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jacobianmod.f90
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! Part of Zinc FE package. Author: John Blackburn
module jacobianmod
implicit none
! New functions for non-linear calculation using Newton-Raphson method
! Supports only C, F matrices and only DLL non-linear functions
! (not single line expressions)
! In this case we need to also link dCfun_du, dCfun_ddu
! In this case we need to also link dffun_du, dffun_ddu
!
! Simplified getQR here does NOT handle surface integrals but DOES
! (optionally) integrate material properties over element.
! Does not use helper functions like getelinfo, getelint as these
! are not suitable to new functionality and also obscures what we
! are doing.
! (can add ALL sparse matrix entries including zeros if this causes problems)
!
! Should be able to test proof of principle for cathodetoken
! and then fullfuel which both only use C, f, fixed nodes, no SURFACE
! getJacobianC
! getJacobianF
! getJacobian2C (by elements)
! getJacobian2F (by elements)
! getsol
! addtoQ
! note flags jac_by_element and centre_eval
contains
! ######################################################################
subroutine getJacobian
use common, only : jac_by_element
if (jac_by_element) then
call getJacobian2C
call getJacobian2F
else
call getJacobianC
call getJacobianF
endif
end subroutine getJacobian
! ######################################################################
subroutine getJacobianC
! ----------------------------------------------------------------------
! Update Q matrix to equal the Jacobian. iQ, jQ. Q must have already been
! set and heapsorted and archived (irowst,irowed). We assume J has the
! same sparsity structure as Q, if not we are in trouble!
! This routine loops over node pairs (and triplets) and then loops
! over elements connected to these to discover the the Jacobian
! This routine add C-related terms
! ----------------------------------------------------------------------
use common
use geom
use shape
use matrices
use indexQ
integer ia,ja,ka,ig,jg,kg,ib,jb,kb,ie,je,ke,iep,ind,la,lg,lb
integer inode,jnode,knode,icomb(2,3)
logical igin,jgin,kgin,ibin,jbin,kbin,iein,jein,kein,foundg,foundb
integer itab(8,4,3),itabsrt(8,3)
double precision rtabsrt(8,3),rtab(8,3),ul(8,nvar),dCdu(nvar),dCddu(nvar,3)
double precision elint(nvar,nvar,nvar),elint1(3,3),elint2(3,3,3)
double precision jac(3,3),invjac(3,3),jacdet,r(3)
double precision term2(nvar,nvar),dNa(3),dNg(3),dNb(3)
integer ixi,ieta,imu,i1,j1,k1,irege
double precision xi,eta,mu,dur(nvar,3),ur(nvar),tot,trailer
integer ii,jj,kk,ll,mm,nn,icol,irow,l,ip
character(EXPRLEN) token
integer iusel(0:imax-1,0:jmax-1,0:kmax-1)
integer, parameter :: ies(8)=[1, 1, 1, 1,-1,-1,-1,-1]
integer, parameter :: jes(8)=[1, 1,-1,-1, 1, 1,-1,-1]
integer, parameter :: kes(8)=[1,-1, 1,-1, 1,-1, 1,-1]
