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cuboid.f90
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module cuboid
implicit none
private
public getQcuboid,getQcuboid2,getRcuboid,getJacobianCuboid
integer, parameter :: xbar(8)=[-1, 1, 1,-1, -1, 1, 1,-1]
integer, parameter :: ybar(8)=[-1,-1, 1, 1, -1,-1, 1, 1]
integer, parameter :: zbar(8)=[-1,-1,-1,-1, 1, 1, 1, 1]
double precision g_rtabsrt(8,3)
double precision g_xmin,g_xmax, g_ymin,g_ymax, g_zmin,g_zmax
interface Ix
module procedure Ix0,Ix1,Ix2,Ix3
end interface Ix
interface Iy
module procedure Iy0,Iy1,Iy2,Iy3
end interface Iy
interface Iz
module procedure Iz0,Iz1,Iz2,Iz3
end interface Iz
contains
subroutine getQcuboid(rmFixed)
use common
use matrices
use indexq
use iofile
logical rmFixed,inin,jnin,knin,iein,jein,kein,found
integer i,j,k,in,jn,kn,iep,ie,je,ke,iCCx
integer L1,L2,ip,inode,jnode,knode,i1,j1,k1,irege,itabsrt(8,3)
double precision xmax,ymax,zmax,xmin,ymin,zmin,dx,dy,dz,rtabsrt(8,3),xL1,yL1,zL1,xL2,yL2,zL2
double precision rc(3),elint(3,3),tot,ur(nvar),dur(nvar,3)
integer ii,kk,ialpha,ibeta,jj,ll,lenQst,L
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]
integer, parameter :: x=1, y=2, z=3
if (rmFixed) call prterr('getQcuboid: removeFixed not supported')
print *,'Calculating Q matrix (assume all elements are cuboids)'
lenQ=0
do k=0,kmax
write (*,*) 'k-plane:',k,'/',kmax
do j=0,jmax
do i=0,imax
do in=i-1,i+1
do jn=j-1,j+1
do kn=k-1,k+1
inin=(in.ge.0.and.in.le.imax)
jnin=(jn.ge.0.and.jn.le.jmax)
knin=(kn.ge.0.and.kn.le.kmax)
if (inin.and.jnin.and.knin) then
lenQst=lenQ+1
do iep=1,8
ie=ies(iep)
je=jes(iep)
ke=kes(iep)
iein=(i+ie.ge.0.and.i+ie.le.imax)
jein=(j+je.ge.0.and.j+je.le.jmax)
kein=(k+ke.ge.0.and.k+ke.le.kmax)
if (iein.and.jein.and.kein) then
i1=i+(ie-1)/2
j1=j+(je-1)/2
k1=k+(ke-1)/2 ! for 2D, k=0, ke=1 => k1=0
irege=iregup(i1,j1,k1)
itabsrt(1,:)=[i1, j1, k1]
itabsrt(2,:)=[i1+1, j1, k1]
itabsrt(3,:)=[i1+1,j1+1, k1]
itabsrt(4,:)=[i1 ,j1+1, k1]
itabsrt(5,:)=[i1, j1,k1+1]
itabsrt(6,:)=[i1+1, j1,k1+1]
itabsrt(7,:)=[i1+1,j1+1,k1+1]
itabsrt(8,:)=[i1 ,j1+1,k1+1]
found=.false.
do ip=1,8
if (itabsrt(ip,1).eq.in.and.itabsrt(ip,2).eq.jn.and.itabsrt(ip,3).eq.kn) found=.true.
enddo
if (found) then
L1=0; L2=0
do ip=1,8
inode=itabsrt(ip,1)
jnode=itabsrt(ip,2)
knode=itabsrt(ip,3)
if (inode.eq.i.and.jnode.eq.j.and.knode.eq.k) L1=ip
if (inode.eq.in.and.jnode.eq.jn.and.knode.eq.kn) L2=ip
enddo
if (L1==0.or.L2==0) call prterr('Error in getQ, bad L1,L2')
xmax=rnode(i1+1,j1,k1,1); xmin=rnode(i1,j1,k1,1)
ymax=rnode(i1,j1+1,k1,2); ymin=rnode(i1,j1,k1,2)
zmax=rnode(i1,j1,k1+1,3); zmin=rnode(i1,j1,k1,3)
dx=xmax-xmin
dy=ymax-ymin
dz=zmax-zmin
do L=1,8
rtabsrt(L,:)=rnode(itabsrt(L,1),itabsrt(L,2),itabsrt(L,3),:)
enddo
rc=0
do L=1,8
rc=rc+rtabsrt(L,:)
enddo
rc=rc/8
call getelinfo(itabsrt,rtabsrt,ur,dur)
