!----- AGPL -------------------------------------------------------------------- ! ! Copyright (C) Stichting Deltares, 2017-2019. ! ! This file is part of Delft3D (D-Flow Flexible Mesh component). ! ! Delft3D is free software: you can redistribute it and/or modify ! it under the terms of the GNU Affero General Public License as ! published by the Free Software Foundation version 3. ! ! Delft3D is distributed in the hope that it will be useful, ! but WITHOUT ANY WARRANTY; without even the implied warranty of ! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ! GNU Affero General Public License for more details. ! ! You should have received a copy of the GNU Affero General Public License ! along with Delft3D. If not, see . ! ! contact: delft3d.support@deltares.nl ! Stichting Deltares ! P.O. Box 177 ! 2600 MH Delft, The Netherlands ! ! All indications and logos of, and references to, "Delft3D", ! "D-Flow Flexible Mesh" and "Deltares" are registered trademarks of Stichting ! Deltares, and remain the property of Stichting Deltares. All rights reserved. ! !------------------------------------------------------------------------------- ! $Id$ ! $HeadURL$ !> initialize matrix for first-order upwind discretization of advection !> Cartesian cell-centered vector components are numbered as !> ( ucx_1, ucy_1, ucx_2, ucy_2, ..., ...) subroutine inisolver_advec(ierror) use m_flowgeom use m_alloc use m_solver use m_advec implicit none integer, intent(inout) :: ierror integer :: irow, irowother, icolumn, ipoint integer :: kk, kkb, kkother, k1, k2, LL integer :: i, ishift integer :: numnonzeros ierror = 1 ! construct interpolation matrix in CRS format numnonzeros = 4*Lnx call realloc(iI, Lnx+1, keepExisting=.false., fill=0) call realloc(jI, numnonzeros, keepExisting=.false., fill=0) call realloc(aI, numnonzeros, keepExisting=.false., fill=0d0) ipoint = 0 irow = 0 do LL=1,Lnx irow = irow+1 iI(irow) = ipoint+1 k1 = ln(1,LL) k2 = ln(2,LL) ! x-component first flownode ipoint = ipoint+1 jI(ipoint) = (k1-1)*2 + 1 aI(ipoint) = acL(LL)*csu(LL) ! y-component first flownode ipoint = ipoint+1 jI(ipoint) = (k1-1)*2 + 2 aI(ipoint) = acL(LL)*snu(LL) ! x-component second flownode ipoint = ipoint+1 jI(ipoint) = (k2-1)*2 + 1 aI(ipoint) = (1d0-acL(LL))*csu(LL) ! y-component second flownode ipoint = ipoint+1 jI(ipoint) = (k2-1)*2 + 2 aI(ipoint) = (1d0-acL(LL))*snu(LL) end do iI(irow+1) = ipoint+1 ! construct reconstruction matrix in CRS format ! count number of non-zeros numnonzeros = 0 do kk=1,Ndxi numnonzeros = numnonzeros + 2*nd(kk)%lnx end do do kkb=Ndxi+1,Ndx ! boundaries: apply Neumann conditions (copy from inside) LL = iabs(nd(kkb)%ln(1)) ! only one flowlink connected to boundary flownode kk = ln(1,LL) + ln(2,LL) - kkb numnonzeros = numnonzeros + 2*nd(kk)%lnx end do ! allocate call realloc(iR, 2*Ndx+1, keepExisting=.false., fill=0) call realloc(jR, numnonzeros, keepExisting=.false., fill=0) call realloc(aR, numnonzeros, keepExisting=.false., fill=0d0) ! fill entries ipoint = 0 irow = 0 do kkb=1,Ndx if ( kkb.le.Ndxi ) then kk = kkb else ! boundaries: apply homogeneous Neumann condition (copy from inside) LL = iabs(nd(kkb)%ln(1)) ! only one flowlink connected to boundary flownode kk = ln(1,LL) + ln(2,LL) - kkb end if ! x-component irow = irow+1 iR(irow) = ipoint+1 ! shift between x-component and y-component ishift = nd(kk)%lnx ! y-component (next row) iR(irow+1) = iR(irow)+ishift do i=1,nd(kk)%lnx LL = iabs(nd(kk)%ln(i)) ! x-component ipoint = ipoint+1 jR(ipoint) = LL ! y-component (next row) jR(ipoint+ishift) = LL if ( ln(1,LL).eq.kk ) then aR(ipoint) = wcx1(LL) aR(ipoint+ishift) = wcy1(LL) else aR(ipoint) = wcx2(LL) aR(ipoint+ishift) = wcy2(LL) end if end do ! shift to y-component ipoint = ipoint+ishift irow = irow+1 end do iR(irow+1) = ipoint+1 ! construct collocated discretization matrix ! count number of non-zeros: use reconstruction matrix numnonzeros = 2*Ndx + (iR(2*Ndx+1)-1) ! allocate call realloc(iC, 2*Ndx+1, keepExisting=.false., fill=0) call realloc(jC, numnonzeros, keepExisting=.false., fill=0) call realloc(aC, numnonzeros, keepExisting=.false., fill=0d0) call realloc(dfluxfac, (/ 2, Lnx /), keepExisting=.false., fill=0d0) ! fill entries ipoint = 0 irow = 0 do kk=1,Ndxi irow = irow+1 iC(irow) = ipoint+1 ! shift