable:: workvec(:)
TYPE MATARR
INTEGER :: mdim
REAL(SZ), POINTER :: ARRVAL(:,:)
END TYPE MATARR
TYPE VECARR
INTEGER :: mdim
REAL(SZ), POINTER :: VECVAL(:)
END TYPE VECARR
CONTAINS
!C=================== High-level subroutines ====================
SUBROUTINE AllocMatArr( msarr, iidim )
IMPLICIT NONE
INTEGER :: iidim
TYPE(MATARR) :: msarr
msarr%mdim = iidim
IF ( associated(msarr%arrval) ) THEN
deallocate(msarr%arrval)
nullify(msarr%arrval)
END IF
ALLOCATE(msarr%arrval(iidim,iidim))
RETURN
END SUBROUTINE AllocMatArr
SUBROUTINE AllocVecArr( msvec, iidim )
IMPLICIT NONE
INTEGER :: iidim
TYPE(VECARR) :: msvec
msvec%mdim = iidim
IF ( associated(msvec%vecval) ) THEN
deallocate(msvec%vecval)
nullify(msvec%vecval)
END IF
ALLOCATE(msvec%vecval(iidim))
RETURN
END SUBROUTINE AllocVecArr
SUBROUTINE GetDefaultCub2D( p )
IMPLICIT NONE
INTEGER:: p
IF ( associated(cub2d) ) THEN
deallocate(cub2d) ;
END IF
IF ( allocated(brscub2d) ) THEN
deallocate(brscub2d) ;
END IF
IF ( allocated(workvec) ) THEN
deallocate(workvec) ;
END IF
pcub = p ;
CALL GetQuadrature2DTri( cub2d, pcub ) ;
ncubs = ubound( cub2d, 1 ) ;
ALLOCATE( brscub2d(ncubs,3) ) ;
CALL rsbarycentriccoords( brscub2d,
& cub2d(:,1), cub2d(:,2), ncubs ) ;
allocate( workvec(ncubs) ) ;
RETURN ;
END SUBROUTINE GetDefaultCub2D
SUBROUTINE FetchDefaultNcub2d( nn )
IMPLICIT NONE
INTEGER:: nn
nn = ncubs ;
RETURN ;
END SUBROUTINE FetchDefaultNcub2d
SUBROUTINE InterpDefaultCub2D( fxy, fv )
IMPLICIT NONE
REAL(SZ), dimension(:):: fxy, fv
CALL barycentricinterp( fxy, fv, brscub2d, ncubs ) ;
RETURN ;
END SUBROUTINE InterpDefaultCub2D
!c
!c Compute elemental:
!c
!c S = (1/(A/2)) \int f_{h} phi_{i} phi_{j}
!c
SUBROUTINE CompElmMsfh( S, fv )
IMPLICIT NONE
INTEGER:: II, JJ
REAL(SZ):: S(3,3), fv(:)
workvec = 0.D0 ;
CALL InterpDefaultCub2D( workvec, fv ) ;
DO II = 1, 3
DO JJ = 1, 3
S(II,JJ) = sum(workvec*cub2d(:,3)*
& brscub2d(:,II)*brscub2d(:,JJ)) ;
END DO
END DO
RETURN ;
END SUBROUTINE CompElmMsfh
C============================================================
!
! Linear interpolation on triangle
!
! given \lambda | (r,s) return f(xy)
SUBROUTINE barycentricinterp( fxy, fv, brs, nrs )
IMPLICIT NONE
INTEGER:: nrs
REAL(SZ), dimension(:):: fxy, fv
REAL(SZ):: brs(:,:)
fxy(1:nrs) = fv(1)*brs(1:nrs,1) +
& fv(2)*brs(1:nrs,2) + fv(3)*brs(1:nrs,3) ;
RETURN ;
END SUBROUTINE barycentricinterp
!c RS to lambda
SUBROUTINE rsbarycentriccoords( brs, r, s, nrs )
IMPLICIT NONE
INTEGER:: nrs
REAL(SZ):: brs(:,:), r(:), s(:)
INTEGER:: I
brs(1:nrs,1) = -0.5D0*(r(1:nrs) + s(1:nrs)) ;
brs(1:nrs,2) = 0.5D0*(r(1:nrs) + 1.D0) ;
brs(1:nrs,3) = 0.5D0*(s(1:nrs) + 1.D0) ;
RETURN ;
END SUBROUTINE rsbarycentriccoords
!c
!c ref element: -1 < x,y < 1, x + y = 0
SUBROUTINE GetQuadrature2DTri( cub2d, pcub )
IMPLICIT NONE
INTEGER:: pcub
REAL(SZ), pointer:: cub2d(:,:)
INTEGER:: p1D, sk, ii, jj, ncub
REAL(SZ), allocatable:: x1D(:,:), x2D(:,:)
SELECT CASE( pcub )
case( 1 )
allocate(cub2d(1,3)) ;
cub2d( 1, :) = (/ -3.333333333333330d-01, -3.333333333333330d-01, 2.000000000000000d+00 /) ;
case( 2 )
allocate(cub2d(3,3)) ;
cub2d( 1, :) = (/ -6.666666666666670d-01, -6.666666666666670d-01, 6.666666666666670d-01 /) ;
cub2d( 2, :) = (/ 3.333333333333330d-01, -6.666666666666670d-01, 6.666666666666670d-01 /) ;