xL1=rtabsrt(L1,1) ! rnode(i,j,k,1)
yL1=rtabsrt(L1,2)
zL1=rtabsrt(L1,3)
xL2=rtabsrt(L2,1) ! rnode(in,jn,kn,1)
yL2=rtabsrt(L2,2)
zL2=rtabsrt(L2,3)
! print *,xL1,yL1,zL1,'?=',rnode(i,j,k,:)
! print *,xL2,yL2,zL2,'?=',rnode(in,jn,kn,:)
! stop
! double precision g_xmin,g_xmax, g_ymin,g_ymax, g_zmin,g_zmax
elint(x,x)=xbar(L1)*xbar(L2)/dx &
*dintf(ymin, ymax, ybar(L1)/dy, yL1, ybar(L2)/dy, yL2) &
*dintf(zmin, zmax, zbar(L1)/dz, zL1, zbar(L2)/dz, zL2)
elint(y,y)=ybar(L1)*ybar(L2)/dy &
*dintf(xmin, xmax, xbar(L1)/dx, xL1, xbar(L2)/dx, xL2) &
*dintf(zmin, zmax, zbar(L1)/dz, zL1, zbar(L2)/dz, zL2)
elint(z,z)=zbar(L1)*zbar(L2)/dz &
*dintf(xmin, xmax, xbar(L1)/dx, xL1, xbar(L2)/dx, xL2) &
*dintf(ymin, ymax, ybar(L1)/dy, yL1, ybar(L2)/dy, yL2)
!----------------------------------------------------------------------
elint(x,y)=xbar(L1)*ybar(L2)/(dx*dy) &
*(xmax+xbar(L2)*(xmax-xL2)**2/(2*dx)-xmin-xbar(L2)*(xmin-xL2)**2/(2*dx)) &
*(ymax+ybar(L1)*(ymax-yL1)**2/(2*dy)-ymin-ybar(L1)*(ymin-yL1)**2/(2*dy)) &
*dintf(zmin, zmax, zbar(l1)/dz, zL1, zbar(L2)/dz, zL2)
elint(y,x)=ybar(L1)*xbar(L2)/(dy*dx) &
*(ymax+ybar(L2)*(ymax-yL2)**2/(2*dy)-ymin-ybar(L2)*(ymin-yL2)**2/(2*dy)) &
*(xmax+xbar(L1)*(xmax-xL1)**2/(2*dx)-xmin-xbar(L1)*(xmin-xL1)**2/(2*dx)) &
*dintf(zmin, zmax, zbar(l1)/dz, zL1, zbar(L2)/dz, zL2)
!----------------------------------------------------------------------
elint(x,z)=xbar(L1)*zbar(L2)/(dx*dz) &
*(xmax+xbar(L2)*(xmax-xL2)**2/(2*dx)-xmin-xbar(L2)*(xmin-xL2)**2/(2*dx)) &
*(zmax+zbar(L1)*(zmax-zL1)**2/(2*dz)-zmin-zbar(L1)*(zmin-zL1)**2/(2*dz)) &
*dintf(ymin, ymax, ybar(L1)/dy, yL1, ybar(L2)/dy, yL2)
elint(z,x)=zbar(L1)*xbar(L2)/(dz*dx) &
*(zmax+zbar(L2)*(zmax-zL2)**2/(2*dz)-zmin-zbar(L2)*(zmin-zL2)**2/(2*dz)) &
*(xmax+xbar(L1)*(xmax-xL1)**2/(2*dx)-xmin-xbar(L1)*(xmin-xL1)**2/(2*dx)) &
*dintf(ymin, ymax, ybar(L1)/dy, yL1, ybar(L2)/dy, yL2)
!----------------------------------------------------------------------
elint(y,z)=ybar(L1)*zbar(L2)/(dy*dz) &
*(ymax+ybar(L2)*(ymax-yL2)**2/(2*dy)-ymin-ybar(L2)*(ymin-yL2)**2/(2*dy)) &
*(zmax+zbar(L1)*(zmax-zL1)**2/(2*dz)-zmin-zbar(L1)*(zmin-zL1)**2/(2*dz)) &
*dintf(xmin, xmax, xbar(L1)/dx, xL1, xbar(L2)/dx, xL2)
elint(z,y)=zbar(L1)*ybar(L2)/(dz*dy) &
*(zmax+zbar(L2)*(zmax-zL2)**2/(2*dz)-zmin-zbar(L2)*(zmin-zL2)**2/(2*dz)) &
*(ymax+ybar(L1)*(ymax-yL1)**2/(2*dy)-ymin-ybar(L1)*(ymin-yL1)**2/(2*dy)) &
*dintf(xmin, xmax, xbar(L1)/dx, xL1, xbar(L2)/dx, xL2)
do ii=1,nvar
do kk=1,nvar
ialpha=indQ(i,j,k,ii)
ibeta =indQ(in,jn,kn,kk)
tot=0
do jj=1,3
do ll=1,3
tot=tot+CCval(irege,ii,jj,kk,ll,ur,dur,rc,iCCx)*elint(jj,ll)
enddo
enddo
! tot=tot+aaval(irege,ii,kk,ur,dur,rc,iaax)*elintNN
if (tot /= 0.or.newton=="YES") then
found=.false.
do ip=lenQst,lenQ ! prev lenQst,lenQ
if (iQ(ip) == ialpha.and.jQ(ip) == ibeta) then
Qval(ip)=Qval(ip)+tot
found=.true.