print *,'Preparing Jacobian (getJacobianC)'
iusel=0
do ia=0,imax
print *,'i-plane: ',ia,' / ',imax
do ja=0,jmax
do ka=0,kmax ! alpha node loop
do ig=ia-1,ia+1
do jg=ja-1,ja+1
do kg=ka-1,ka+1 ! gamma node loop
igin = ig>=0.and.ig<=imax
jgin = jg>=0.and.jg<=jmax
kgin = kg>=0.and.kg<=kmax
if (.not.(igin.and.jgin.and.kgin)) cycle ! gamma node must exist
term2=0 ! will be term2 (for each ii,nn) by end of beta loop
do ib=ia-1,ia+1
do jb=ja-1,ja+1
do kb=ka-1,ka+1
ibin = ib>=0.and.ib<=imax
jbin = jb>=0.and.jb<=jmax
kbin = kb>=0.and.kb<=kmax
if (.not.(ibin.and.jbin.and.kbin)) cycle ! node must exist
! ----------------------------------------------------------------------
! Loop over elements connected to alpha, gamma and beta (if any exist)
! Note alpha=gamma etc are allowed
! ----------------------------------------------------------------------
elint=0 ! will be sum of integrals when iep loop completes
do iep=1,8
ie=ies(iep)
je=jes(iep)
ke=kes(iep)
iein = ia+ie>=0.and.ia+ie<=imax
jein = ja+je>=0.and.ja+je<=jmax
kein = ka+ke>=0.and.ka+ke<=kmax
if (.not.(iein.and.jein.and.kein)) cycle ! element must exist
! ----------------------------------------------------------------------
! Find itab, rtab for element. Use itab to check both gamma and beta
! nodes are attached to candidate element else cycle element loop
! If all is well use sort to determine itabsrt, rtabsrt
! ----------------------------------------------------------------------
icomb(1,1)=ia
icomb(1,2)=ja
icomb(1,3)=ka
icomb(2,1)=ia+ie
icomb(2,2)=ja+je
icomb(2,3)=ka+ke
call getel(icomb,rnode,imax,jmax,kmax,itab,rtab)
foundg=.false.
foundb=.false.
do ind=1,8
if (itab(ind,1,1)==ig.and.itab(ind,1,2)==jg.and.itab(ind,1,3)==kg) foundg=.true.
if (itab(ind,1,1)==ib.and.itab(ind,1,2)==jb.and.itab(ind,1,3)==kb) foundb=.true.
enddo
if (.not.(foundg.and.foundb)) cycle
call sort(itab,rtab,itabsrt,rtabsrt)
! ----------------------------------------------------------------------
! Find local numbers for alpha, gamma, beta: la, lg, lb
! ----------------------------------------------------------------------
la=0; lg=0; lb=0
do ip=1,8
inode=itabsrt(ip,1)
jnode=itabsrt(ip,2)
knode=itabsrt(ip,3)
if (inode==ia.and.jnode==ja.and.knode==ka) la=ip
if (inode==ig.and.jnode==jg.and.knode==kg) lg=ip
if (inode==ib.and.jnode==jb.and.knode==kb) lb=ip
enddo
if (la==0.or.lg==0.or.lb==0) then
print *,'Error: getJacobian: failed to find la,lg or lb'
stop
endif
! ----------------------------------------------------------------------
! Find the element's region number and local solution at nodes
! surrounding element
! Update iusel which states how many times element used
! ----------------------------------------------------------------------
i1=ia+(ie-1)/2
j1=ja+(je-1)/2
k1=ka+(ke-1)/2
irege=iregup(i1,j1,k1)
do l=1,8
inode=itabsrt(l,1)
jnode=itabsrt(l,2)
knode=itabsrt(l,3)
do ii=1,nvar
