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!------------------------------------------------------------------------------|
!------------------------------------------------------------------------------|
! |
! ||===\\ |
! || \\ |
! || || //==\\ || || //==|| ||/==\\ |
! || || || || || || || || || || |
! || // || || || || || || || |
! ||===// \\==// \\==\\ \\==\\ || |
! |
!------------------------------------------------------------------------------|
!------------------------------------------------------------------------------|
! |
! COMPUTE_DHDX_DHDY_DHDZ Nov. 2006 |
! |
!------------------------------------------------------------------------------|
!------------------------------------------------------------------------------|
subroutine compute_dhdx_dhdy_dhdz (mpe,r,s,t,x,y,z,dhdx,dhdy,dhdz,volume)
!------------------------------------------------------------------------------|
!(((((((((((((((( Purpose of the routine ))))))))))))))))))))))))))))))))))))))
!------------------------------------------------------------------------------|
!------------------------------------------------------------------------------|
!(((((((((((((((( declaration of the subroutine arguments ))))))))))))))))))))
!------------------------------------------------------------------------------|
implicit none
integer mpe
double precision r,s,t
double precision x(mpe),y(mpe),z(mpe)
double precision dhdx(mpe),dhdy(mpe),dhdz(mpe)
double precision volume
!------------------------------------------------------------------------------|
!(((((((((((((((( declaration of the subroutine internal variables )))))))))))))
!------------------------------------------------------------------------------|
double precision,dimension(:),allocatable :: h,dhdr,dhds,dhdt
double precision jcb(3,3),jcbi(3,3)
double precision eps
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integer nint
!-------------------------------------------------------------------------------
!-------------------------------------------------------------------------------
nint=8
eps=tiny(eps)
allocate (h(mpe) ,stat=err) ; if (err.ne.0) call stop_run ('Error alloc h in compute_dhdx_dhdy_dhdz$')
allocate (dhdr(mpe),stat=err) ; if (err.ne.0) call stop_run ('Error alloc dhdr in compute_dhdx_dhdy_dhdz$')
allocate (dhds(mpe),stat=err) ; if (err.ne.0) call stop_run ('Error alloc dhds in compute_dhdx_dhdy_dhdz$')
allocate (dhdt(mpe),stat=err) ; if (err.ne.0) call stop_run ('Error alloc dhdt in compute_dhdx_dhdy_dhdz$')
h(1)=(1.d0-r)*(1.d0-s)*(1.d0-t)/8.d0
h(2)=(1.d0+r)*(1.d0-s)*(1.d0-t)/8.d0
h(3)=(1.d0-r)*(1.d0+s)*(1.d0-t)/8.d0
h(4)=(1.d0+r)*(1.d0+s)*(1.d0-t)/8.d0
h(5)=(1.d0-r)*(1.d0-s)*(1.d0+t)/8.d0
h(6)=(1.d0+r)*(1.d0-s)*(1.d0+t)/8.d0
h(7)=(1.d0-r)*(1.d0+s)*(1.d0+t)/8.d0
h(8)=(1.d0+r)*(1.d0+s)*(1.d0+t)/8.d0
dhdr(1)=-(1.d0-s)*(1.d0-t)/8.d0
dhdr(2)=(1.d0-s)*(1.d0-t)/8.d0
dhdr(3)=-(1.d0+s)*(1.d0-t)/8.d0
dhdr(4)=(1.d0+s)*(1.d0-t)/8.d0
dhdr(5)=-(1.d0-s)*(1.d0+t)/8.d0
dhdr(6)=(1.d0-s)*(1.d0+t)/8.d0
dhdr(7)=-(1.d0+s)*(1.d0+t)/8.d0
dhdr(8)=(1.d0+s)*(1.d0+t)/8.d0
dhds(1)=-(1.d0-r)*(1.d0-t)/8.d0
dhds(2)=-(1.d0+r)*(1.d0-t)/8.d0
dhds(3)=(1.d0-r)*(1.d0-t)/8.d0
dhds(4)=(1.d0+r)*(1.d0-t)/8.d0
dhds(5)=-(1.d0-r)*(1.d0+t)/8.d0
dhds(6)=-(1.d0+r)*(1.d0+t)/8.d0
dhds(7)=(1.d0-r)*(1.d0+t)/8.d0
dhds(8)=(1.d0+r)*(1.d0+t)/8.d0
dhdt(1)=-(1.d0-r)*(1.d0-s)/8.d0
dhdt(2)=-(1.d0+r)*(1.d0-s)/8.d0
dhdt(3)=-(1.d0-r)*(1.d0+s)/8.d0
dhdt(4)=-(1.d0+r)*(1.d0+s)/8.d0
dhdt(5)=(1.d0-r)*(1.d0-s)/8.d0
dhdt(6)=(1.d0+r)*(1.d0-s)/8.d0
dhdt(7)=(1.d0-r)*(1.d0+s)/8.d0
dhdt(8)=(1.d0+r)*(1.d0+s)/8.d0
jcb=0.