cub2d( 3, :) = (/ -6.666666666666670d-01, 3.333333333333330d-01, 6.666666666666670d-01 /) ;
case( 3 )
allocate(cub2d(6,3)) ;
cub2d( 1, :) = (/ -8.168475729804580d-01, -8.168475729804580d-01, 2.199034873106440d-01 /) ;
cub2d( 2, :) = (/ 6.336951459609170d-01, -8.168475729804590d-01, 2.199034873106440d-01 /) ;
cub2d( 3, :) = (/ -8.168475729804590d-01, 6.336951459609170d-01, 2.199034873106440d-01 /) ;
cub2d( 4, :) = (/ -1.081030181680700d-01, -1.081030181680700d-01, 4.467631793560230d-01 /) ;
cub2d( 5, :) = (/ -7.837939636638600d-01, -1.081030181680700d-01, 4.467631793560230d-01 /) ;
cub2d( 6, :) = (/ -1.081030181680700d-01, -7.837939636638600d-01, 4.467631793560230d-01 /) ;
case( 4 )
allocate(cub2d(6,3)) ;
cub2d( 1, :) = (/ -8.168475729804580d-01, -8.168475729804580d-01, 2.199034873106440d-01 /) ;
cub2d( 2, :) = (/ 6.336951459609170d-01, -8.168475729804590d-01, 2.199034873106440d-01 /) ;
cub2d( 3, :) = (/ -8.168475729804590d-01, 6.336951459609170d-01, 2.199034873106440d-01 /) ;
cub2d( 4, :) = (/ -1.081030181680700d-01, -1.081030181680700d-01, 4.467631793560230d-01 /) ;
cub2d( 5, :) = (/ -7.837939636638600d-01, -1.081030181680700d-01, 4.467631793560230d-01 /) ;
cub2d( 6, :) = (/ -1.081030181680700d-01, -7.837939636638600d-01, 4.467631793560230d-01 /) ;
case( 5 )
allocate(cub2d(7,3)) ;
cub2d( 1, :) = (/ -3.333333333333330d-01, -3.333333333333330d-01, 4.500000000000000d-01 /) ;
cub2d( 2, :) = (/ -5.971587178977000d-02, -5.971587178977000d-02, 2.647883055770120d-01 /) ;
cub2d( 3, :) = (/ -8.805682564204600d-01, -5.971587178977000d-02, 2.647883055770120d-01 /) ;
cub2d( 4, :) = (/ -5.971587178977000d-02, -8.805682564204600d-01, 2.647883055770120d-01 /) ;
cub2d( 5, :) = (/ -7.974269853530870d-01, -7.974269853530870d-01, 2.518783610896540d-01 /) ;
cub2d( 6, :) = (/ 5.948539707061750d-01, -7.974269853530870d-01, 2.518783610896540d-01 /) ;
cub2d( 7, :) = (/ -7.974269853530870d-01, 5.948539707061750d-01, 2.518783610896540d-01 /) ;
case( 6 )
allocate(cub2d(12,3)) ;
cub2d( 1, :) = (/ -5.014265096581790d-01, -5.014265096581790d-01, 2.335725514527590d-01 /) ;
cub2d( 2, :) = (/ 2.853019316358000d-03, -5.014265096581790d-01, 2.335725514527590d-01 /) ;
cub2d( 3, :) = (/ -5.014265096581790d-01, 2.853019316358000d-03, 2.335725514527590d-01 /) ;
cub2d( 4, :) = (/ -8.738219710169960d-01, -8.738219710169960d-01, 1.016898127404140d-01 /) ;
cub2d( 5, :) = (/ 7.476439420339910d-01, -8.738219710169960d-01, 1.016898127404140d-01 /) ;
cub2d( 6, :) = (/ -8.738219710169960d-01, 7.476439420339910d-01, 1.016898127404140d-01 /) ;
cub2d( 7, :) = (/ -3.792950979324310d-01, -8.937099003103660d-01, 1.657021512367470d-01 /) ;
cub2d( 8, :) = (/ -8.937099003103660d-01, -3.792950979324310d-01, 1.657021512367470d-01 /) ;
cub2d( 9, :) = (/ 2.730049982427970d-01, -8.937099003103660d-01, 1.657021512367470d-01 /) ;
cub2d( 10, :) = (/ -8.937099003103660d-01, 2.730049982427970d-01, 1.657021512367470d-01 /) ;
cub2d( 11, :) = (/ 2.730049982427970d-01, -3.792950979324310d-01, 1.657021512367470d-01 /) ;
cub2d( 12, :) = (/ -3.792950979324310d-01, 2.730049982427970d-01, 1.657021512367470d-01 /) ;
CASE DEFAULT
PRINT*, "Error: Quadrature for pcub = ", pcub, " has not yet been implemented" ;
END SELECT
END SUBROUTINE GetQuadrature2DTri
END MODULE QUADRATURETRI