ul(l,ii)=vec(indQ(inode,jnode,knode,ii))
enddo
enddo
iusel(i1,j1,k1)=iusel(i1,j1,k1)+1
! ----------------------------------------------------------------------
! Integrate
! ----------------------------------------------------------------------
elint1=0 ! For centre_eval
elint2=0 ! For centre_eval
do ixi=1,ng_xi
do ieta=1,ng_eta
do imu=1,ng_mu
xi=gauss(ng_xi,ixi)
eta=gauss(ng_eta,ieta)
mu=gauss(ng_mu,imu)
call jacobian(xi,eta,mu,rtabsrt,jac,invjac,jacdet)
call getdN(la,xi,eta,mu,invjac,dNa) ! dN_alpha/dr
call getdN(lg,xi,eta,mu,invjac,dNg)
call getdN(lb,xi,eta,mu,invjac,dNb)
trailer=jacdet*wt(ng_xi,ixi)*wt(ng_eta,ieta)*wt(ng_mu,imu)
! ----------------------------------------------------------------------
! For centre eval, calculate shape function integrals
! ----------------------------------------------------------------------
if (centre_eval) then
do jj=1,3
do ll=1,3
elint1(jj,ll)=elint1(jj,ll)+dNa(jj)*dNb(ll)*Nl(lg,xi,eta,mu)*trailer
do mm=1,3
elint2(jj,ll,mm)=elint2(jj,ll,mm)+dNa(jj)*dNb(ll)*dNg(mm)*trailer
enddo
enddo
enddo
else
! ----------------------------------------------------------------------
! else Calculate local solution, accumulate elint directly
! ----------------------------------------------------------------------
call getsol(ul,invjac,rtabsrt, xi,eta,mu, ur,dur,r)
do ii=1,nvar
do kk=1,nvar
do nn=1,nvar
do jj=1,3
do ll=1,3
if (iCC(irege,ii,jj,kk,ll)==3) then
token=sCC(irege,ii,jj,kk,ll)
call dCfun_du (token,r(1),r(2),r(3),ur,dur,nvar,istep, &
ireg,iregup,rnode,vec,imax,jmax,kmax,dCdu)
call dCfun_ddu(token,r(1),r(2),r(3),ur,dur,nvar,istep, &
ireg,iregup,rnode,vec,imax,jmax,kmax,dCddu)
! dCdu= dCfun_du(token,ur,dur) ! variation with u
! dCddu=dCfun_ddu(token,ur,dur) ! variation with du/dr
tot=dCdu(nn)*Nl(lg,xi,eta,mu)
do mm=1,3
tot=tot+dCddu(nn,mm)*dNg(mm)
enddo
elint(ii,kk,nn)=elint(ii,kk,nn)+dNa(jj)*dNb(ll)*tot*trailer
endif
enddo
enddo
enddo
enddo
enddo
endif
enddo ! integration loops
enddo
enddo
! ----------------------------------------------------------------------
! For centre eval, form elint, which is a sum over integrals for
! each element. Also sum over jj,ll for each ii,kk,nn
! ----------------------------------------------------------------------
if (centre_eval) then
call jacobian(zero,zero,zero, rtabsrt,jac,invjac,jacdet)
call getsol(ul,invjac, rtabsrt, zero,zero,zero, ur,dur,r)
do ii=1,nvar
do kk=1,nvar
do nn=1,nvar
do jj=1,3
do ll=1,3
if (iCC(irege,ii,jj,kk,ll)==3) then
token=sCC(irege,ii,jj,kk,ll)
! dCdu =dCfun_du (token,ur,dur)
! dCddu=dCfun_ddu(token,ur,dur)
call dCfun_du (token,r(1),r(2),r(3),ur,dur,nvar,istep, &
ireg,iregup,rnode,vec,imax,jmax,kmax,dCdu)
call dCfun_ddu(token,r(1),r(2),r(3),ur,dur,nvar,istep, &
ireg,iregup,rnode,vec,imax,jmax,kmax,dCddu)
elint(ii,kk,nn)=elint(ii,kk,nn)+dCdu(nn)*elint1(jj,ll) &
+dCddu(nn,1)*elint2(jj,ll,1)+dCddu(nn,2)*elint2(jj,ll,2)+dCddu(nn,3)*elint2(jj,ll,3)