do k=1,mpe
jcb(1,1)=jcb(1,1)+dhdr(k)*x(k)
jcb(1,2)=jcb(1,2)+dhdr(k)*y(k)
jcb(1,3)=jcb(1,3)+dhdr(k)*z(k)
jcb(2,1)=jcb(2,1)+dhds(k)*x(k)
jcb(2,2)=jcb(2,2)+dhds(k)*y(k)
jcb(2,3)=jcb(2,3)+dhds(k)*z(k)
jcb(3,1)=jcb(3,1)+dhdt(k)*x(k)
jcb(3,2)=jcb(3,2)+dhdt(k)*y(k)
jcb(3,3)=jcb(3,3)+dhdt(k)*z(k)
enddo
volume=jcb(1,1)*jcb(2,2)*jcb(3,3) &
+jcb(1,2)*jcb(2,3)*jcb(3,1) &
+jcb(2,1)*jcb(3,2)*jcb(1,3) &
-jcb(1,3)*jcb(2,2)*jcb(3,1) &
-jcb(1,2)*jcb(2,1)*jcb(3,3) &
-jcb(2,3)*jcb(3,2)*jcb(1,1)
if (volume.le.eps) then
call stop_run ('Element bow-tied or collapsed in make_matrix$')
endif
jcbi(1,1)=(jcb(2,2)*jcb(3,3)-jcb(2,3)*jcb(3,2))/volume
jcbi(2,1)=(jcb(2,3)*jcb(3,1)-jcb(2,1)*jcb(3,3))/volume
jcbi(3,1)=(jcb(2,1)*jcb(3,2)-jcb(2,2)*jcb(3,1))/volume
jcbi(1,2)=(jcb(1,3)*jcb(3,2)-jcb(1,2)*jcb(3,3))/volume
jcbi(2,2)=(jcb(1,1)*jcb(3,3)-jcb(1,3)*jcb(3,1))/volume
jcbi(3,2)=(jcb(1,2)*jcb(3,1)-jcb(1,1)*jcb(3,2))/volume
jcbi(1,3)=(jcb(1,2)*jcb(2,3)-jcb(1,3)*jcb(2,2))/volume
jcbi(2,3)=(jcb(1,3)*jcb(2,1)-jcb(1,1)*jcb(2,3))/volume
jcbi(3,3)=(jcb(1,1)*jcb(2,2)-jcb(1,2)*jcb(2,1))/volume
do k=1,mpe
dhdx(k)=jcbi(1,1)*dhdr(k)+jcbi(1,2)*dhds(k)+jcbi(1,3)*dhdt(k)
dhdy(k)=jcbi(2,1)*dhdr(k)+jcbi(2,2)*dhds(k)+jcbi(2,3)*dhdt(k)
dhdz(k)=jcbi(3,1)*dhdr(k)+jcbi(3,2)*dhds(k)+jcbi(3,3)*dhdt(k)
enddo
deallocate (h)
deallocate (dhdr)
deallocate (dhds)
deallocate (dhdt)
return
end
!-------------------------------------------------------------------------------
!-------------------------------------------------------------------------------