exit
endif
enddo
if (.not.found) then
lenQ=lenQ+1
iQ(lenQ)=ialpha
jQ(lenQ)=ibeta
Qval(lenQ)=tot
endif
endif
enddo ! var number ii
enddo
endif ! found=true
endif ! iein
enddo ! iep
endif ! inin
enddo
enddo
enddo
enddo
enddo
enddo
end subroutine getQcuboid
! ######################################################################
subroutine getQcuboid2(rmFixed)
use common
use matrices
use indexq
use iofile
logical rmFixed
double precision tot,rtabsrt(8,3)
double precision xmin,xmax,ymin,ymax,zmin,zmax,dx,dy,dz,rc(3),ur(nvar),dur(nvar,3)
double precision elint(3,3),xL1,yL1,zL1,xL2,yL2,zL2
integer, parameter :: x=1, y=2, z=3
integer i,j,k,irege,L,L1,L2,ii,kk,jj,ll,ip,ialpha,ibeta,iCCx
integer itabsrt(8,3),iL1,jL1,kL1,iL2,jL2,kL2,endprevrow,lenQst
logical found
if (rmFixed) call prterr('getQcuboid: removeFixed not supported')
print *,'Calculating Q-matrix (assume all elements are cuboids)'
lenQ=0
lenQst=1
do i=0,imax-1
write (*,*) 'i-plane:',i,'/',imax
do j=0,jmax-1
do k=0,kmax-1
print *,i,j,k,lenQ,lenQst
irege=iregup(i,j,k)
itabsrt(1,:)=[i, j, k]
itabsrt(2,:)=[i+1, j, k]
itabsrt(3,:)=[i+1,j+1, k]
itabsrt(4,:)=[i ,j+1, k]
itabsrt(5,:)=[i, j,k+1]
itabsrt(6,:)=[i+1, j,k+1]
itabsrt(7,:)=[i+1,j+1,k+1]
itabsrt(8,:)=[i ,j+1,k+1]
xmax=rnode(i+1,j,k,1); xmin=rnode(i,j,k,1)
ymax=rnode(i,j+1,k,2); ymin=rnode(i,j,k,2)
zmax=rnode(i,j,k+1,3); zmin=rnode(i,j,k,3)
dx=xmax-xmin
dy=ymax-ymin
dz=zmax-zmin
do L=1,8
rtabsrt(L,:)=rnode(itabsrt(L,1),itabsrt(L,2),itabsrt(L,3),:)
enddo
rc=0
do L=1,8
rc=rc+rtabsrt(L,:)
enddo
rc=rc/8
call getelinfo(itabsrt,rtabsrt,ur,dur)
do L1=1,8
do L2=1,8
iL1=itabsrt(L1,1)
jL1=itabsrt(L1,2)
kL1=itabsrt(L1,3)
iL2=itabsrt(L2,1)
jL2=itabsrt(L2,2)
kL2=itabsrt(L2,3)
xL1=rtabsrt(L1,1)
yL1=rtabsrt(L1,2)
zL1=rtabsrt(L1,3)
xL2=rtabsrt(L2,1)
yL2=rtabsrt(L2,2)
zL2=rtabsrt(L2,3)
elint(x,x)=xbar(L1)*xbar(L2)/dx &
*dintf(ymin, ymax, ybar(L1)/dy, yL1, ybar(L2)/dy, yL2) &
*dintf(zmin, zmax, zbar(L1)/dz, zL1, zbar(L2)/dz, zL2)
elint(y,y)=ybar(L1)*ybar(L2)/dy &
*dintf(xmin, xmax, xbar(L1)/dx, xL1, xbar(L2)/dx, xL2) &
*dintf(zmin, zmax, zbar(L1)/dz, zL1, zbar(L2)/dz, zL2)
elint(z,z)=zbar(L1)*zbar(L2)/dz &
*dintf(xmin, xmax, xbar(L1)/dx, xL1, xbar(L2)/dx, xL2) &
*dintf(ymin, ymax, ybar(L1)/dy, yL1, ybar(L2)/dy, yL2)
!----------------------------------------------------------------------
elint(x,y)=xbar(L1)*ybar(L2)/(dx*dy) &
*(xmax+xbar(L2)*(xmax-xL2)**2/(2*dx)-xmin-xbar(L2)*(xmin-xL2)**2/(2*dx)) &
*(ymax+ybar(L1)*(ymax-yL1)**2/(2*dy)-ymin-ybar(L1)*(ymin-yL1)**2/(2*dy)) &
*dintf(zmin, zmax, zbar(l1)/dz, zL1, zbar(L2)/dz, zL2)
elint(y,x)=ybar(L1)*xbar(L2)/(dy*dx) &
*(ymax+ybar(L2)*(ymax-yL2)**2/(2*dy)-ymin-ybar(L2)*(ymin-yL2)**2/(2*dy)) &
*(xmax+xbar(L1)*(xmax-xL1)**2/(2*dx)-xmin-xbar(L1)*(xmin-xL1)**2/(2*dx)) &
*dintf(zmin, zmax, zbar(l1)/dz, zL1, zbar(L2)/dz, zL2)
!----------------------------------------------------------------------
elint(x,z)=xbar(L1)*zbar(L2)/(dx*dz) &
*(xmax+xbar(L2)*(xmax-xL2)**2/(2*dx)-xmin-xbar(L2)*(xmin-xL2)**2/(2*dx)) &
*(zmax+zbar(L1)*(zmax-zL1)**2/(2*dz)-zmin-zbar(L1)*(zmin-zL1)**2/(2*dz)) &
*dintf(ymin, ymax, ybar(L1)/dy, yL1, ybar(L2)/dy, yL2)