endif
enddo
enddo
enddo
enddo
enddo
endif
enddo ! loop over elements
! ----------------------------------------------------------------------
! We have now summed integrals over all elements connected to alpha, beta, gamma
! nodes. Can now prepare contribution to J(i,alpha,n,gamma)
! ----------------------------------------------------------------------
do ii=1,nvar
do nn=1,nvar
do kk=1,nvar
term2(ii,nn)=term2(ii,nn)+vec(indQ(ib,jb,kb,kk))*elint(ii,kk,nn)
enddo
enddo
enddo
enddo ! loop over beta
enddo
enddo
! ----------------------------------------------------------------------
! Now add term2 to Q
! ----------------------------------------------------------------------
do ii=1,nvar
do nn=1,nvar
irow=indQ(ia,ja,ka,ii)
icol=indQ(ig,jg,kg,nn)
! print *,'irow=',ia,ja,ka,ii
! print *,'icol=',ig,jg,kg,nn
call addtoQ(irow,icol,term2(ii,nn))
enddo
enddo
enddo ! loop over gamma
enddo
enddo
enddo ! loop over alpha
enddo
enddo
print *,'El usage: ',minval(iusel),' to ',maxval(iusel)
end subroutine getJacobianC
! ######################################################################
subroutine getJacobianF
! ----------------------------------------------------------------------
! As getJacobianC but now add f term
! ----------------------------------------------------------------------
use common
use shape
use geom
use matrices
use indexQ
integer ia,ja,ka,ig,jg,kg,ie,je,ke,iep,ind,la,lg
integer inode,jnode,knode,irege
logical igin,jgin,kgin,iein,jein,kein,foundg
integer icomb(2,3),itab(8,4,3),itabsrt(8,3)
double precision rtabsrt(8,3),rtab(8,3),ul(8,nvar),dfdu(nvar),dfddu(nvar,3)
double precision elint(nvar,nvar),elint1,elint2(3),dNa(3),dNg(3)
double precision jac(3,3),invjac(3,3),jacdet,tot,r(3)
integer ixi,ieta,imu,ip
double precision xi,eta,mu,dur(nvar,3),ur(nvar),trailer
integer ii,mm,nn,icol,irow,l,i1,j1,k1
character(EXPRLEN) token
integer iusel(0:imax-1,0:jmax-1,0:kmax-1)
integer, parameter :: ies(8)=[1, 1, 1, 1,-1,-1,-1,-1]
integer, parameter :: jes(8)=[1, 1,-1,-1, 1, 1,-1,-1]
integer, parameter :: kes(8)=[1,-1, 1,-1, 1,-1, 1,-1]
iusel=0
print *,'Preparing Jacobian (getJacobianF)'
do ia=0,imax
print *,'i-plane: ',ia,' / ',imax
do ja=0,jmax
do ka=0,kmax
do ig=ia-1,ia+1
do jg=ja-1,ja+1
do kg=ka-1,ka+1
igin = ig>=0.and.ig<=imax
jgin = jg>=0.and.jg<=jmax
kgin = kg>=0.and.kg<=kmax
if (.not.(igin.and.jgin.and.kgin)) cycle ! node must exist
elint=0
do iep=1,8
ie=ies(iep)
je=jes(iep)
ke=kes(iep)
iein = ia+ie>=0.and.ia+ie<=imax
jein = ja+je>=0.and.ja+je<=jmax
kein = ka+ke>=0.and.ka+ke<=kmax
if (.not.(iein.and.jein.and.kein)) cycle ! element must exist
icomb(1,1)=ia
icomb(1,2)=ja
icomb(1,3)=ka
icomb(2,1)=ia+ie
icomb(2,2)=ja+je
icomb(2,3)=ka+ke
call getel(icomb,rnode,imax,jmax,kmax,itab,rtab)
foundg=.false.
do ind=1,8
if (itab(ind,1,1)==ig.and.itab(ind,1,2)==jg.and.itab(ind,1,3)==kg) foundg=.true.
enddo
if (.not.foundg) cycle
call sort(itab,rtab,itabsrt,rtabsrt)
! ----------------------------------------------------------------------
! Discover if alpha, beta and gamma nodes are all within the element
! (alpha is bound to be but check anyway)
! ----------------------------------------------------------------------
la=0; lg=0
do ip=1,8
inode=itabsrt(ip,1)
jnode=itabsrt(ip,2)
knode=itabsrt(ip,3)
if (inode==ia.and.jnode==ja.and.knode==ka) la=ip
if (inode==ig.and.jnode==jg.and.knode==kg) lg=ip
enddo
if (la==0.or.lg==0) then
print *,'Error: getJacobian: failed to find la,lg or lb'
stop
endif
! ----------------------------------------------------------------------
! Find the element's region number and local solution at nodes
! surrounding element
! Update iusel which states how many times element used
! ----------------------------------------------------------------------
i1=ia+(ie-1)/2
j1=ja+(je-1)/2
k1=ka+(ke-1)/2
irege=iregup(i1,j1,k1)
do l=1,8
inode=itabsrt(l,1)
jnode=itabsrt(l,2)
knode=itabsrt(l,3)
do ii=1,nvar
ul(l,ii)=vec(indQ(inode,jnode,knode,ii))
enddo
enddo
iusel(i1,j1,k1)=iusel(i1,j1,k1)+1
! ----------------------------------------------------------------------
! Integrate
! ----------------------------------------------------------------------
elint1=0
elint2=0
do ixi=1,ng_xi
do ieta=1,ng_eta
do imu=1,ng_mu
xi=gauss(ng_xi,ixi)
eta=gauss(ng_eta,ieta)
mu=gauss(ng_mu,imu)
call jacobian(xi,eta,mu,rtabsrt,jac,invjac,jacdet)
call getdN(la,xi,eta,mu,invjac,dNa) ! dN_alpha/dr
call getdN(lg,xi,eta,mu,invjac,dNg)
trailer=jacdet*wt(ng_xi,ixi)*wt(ng_eta,ieta)*wt(ng_mu,imu)
if (centre_eval) then
elint1=elint1+Nl(la,xi,eta,mu)*Nl(lg,xi,eta,mu)*trailer
do mm=1,3
elint2(mm)=elint2(mm)+Nl(la,xi,eta,mu)*dNg(mm)*trailer
enddo
else
call getsol(ul,invjac,rtabsrt, xi,eta,mu, ur,dur,r)
do ii=1,nvar
do nn=1,nvar
if (iff(irege,ii)==3) then
token=sff(irege,ii)
! dfdu=dffun_du(token,ur,dur)
! dfddu=dffun_ddu(token,ur,dur)
call dffun_du (token,r(1),r(2),r(3),ur,dur,nvar,istep, &
ireg,iregup,rnode,vec,imax,jmax,kmax,dfdu)
call dffun_ddu(token,r(1),r(2),r(3),ur,dur,nvar,istep, &
ireg,iregup,rnode,vec,imax,jmax,kmax,dfddu)
tot=dfdu(nn)*Nl(lg,xi,eta,mu)
do mm=1,3
tot=tot+dfddu(nn,mm)*dNg(mm)
enddo
elint(ii,nn)=elint(ii,nn)+Nl(la,xi,eta,mu)*tot*trailer
endif
enddo
enddo
endif
enddo ! end integral
enddo
enddo
! ----------------------------------------------------------------------
! In case of centre_eval
! ----------------------------------------------------------------------
if (centre_eval) then
call jacobian(zero,zero,zero,rtabsrt,jac,invjac,jacdet)
call getsol(ul,invjac,rtabsrt, zero,zero,zero, ur,dur,r)
do ii=1,nvar
do nn=1,nvar
if (iff(irege,ii)==3) then
token=sff(irege,ii)
! dfdu=dffun_du(token,ur,dur)
! dfddu=dffun_ddu(token,ur,dur)
call dffun_du (token,r(1),r(2),r(3),ur,dur,nvar,istep, &
ireg,iregup,rnode,vec,imax,jmax,kmax,dfdu)
call dffun_ddu(token,r(1),r(2),r(3),ur,dur,nvar,istep, &
ireg,iregup,rnode,vec,imax,jmax,kmax,dfddu)
elint(ii,nn)=elint(ii,nn)+dfdu(nn)*elint1 &
+dfddu(nn,1)*elint2(1) &
+dfddu(nn,2)*elint2(2) &
+dfddu(nn,3)*elint2(3)
endif
enddo
enddo
endif
enddo ! end element loop
do ii=1,nvar
do nn=1,nvar
irow=indQ(ia,ja,ka,ii)
icol=indQ(ig,jg,kg,nn)
call addtoQ(irow,icol,-elint(ii,nn))
enddo
enddo
enddo ! gamma
enddo
enddo
enddo ! alpha
enddo
enddo
print *,'El usage: ',minval(iusel),' to ',maxval(iusel)
end subroutine getJacobianF
! ######################################################################
subroutine getJacobian2C
! ----------------------------------------------------------------------
! Update Q matrix to equal the Jacobian. iQ, jQ. Q must have already been
! set and heapsorted and archived (irowst,irowed). We assume J has the
! same sparsity structure as Q, if not we are in trouble!