elint(z,x)=zbar(L1)*xbar(L2)/(dz*dx) &
*(zmax+zbar(L2)*(zmax-zL2)**2/(2*dz)-zmin-zbar(L2)*(zmin-zL2)**2/(2*dz)) &
*(xmax+xbar(L1)*(xmax-xL1)**2/(2*dx)-xmin-xbar(L1)*(xmin-xL1)**2/(2*dx)) &
*dintf(ymin, ymax, ybar(L1)/dy, yL1, ybar(L2)/dy, yL2)
!----------------------------------------------------------------------
elint(y,z)=ybar(L1)*zbar(L2)/(dy*dz) &
*(ymax+ybar(L2)*(ymax-yL2)**2/(2*dy)-ymin-ybar(L2)*(ymin-yL2)**2/(2*dy)) &
*(zmax+zbar(L1)*(zmax-zL1)**2/(2*dz)-zmin-zbar(L1)*(zmin-zL1)**2/(2*dz)) &
*dintf(xmin, xmax, xbar(L1)/dx, xL1, xbar(L2)/dx, xL2)
elint(z,y)=zbar(L1)*ybar(L2)/(dz*dy) &
*(zmax+zbar(L2)*(zmax-zL2)**2/(2*dz)-zmin-zbar(L2)*(zmin-zL2)**2/(2*dz)) &
*(ymax+ybar(L1)*(ymax-yL1)**2/(2*dy)-ymin-ybar(L1)*(ymin-yL1)**2/(2*dy)) &
*dintf(xmin, xmax, xbar(L1)/dx, xL1, xbar(L2)/dx, xL2)
do ii=1,nvar
do kk=1,nvar
ialpha=indQ(iL1,jL1,kL1,ii)
ibeta =indQ(iL2,jL2,kL2,kk)
tot=0
do jj=1,3
do ll=1,3
tot=tot+CCval(irege,ii,jj,kk,ll,ur,dur,rc,iCCx)*elint(jj,ll)
enddo
enddo
! print *,"tot=",L1,L2,ii,kk,tot
! tot=tot+aaval(irege,ii,kk,ur,dur,rc,iaax)*elintNN
if (tot /= 0.or.newton=="YES") then
found=.false.
do ip=lenQst,lenQ ! prev lenQst,lenQ
if (iQ(ip) == ialpha.and.jQ(ip) == ibeta) then
Qval(ip)=Qval(ip)+tot
found=.true.
exit
endif
enddo
if (.not.found) then
lenQ=lenQ+1
iQ(lenQ)=ialpha
jQ(lenQ)=ibeta
Qval(lenQ)=tot
endif
endif
enddo ! var number
enddo
enddo ! local numbers L1,L2
enddo
enddo ! i,j,k
enddo
if (i /= 0) then
lenQst=endprevrow+1
endif
endprevrow=lenQ
enddo
end subroutine getQcuboid2
! ######################################################################
subroutine getRcuboid(append)
! ----------------------------------------------------------------------
! Form the R vector. Uses rnode, ff, iff, u (non-linear)
! ----------------------------------------------------------------------
use common
use geom
use shape
use indexQ
use matrices
use util
use iofile, only : prterr
logical append
integer itabsrt(2**NDIM,NDIM)
double precision rtabsrt(2**NDIM,NDIM),elintN
double precision ur(nvar),dur(nvar,NDIM),rc(NDIM)
double precision xmax,ymax,zmax,xmin,ymin,zmin,dx,dy,dz,xL1,yL1,zL1
integer i,j,k,iL1,jL1,kL1,irege,ii,L1,ialpha,L
! ----------------------------------------------------------------------
! Loop over nodes. getQ must have been called already so RR has non-zero
! entries by now
! ----------------------------------------------------------------------
print *,'Calculating R matrix'
if (.not.append) RR=0 ! start from scratch
do k=0,kmax-1
do j=0,jmax-1
do i=0,imax-1
irege=iregup(i,j,k)
itabsrt(1,:)=[i, j, k]
itabsrt(2,:)=[i+1, j, k]
itabsrt(3,:)=[i+1,j+1, k]
itabsrt(4,:)=[i ,j+1, k]
itabsrt(5,:)=[i, j,k+1]
itabsrt(6,:)=[i+1, j,k+1]
itabsrt(7,:)=[i+1,j+1,k+1]
itabsrt(8,:)=[i ,j+1,k+1]
xmax=rnode(i+1,j,k,1); xmin=rnode(i,j,k,1)
ymax=rnode(i,j+1,k,2); ymin=rnode(i,j,k,2)
zmax=rnode(i,j,k+1,3); zmin=rnode(i,j,k,3)
dx=xmax-xmin
dy=ymax-ymin
dz=zmax-zmin
do L=1,8
rtabsrt(L,:)=rnode(itabsrt(L,1),itabsrt(L,2),itabsrt(L,3),:)
enddo
rc=0
do L=1,8
rc=rc+rtabsrt(L,:)
enddo
rc=rc/8
call getelinfo(itabsrt,rtabsrt,ur,dur)
do L1=1,8
iL1=itabsrt(L1,1)
jL1=itabsrt(L1,2)
kL1=itabsrt(L1,3)
xL1=rtabsrt(L1,1)
yL1=rtabsrt(L1,2)
zL1=rtabsrt(L1,3)
! ----------------------------------------------------------------------
! Calculate elintN = int N_alpha^(e) dV, alpha -> l1
! for given node and element
! ----------------------------------------------------------------------
elintN=(xmax+xbar(L1)*(xmax-xL1)**2/(2*dx)-xmin-xbar(L1)*(xmin-xL1)**2/(2*dx)) &
*(ymax+ybar(L1)*(ymax-yL1)**2/(2*dy)-ymin-ybar(L1)*(ymin-yL1)**2/(2*dy)) &
*(zmax+zbar(L1)*(zmax-zL1)**2/(2*dz)-zmin-zbar(L1)*(zmin-zL1)**2/(2*dz))
do ii=1,nvar
ialpha=indQ(iL1,jL1,kL1,ii)
RR(ialpha)=RR(ialpha)+ffval(irege,ii,ur,dur,rc)*elintN
enddo
enddo
enddo
enddo
enddo
end subroutine getRcuboid
! ######################################################################
function intf(s,a,b,c,d)
double precision intf,s,a,b,c,d
intf=s+a*(s-b)**2/2+c*(s-d)**2/2+a*c*(s**3/3-s**2/2*(b+d)+s*b*d)
end function intf
! ######################################################################
function dintf(smin,smax,a,b,c,d)
double precision dintf,smin,smax,a,b,c,d
dintf=intf(smax,a,b,c,d)-intf(smin,a,b,c,d)
end function dintf
! ######################################################################
subroutine getJacobianCuboid
call getJacobianCuboidC
call getJacobianCuboidF
end subroutine getJacobianCuboid
! ######################################################################
subroutine getJacobianCuboidC
! ----------------------------------------------------------------------
! Add components to Qval to make it into Jacobian
! Works only for cuboid elements and accounts only for nonlinear C
! ----------------------------------------------------------------------
use common
use matrices
use indexq
integer, parameter :: x=1,y=2,z=3
integer i,j,k,irege,itabsrt(8,3),L,la,lb,lg,ip
integer ia,ja,ka,ib,jb,kb,ig,jg,kg,ii,jj,kk,ll,nn,irow,icol
double precision xmin,xmax,ymin,ymax,zmin,zmax,dx,dy,dz,ur(nvar),dur(nvar,3)
double precision elint2(3,3),elint3(3,3,3),elint(nvar,nvar,nvar),tot
double precision rtabsrt(8,3),dCdu(nvar),dCddu(nvar,3),xc,yc,zc
character(EXPRLEN) token
logical found
print *,'Preparing Jacobian (getJacobianCuboidC)'
do i=0,imax-1
print *,'i-plane: ',i,'/',imax-1
do j=0,jmax-1
do k=0,kmax-1
irege=iregup(i,j,k)
itabsrt(1,:)=[i, j, k]
itabsrt(2,:)=[i+1, j, k]
itabsrt(3,:)=[i+1,j+1, k]
itabsrt(4,:)=[i ,j+1, k]
itabsrt(5,:)=[i, j,k+1]
itabsrt(6,:)=[i+1, j,k+1]
itabsrt(7,:)=[i+1,j+1,k+1]
itabsrt(8,:)=[i ,j+1,k+1]
xmax=rnode(i+1,j,k,1); xmin=rnode(i,j,k,1)
ymax=rnode(i,j+1,k,2); ymin=rnode(i,j,k,2)
zmax=rnode(i,j,k+1,3); zmin=rnode(i,j,k,3)
dx=xmax-xmin; xc=(xmax+xmin)/2
dy=ymax-ymin; yc=(ymax+ymin)/2
dz=zmax-zmin; zc=(zmax+zmin)/2
do L=1,8
rtabsrt(L,:)=rnode(itabsrt(L,1),itabsrt(L,2),itabsrt(L,3),:)
enddo
call getelinfo(itabsrt,rtabsrt,ur,dur) ! get ur, dur at centre
! Global variables for Ix, Iy, Iz functions
g_rtabsrt=rtabsrt
g_xmax=xmax; g_xmin=xmin
g_ymax=ymax; g_ymin=ymin
g_zmax=zmax; g_zmin=zmin
do la=1,8
do lb=1,8
do lg=1,8
ia=itabsrt(la,1)
ja=itabsrt(la,2)
ka=itabsrt(la,3)
ib=itabsrt(lb,1)
jb=itabsrt(lb,2)
kb=itabsrt(lb,3)
ig=itabsrt(lg,1)
jg=itabsrt(lg,2)
kg=itabsrt(lg,3)
! a b
! elint2( , )= Ix(la,lb,lg)*Iy(la,lb,lg)*Iz(la,lb,lg)