! This routine loops over elements then considers pairs or triplets
! at edges of each element to fill Jacobian
! ----------------------------------------------------------------------
use common
use shape
use geom
use matrices
use indexQ
integer i,j,k,in,jn,kn,irege,inode,jnode,knode
integer icomb(2,3),itab(8,4,3),itabsrt(8,3)
double precision rtabsrt(8,3),rtab(8,3),ul(8,nvar),dCdu(nvar),dCddu(nvar,3)
double precision elint(nvar,nvar,nvar),elint1(3,3),elint2(3,3,3),jac(3,3),invjac(3,3),jacdet
integer la,lg,lb,ia,ja,ka,ig,jg,kg,ib,jb,kb
integer ixi,ieta,imu
double precision xi,eta,mu,dur(nvar,3),ur(nvar),tot,trailer,dNa(3),dNb(3),dNg(3),r(3)
integer ii,jj,kk,ll,mm,nn,irow,icol,l
character(EXPRLEN) token
! ----------------------------------------------------------------------
! Loop over elements
! ----------------------------------------------------------------------
print *,'Preparing Jacobian (getJacobian2C)'
do i=0,imax-1
print *,'i-plane: ',i,' / ',imax-1
do j=0,jmax-1
do k=0,kmax-1
in=i+1
jn=j+1
kn=k+1
irege=iregup(i,j,k)
icomb(1,1)=i
icomb(1,2)=j
icomb(1,3)=k
icomb(2,1)=in
icomb(2,2)=jn
icomb(2,3)=kn
call getel(icomb,rnode,imax,jmax,kmax,itab,rtab)
call sort(itab,rtab,itabsrt,rtabsrt)
! ----------------------------------------------------------------------
! Get local solution at nodes surrounding element
! ----------------------------------------------------------------------
do l=1,8
inode=itabsrt(l,1)
jnode=itabsrt(l,2)
knode=itabsrt(l,3)
do ii=1,nvar
ul(l,ii)=vec(indQ(inode,jnode,knode,ii))
enddo
enddo
! ----------------------------------------------------------------------
! Consider every possible triplet of nodes surrounding elements (C matrix)
! ----------------------------------------------------------------------
do la=1,8
do lg=1,8
do lb=1,8
ia=itabsrt(la,1)
ja=itabsrt(la,2)
ka=itabsrt(la,3)
ig=itabsrt(lg,1)
jg=itabsrt(lg,2)
kg=itabsrt(lg,3)
ib=itabsrt(lb,1)
jb=itabsrt(lb,2)
kb=itabsrt(lb,3)
! ----------------------------------------------------------------------
! Calculate integrals over the element
! ----------------------------------------------------------------------
elint=0
elint1=0
elint2=0
do ixi=1,ng_xi
do ieta=1,ng_eta
do imu=1,ng_mu
xi=gauss(ng_xi,ixi)
eta=gauss(ng_eta,ieta)
mu=gauss(ng_mu,imu)
call jacobian(xi,eta,mu,rtabsrt,jac,invjac,jacdet)
call getdN(la,xi,eta,mu,invjac,dNa) ! dN_alpha/dr
call getdN(lg,xi,eta,mu,invjac,dNg)
call getdN(lb,xi,eta,mu,invjac,dNb)
trailer=jacdet*wt(ng_xi,ixi)*wt(ng_eta,ieta)*wt(ng_mu,imu)
! ----------------------------------------------------------------------
! For each ii,nn,kk combination, accumulate integral for C
! (sum over jj,ll spatial directions)
! All of this is for the alpha, gamma node (beta summed automatically)
! ----------------------------------------------------------------------
if (centre_eval) then
do jj=1,3
do ll=1,3
elint1(jj,ll)=elint1(jj,ll)+dNa(jj)*dNb(ll)*Nl(lg,xi,eta,mu)*trailer
do mm=1,3
elint2(jj,ll,mm)=elint2(jj,ll,mm)+dNa(jj)*dNb(ll)*dNg(mm)*trailer
enddo
enddo
enddo
else
call getsol(ul,invjac,rtabsrt, xi,eta,mu, ur,dur,r)
do ii=1,nvar
do nn=1,nvar
do kk=1,nvar
do jj=1,3
do ll=1,3
! Allow only token/DLL non-linear for now
if (iCC(irege,ii,jj,kk,ll)==3) then
token=sCC(irege,ii,jj,kk,ll)
! dCdu= dCfun_du(token,ur,dur) ! variation with u
! dCddu=dCfun_ddu(token,ur,dur) ! variation with du/dr
call dCfun_du (token,r(1),r(2),r(3),ur,dur,nvar,istep, &
ireg,iregup,rnode,vec,imax,jmax,kmax,dCdu)
call dCfun_ddu(token,r(1),r(2),r(3),ur,dur,nvar,istep, &
ireg,iregup,rnode,vec,imax,jmax,kmax,dCddu)
tot=dCdu(nn)*Nl(lg,xi,eta,mu)
do mm=1,3
tot=tot+dCddu(nn,mm)*dNg(mm)
enddo
elint(ii,kk,nn)=elint(ii,kk,nn)+dNa(jj)*dNb(ll)*tot*trailer
endif
enddo
enddo
enddo
enddo
enddo
endif
enddo ! element integral (Gaussian quad)
enddo
enddo
! ----------------------------------------------------------------------
! For centre_eval, form elint
! ----------------------------------------------------------------------
if (centre_eval) then
call jacobian(zero,zero,zero, rtabsrt,jac,invjac,jacdet)
call getsol(ul,invjac, rtabsrt, zero,zero,zero, ur,dur,r)
! print *,'Centre eval!'
do ii=1,nvar
do kk=1,nvar
do nn=1,nvar
do jj=1,3
do ll=1,3
if (iCC(irege,ii,jj,kk,ll)==3) then
token=sCC(irege,ii,jj,kk,ll)
! dCdu=dCfun_du(token,ur,dur)
! dCddu=dCfun_ddu(token,ur,dur)
call dCfun_du(token,r(1),r(2),r(3),ur,dur,nvar,istep, &
ireg,iregup,rnode,vec,imax,jmax,kmax,dCdu)
call dCfun_ddu(token,r(1),r(2),r(3),ur,dur,nvar,istep, &
ireg,iregup,rnode,vec,imax,jmax,kmax,dCddu)
! print *,jj,ll,elint1(jj,ll),elint2(jj,ll,:)
elint(ii,kk,nn)=elint(ii,kk,nn)+dCdu(nn)*elint1(jj,ll) &
+dCddu(nn,1)*elint2(jj,ll,1)+dCddu(nn,2)*elint2(jj,ll,2)+dCddu(nn,3)*elint2(jj,ll,3)
endif
enddo
enddo
! print *,ii,kk,nn,elint(ii,kk,nn)
enddo
enddo
enddo
! stop
endif
! ----------------------------------------------------------------------
! Add contributions to the [alpha,i] and [gamma,n] dofs
! There is an implied sum over [beta,k]
! ----------------------------------------------------------------------
do ii=1,nvar
do nn=1,nvar
tot=0
do kk=1,nvar
tot=tot+vec(indQ(ib,jb,kb,kk))*elint(ii,kk,nn)
enddo
irow=indQ(ia,ja,ka,ii)
icol=indQ(ig,jg,kg,nn)
call addtoQ(irow,icol,tot)
enddo
enddo
enddo ! loop over node triplets
enddo
enddo
enddo ! Element loop
enddo
enddo
end subroutine getJacobian2C