elint2(x,x)= Ix( lg)*Iy(la,lb,lg)*Iz(la,lb,lg) *xbar(la)/dx *xbar(lb)/dx
elint2(x,y)= Ix( lb,lg)*Iy(la, lg)*Iz(la,lb,lg) *xbar(la)/dx *ybar(lb)/dy
elint2(x,z)= Ix( lb,lg)*Iy(la,lb,lg)*Iz(la, lg) *xbar(la)/dx *zbar(lb)/dz
elint2(y,x)= Ix(la, lg)*Iy( lb,lg)*Iz(la,lb,lg) *ybar(la)/dy *xbar(lb)/dx
elint2(y,y)= Ix(la,lb,lg)*Iy( lg)*Iz(la,lb,lg) *ybar(la)/dy *ybar(lb)/dy
elint2(y,z)= Ix(la,lb,lg)*Iy( lb,lg)*Iz(la, lg) *ybar(la)/dy *zbar(lb)/dz
elint2(z,x)= Ix(la, lg)*Iy(la,lb,lg)*Iz( lb,lg) *zbar(la)/dz *xbar(lb)/dx
elint2(z,y)= Ix(la,lb,lg)*Iy(la, lg)*Iz( lb,lg) *zbar(la)/dz *ybar(lb)/dy
elint2(z,z)= Ix(la,lb,lg)*Iy(la,lb,lg)*Iz( lg) *zbar(la)/dz *zbar(lb)/dz
! a b g
! elint3( , , )=Ix(la,lb,lg)*Iy(la,lb,lg)*Iz(la,lb,lg)
elint3(x,x,x)=Ix( )*Iy(la,lb,lg)*Iz(la,lb,lg) *xbar(la)/dx *xbar(lb)/dx *xbar(lg)/dx
elint3(x,x,y)=Ix( lg)*Iy(la,lb )*Iz(la,lb,lg) *xbar(la)/dx *xbar(lb)/dx *ybar(lg)/dy
elint3(x,x,z)=Ix( lg)*Iy(la,lb,lg)*Iz(la,lb ) *xbar(la)/dx *xbar(lb)/dx *zbar(lg)/dz
elint3(x,y,x)=Ix( lb )*Iy(la, lg)*Iz(la,lb,lg) *xbar(la)/dx *ybar(lb)/dy *xbar(lg)/dx
elint3(x,y,y)=Ix( lb,lg)*Iy(la )*Iz(la,lb,lg) *xbar(la)/dx *ybar(lb)/dy *ybar(lg)/dy
elint3(x,y,z)=Ix( lb,lg)*Iy(la, lg)*Iz(la,lb ) *xbar(la)/dx *ybar(lb)/dy *zbar(lg)/dz
elint3(x,z,x)=Ix( lb )*Iy(la,lb,lg)*Iz(la, lg) *xbar(la)/dx *zbar(lb)/dz *xbar(lg)/dx
elint3(x,z,y)=Ix( lb,lg)*Iy(la,lb )*Iz(la, lg) *xbar(la)/dx *zbar(lb)/dz *ybar(lg)/dy
elint3(x,z,z)=Ix( lb,lg)*Iy(la,lb,lg)*Iz(la ) *xbar(la)/dx *zbar(lb)/dz *zbar(lg)/dz
! ----------------------------------------------------------------------
elint3(y,x,x)=Ix(la )*Iy( lb,lg)*Iz(la,lb,lg) *ybar(la)/dy *xbar(lb)/dx *xbar(lg)/dx
elint3(y,x,y)=Ix(la ,lg)*Iy( lb )*Iz(la,lb,lg) *ybar(la)/dy *xbar(lb)/dx *ybar(lg)/dy
elint3(y,x,z)=Ix(la ,lg)*Iy( lb,lg)*Iz(la,lb ) *ybar(la)/dy *xbar(lb)/dx *zbar(lg)/dz
elint3(y,y,x)=Ix(la,lb )*Iy( lg)*Iz(la,lb,lg) *ybar(la)/dy *ybar(lb)/dy *xbar(lg)/dx
elint3(y,y,y)=Ix(la,lb,lg)*Iy( )*Iz(la,lb,lg) *ybar(la)/dy *ybar(lb)/dy *ybar(lg)/dy
elint3(y,y,z)=Ix(la,lb,lg)*Iy( lg)*Iz(la,lb ) *ybar(la)/dy *ybar(lb)/dy *zbar(lg)/dz
elint3(y,z,x)=Ix(la,lb )*Iy( lb,lg)*Iz(la ,lg) *ybar(la)/dy *zbar(lb)/dz *xbar(lg)/dx
elint3(y,z,y)=Ix(la,lb,lg)*Iy( lb )*Iz(la ,lg) *ybar(la)/dy *zbar(lb)/dz *ybar(lg)/dy
elint3(y,z,z)=Ix(la,lb,lg)*Iy( lb,lg)*Iz(la ) *ybar(la)/dy *zbar(lb)/dz *zbar(lg)/dz
! ----------------------------------------------------------------------
elint3(z,x,x)=Ix(la )*Iy(la,lb,lg)*Iz( lb,lg) *zbar(la)/dz *xbar(lb)/dx *xbar(lg)/dx
elint3(z,x,y)=Ix(la ,lg)*Iy(la,lb )*Iz( lb,lg) *zbar(la)/dz *xbar(lb)/dx *ybar(lg)/dy
elint3(z,x,z)=Ix(la ,lg)*Iy(la,lb,lg)*Iz( lb ) *zbar(la)/dz *xbar(lb)/dx *zbar(lg)/dz
elint3(z,y,x)=Ix(la,lb )*Iy(la ,lg)*Iz( lb,lg) *zbar(la)/dz *ybar(lb)/dy *xbar(lg)/dx
elint3(z,y,y)=Ix(la,lb,lg)*Iy(la )*Iz( lb,lg) *zbar(la)/dz *ybar(lb)/dy *ybar(lg)/dy
elint3(z,y,z)=Ix(la,lb,lg)*Iy(la ,lg)*Iz( lb ) *zbar(la)/dz *ybar(lb)/dy *zbar(lg)/dz
elint3(z,z,x)=Ix(la,lb )*Iy(la,lb,lg)*Iz( lg) *zbar(la)/dz *zbar(lb)/dz *xbar(lg)/dx
elint3(z,z,y)=Ix(la,lb,lg)*Iy(la,lb )*Iz( lg) *zbar(la)/dz *zbar(lb)/dz *ybar(lg)/dy
elint3(z,z,z)=Ix(la,lb,lg)*Iy(la,lb,lg)*Iz( ) *zbar(la)/dz *zbar(lb)/dz *zbar(lg)/dz
elint=0
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,xc,yc,zc,ur,dur,nvar,istep, &
ireg,iregup,rnode,vec,imax,jmax,kmax,dCdu)
call dCfun_ddu(token,xc,yc,zc,ur,dur,nvar,istep, &
ireg,iregup,rnode,vec,imax,jmax,kmax,dCddu)
! dCdu=dCfun_du(token,ur,dur)
! dCddu=dCfun_ddu(token,ur,dur)
elint(ii,kk,nn)=elint(ii,kk,nn)+dCdu(nn)*elint2(jj,ll) &
+dCddu(nn,1)*elint3(jj,ll,1) &
+dCddu(nn,2)*elint3(jj,ll,2) &
+dCddu(nn,3)*elint3(jj,ll,3)
endif
enddo
enddo
enddo
enddo
enddo
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)
if (iunk(irow) == 0) cycle ! no contribution to jacobian in fixed node
if (irowst(irow) == 1.and.irowed(irow) == 0) then
print *,'getJacobian: Found empty row, fail!'
stop
endif
found=.false.
do ip=irowst(irow),irowed(irow)
if (jQ(ip)==icol) then
found=.true.
Qval(ip)=Qval(ip)+tot
exit
endif
enddo
if (.not.found) then
print *,'getJacobianCuboidC, element not found',irow,icol,tot
stop
endif
enddo
enddo
enddo ! la,lb,lg
enddo
enddo
enddo ! i,j,k
enddo
enddo
end subroutine getJacobianCuboidC
! ######################################################################
subroutine getJacobianCuboidF
use common
use matrices
use indexq
integer i,j,k,irege,itabsrt(8,3),L,la,lg,ip
integer ia,ja,ka,ig,jg,kg,ii,nn,irow,icol
double precision xmin,xmax,ymin,ymax,zmin,zmax,dx,dy,dz,ur(nvar),dur(nvar,3)
double precision elint2,elint3(3),tot,xc,yc,zc
double precision rtabsrt(8,3),dfdu(nvar),dfddu(nvar,3)
character(EXPRLEN) token
logical found
print *,'Preparing Jacobian (getJacobianCuboidF)'
do i=0,imax-1
print *,'i-plane: ',i,'/',imax-1
do j=0,jmax-1
do k=0,kmax-1
irege=iregup(i,j,k)
itabsrt(1,:)=[i, j, k]
itabsrt(2,:)=[i+1, j, k]
itabsrt(3,:)=[i+1,j+1, k]
itabsrt(4,:)=[i ,j+1, k]
itabsrt(5,:)=[i, j,k+1]
itabsrt(6,:)=[i+1, j,k+1]
itabsrt(7,:)=[i+1,j+1,k+1]
itabsrt(8,:)=[i ,j+1,k+1]
xmax=rnode(i+1,j,k,1); xmin=rnode(i,j,k,1)
ymax=rnode(i,j+1,k,2); ymin=rnode(i,j,k,2)
zmax=rnode(i,j,k+1,3); zmin=rnode(i,j,k,3)
dx=xmax-xmin; xc=(xmax+xmin)/2
dy=ymax-ymin; yc=(ymax+ymin)/2
dz=zmax-zmin; zc=(zmax+zmin)/2
do L=1,8
rtabsrt(L,:)=rnode(itabsrt(L,1),itabsrt(L,2),itabsrt(L,3),:)
enddo
call getelinfo(itabsrt,rtabsrt,ur,dur) ! get ur, dur at centre
! Global variables for Ix, Iy, Iz functions
g_rtabsrt=rtabsrt
g_xmax=xmax; g_xmin=xmin
g_ymax=ymax; g_ymin=ymin
g_zmax=zmax; g_zmin=zmin
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)
elint2=Ix(la,lg)*Iy(la,lg)*Iz(la,lg)
elint3(1)=Ix(la )*Iy(la,lg)*Iz(la,lg)*xbar(lg)/dx
elint3(2)=Ix(la,lg)*Iy(la )*Iz(la,lg)*ybar(lg)/dy
elint3(3)=Ix(la,lg)*Iy(la,lg)*Iz(la )*zbar(lg)/dz
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,xc,yc,zc,ur,dur,nvar,istep, &
ireg,iregup,rnode,vec,imax,jmax,kmax,dfdu)
call dffun_ddu(token,xc,yc,zc,ur,dur,nvar,istep, &
ireg,iregup,rnode,vec,imax,jmax,kmax,dfddu)
tot=-dfdu(nn)*elint2 &
-dfddu(nn,1)*elint3(1) &
-dfddu(nn,2)*elint3(2) &
-dfddu(nn,3)*elint3(3)
irow=indQ(ia,ja,ka,ii)
icol=indQ(ig,jg,kg,nn)
if (iunk(irow)==0) cycle ! very important
if (irowst(irow) == 1.and.irowed(irow) == 0) then
print *,'getJacobian: Found empty row, fail!'