! ######################################################################
subroutine getJacobian2F
use common
use shape
use geom
use matrices
use indexQ
integer i,j,k,in,jn,kn,irege,inode,jnode,knode
integer icomb(2,3),itab(8,4,3),itabsrt(8,3)
double precision rtabsrt(8,3),ul(8,nvar),dfdu(nvar),dfddu(nvar,3),rtab(8,3)
double precision elint(nvar,nvar),elint1,elint2(3),jac(3,3),invjac(3,3),jacdet
integer la,lg,ia,ja,ka,ig,jg,kg,icol,irow,l
integer ixi,ieta,imu
double precision xi,eta,mu,dur(nvar,3),ur(nvar),tot,trailer,dNa(3),dNg(3),r(3)
integer ii,mm,nn
character(EXPRLEN) token
! ----------------------------------------------------------------------
! Loop over elements
! ----------------------------------------------------------------------
print *,'Preparing Jacobian (getJacobian2F)'
do i=0,imax-1
print *,'i-plane: ',i,' / ',imax-1
do j=0,jmax-1
do k=0,kmax-1
in=i+1
jn=j+1
kn=k+1
irege=iregup(i,j,k)
icomb(1,1)=i
icomb(1,2)=j
icomb(1,3)=k
icomb(2,1)=in
icomb(2,2)=jn
icomb(2,3)=kn
call getel(icomb,rnode,imax,jmax,kmax,itab,rtab)
call sort(itab,rtab,itabsrt,rtabsrt)
! ----------------------------------------------------------------------
! Get local solution at nodes surrounding element
! ----------------------------------------------------------------------
do l=1,8
inode=itabsrt(l,1)
jnode=itabsrt(l,2)
knode=itabsrt(l,3)
do ii=1,nvar
ul(l,ii)=vec(indQ(inode,jnode,knode,ii))
enddo
enddo
! ----------------------------------------------------------------------
! Consider every possible pair of nodes surrounding elements (C matrix)
! ----------------------------------------------------------------------
do la=1,8
do lg=1,8
ia=itabsrt(la,1)
ja=itabsrt(la,2)
ka=itabsrt(la,3)
ig=itabsrt(lg,1)
jg=itabsrt(lg,2)
kg=itabsrt(lg,3)
! ----------------------------------------------------------------------
! Calculate integrals over the element
! ----------------------------------------------------------------------
elint=0
elint1=0
elint2=0
do ixi=1,ng_xi
do ieta=1,ng_eta
do imu=1,ng_mu
xi=gauss(ng_xi,ixi)
eta=gauss(ng_eta,ieta)
mu=gauss(ng_mu,imu)
call jacobian(xi,eta,mu,rtabsrt,jac,invjac,jacdet)
call getdN(la,xi,eta,mu,invjac,dNa) ! dN_alpha/dr
call getdN(lg,xi,eta,mu,invjac,dNg)
trailer=jacdet*wt(ng_xi,ixi)*wt(ng_eta,ieta)*wt(ng_mu,imu)
if (centre_eval) then
elint1=elint1+Nl(la,xi,eta,mu)*Nl(lg,xi,eta,mu)*trailer
do mm=1,3
elint2(mm)=elint2(mm)+Nl(la,xi,eta,mu)*dNg(mm)*trailer
enddo
else
! ----------------------------------------------------------------------
! For each ii, nn combination, accumulate integral for f
! ----------------------------------------------------------------------
call getsol(ul,invjac,rtabsrt, xi,eta,mu, ur,dur,r)
do ii=1,nvar
do nn=1,nvar