stop
endif
found=.false.
do ip=irowst(irow),irowed(irow)
if (jQ(ip)==icol) then
found=.true.
Qval(ip)=Qval(ip)+tot
exit
endif
enddo
if (.not.found) then
print *,'getJacobianCuboidF, element not found',irow,icol,tot
stop
endif
endif
enddo ! nn=1,nvar
enddo
enddo ! la,lg
enddo
enddo
enddo
enddo
end subroutine getJacobianCuboidF
! ######################################################################
function Ix0()
double precision Ix0
Ix0=g_xmax-g_xmin
end function Ix0
function Ix1(l)
integer l
double precision Ix1,xl,dx
xl=g_rtabsrt(l,1)
dx=g_xmax-g_xmin
Ix1=g_xmax+xbar(l)/dx*(g_xmax-xl)**2/2 - (g_xmin+xbar(l)/dx*(g_xmin-xl)**2/2)
end function Ix1
function Ix2(l1,l2)
integer l1,l2
double precision Ix2,xl1,xl2,dx
xl1=g_rtabsrt(l1,1)
xl2=g_rtabsrt(l2,1)
dx=g_xmax-g_xmin
Ix2= Ix2i(g_xmax,xbar(l1),xbar(l2),xl1,xl2,dx) &
-Ix2i(g_xmin,xbar(l1),xbar(l2),xl1,xl2,dx)
end function Ix2
function Ix3(l1,l2,l3)
integer l1,l2,l3
double precision Ix3,xl1,xl2,xl3,dx
xl1=g_rtabsrt(l1,1)
xl2=g_rtabsrt(l2,1)
xl3=g_rtabsrt(l3,1)
dx=g_xmax-g_xmin
Ix3= Ix3i(g_xmax,xbar(l1),xbar(l2),xbar(l3),xl1,xl2,xl3,dx) &
-Ix3i(g_xmin,xbar(l1),xbar(l2),xbar(l3),xl1,xl2,xl3,dx)
end function Ix3
! ######################################################################
function Iy0()
double precision Iy0
Iy0=g_ymax-g_ymin
end function Iy0
function Iy1(l)
integer l
double precision Iy1,yl,dy
yl=g_rtabsrt(l,2)
dy=g_ymax-g_ymin
Iy1=g_ymax+ybar(l)/dy*(g_ymax-yl)**2/2 - (g_ymin+ybar(l)/dy*(g_ymin-yl)**2/2)
end function Iy1
function Iy2(l1,l2)
integer l1,l2
double precision Iy2,yl1,yl2,dy
yl1=g_rtabsrt(l1,2)
yl2=g_rtabsrt(l2,2)
dy=g_ymax-g_ymin
Iy2= Ix2i(g_ymax,ybar(l1),ybar(l2),yl1,yl2,dy) &
-Ix2i(g_ymin,ybar(l1),ybar(l2),yl1,yl2,dy)
end function Iy2
function Iy3(l1,l2,l3)
integer l1,l2,l3
double precision Iy3,yl1,yl2,yl3,dy
yl1=g_rtabsrt(l1,2)
yl2=g_rtabsrt(l2,2)
yl3=g_rtabsrt(l3,2)
dy=g_ymax-g_ymin
Iy3= Ix3i(g_ymax,ybar(l1),ybar(l2),ybar(l3),yl1,yl2,yl3,dy) &
-Ix3i(g_ymin,ybar(l1),ybar(l2),ybar(l3),yl1,yl2,yl3,dy)
end function Iy3
! ######################################################################
function Iz0()
double precision Iz0
Iz0=g_zmax-g_zmin
end function Iz0
function Iz1(l)
integer l
double precision Iz1,zl,dz
zl=g_rtabsrt(l,3)
dz=g_zmax-g_zmin
Iz1=g_zmax+zbar(l)/dz*(g_zmax-zl)**2/2 - (g_zmin+zbar(l)/dz*(g_zmin-zl)**2/2)
end function Iz1
function Iz2(l1,l2)
integer l1,l2
double precision Iz2,zl1,zl2,dz
zl1=g_rtabsrt(l1,3)
zl2=g_rtabsrt(l2,3)
dz=g_zmax-g_zmin