between x-component and y-component ishift = 1+nd(kk)%lnx ! y-component (next row) iC(irow+1) = iC(irow)+ishift ! diagonal entry x-component ipoint = ipoint+1 icolumn = irow jC(ipoint) = icolumn ac(ipoint) = 1d0 ! some non-zero dummy value ! diagonal entry y-component jc(ipoint+ishift) = irow+1 ac(ipoint+ishift) = 2d0 ! some non-zero dummy value ! off-diagonals do i=1,nd(kk)%lnx ipoint = ipoint+1 LL = iabs(nd(kk)%ln(i)) kkother = ln(1,LL)+ln(2,LL)-kk icolumn = (kkother-1)*2 + 1 ! x-component jc(ipoint) = icolumn ac(ipoint) = 3d0 ! some non-zero dummy value ! y-component jc(ipoint+ishift) = icolumn+1 ac(ipoint+ishift) = 4d0 ! some non-zero dummy value end do ! shift to y-component ipoint = ipoint+ishift irow = irow+1 end do ! boundaries: apply homogeneous Neumann condition (copy from inside) do kk=Ndxi+1,Ndx irow = irow+1 ic(irow) = ipoint+1 LL = iabs(nd(kk)%ln(1)) ! only one flowlink attached to boundary flownode kkother = ln(1,LL) + ln(2,LL) - kk ! ln(2,LL) ! x-component irowother = (kkother-1)*2+1 do i=iC(irowother),iC(irowother+1)-1 ipoint = ipoint+1 jC(ipoint) = jC(i) end do ! y-component irow = irow+1 ic(irow) = ipoint+1 irowother = (kkother-1)*2+2 do i=iC(irowother),iC(irowother+1)-1 ipoint = ipoint+1 jC(ipoint) = jC(i) end do end do ic(irow+1) = ipoint+1 ! compute sparsity pattern of work matrix W = C R ! allocate work array call realloc(iwork, 2*Ndx, keepExisting=.false., fill=0) ! estimate number of non zeros of W=CR ! call amub_countonly(2*Ndx,Lnx,aC,jC,iC,aR,jR,iR,iwork,numnonzeros) ! allocate call realloc(iW, 2*Ndx, keepExisting=.false., fill=0) call realloc(jW, numnonzeros, keepExisting=.false., fill=0) call realloc(aW, numnonzeros, keepExisting=.false., fill=0d0) ! get sparsity pattern call amub (2*Ndx,Lnx,0,aC,jC,iC,aR,jR,iR,aW,jW,iW,numnonzeros,iwork,ierror) if ( ierror.ne.0 ) goto 1234 ! compute sparsity pattern of whole matrix A = I W (= I C R) ! allocate work array call realloc(iwork, 2*Ndx, keepExisting=.false., fill=0) ! estimate number of non zeros of W=CR ! call amub_countonly(Lnx,2*Ndx,aI,jI,iI,aW,jW,iW,iwork,numnonzeros) ! settings call SolverSettings(solver_advec, Lnx, numnonzeros) ! allocate ! call allocSolver(solver_advec, ierror) ! get sparsity pattern call amub (Lnx,2*Ndx,0,aI,jI,iI,aW,jW,iW,solver_advec%a,solver_advec%ja,solver_advec%ia,solver_advec%numnonzeros,iwork,ierror) if ( ierror.ne.0 ) goto 1234 if ( jaoutput.eq.1 ) then call writematrix('Imat.m', Lnx, iI, jI, aI, 'I') call writematrix('Rmat.m', 2*Ndx, iR, jR, aR, 'R') call writematrix('Cmat.m', 2*Ndx, iC, jC, aC, 'C') solver_advec%a = 1d0 call writematrix('Amat.m', Lnx, solver_advec%ia, solver_advec%ja, solver_advec%a, 'A') end if ierror = 0 1234 continue return end subroutine inisolver_advec !> default solver settings subroutine SolverSettings(solver, numrows, numnonzeros) use m_solver implicit none type(tsolver), intent(inout) :: solver !< solver integer, intent(in) :: numrows !< number of rows integer, intent(in) :: numnonzeros !< number of nonzero elements solver%numrows = numrows solver%numnonzeros = numnonzeros solver%numnonzerosprecond = 30*numrows solver%nwork = 2*solver%numnonzerosprecond !! ipar(1) = 0 ! initialized in "itaux" solver%ipar(2) = 1 ! no (0), left (1), right (2), both (3) precond solver%ipar(3) = 1 ! stopping criteria solver%ipar(4) = solver%nwork ! number of elems in array 'wk' solver%ipar(5) = 10 ! size of Krylov subspace in GMRES and variants solver%ipar(6) = 1000 ! max number of mat-vec multiplies solver%fpar(1) = 0.0D-16 ! relative tolerance ('exact' solve, except solver%fpar(2) = 1.0d-14 ! absolute tolerance solver%lfil = 3 solver%alpha = 1d0 solver%tol = 0.50D-2 solver%jabcgstab = 1 end subroutine SolverSettings !> construct matrix for first-order upwind discretization of advection subroutine fillsystem_advec(ierror) use m_flowgeom use m_flow, only : vol1, qa, Au use m_advec use m_alloc implicit none integer, intent(inout) :: ierror ! double precision, dimension(:,:), allocatable :: dfluxfac double precision :: dfac double precision :: ux, uy integer :: i, irow, irowother, idir, icolumn, ishift integer :: ipoint, ipointdiag integer :: k1, k2, kk, kkother, LL ierror = 1 ! call realloc(dfluxfac, (/ 2, Lnx /), keepExisting=.false., fill=0d0) ux = 1d0 uy = 0.1d0 do LL=1,Lnx k1 = ln(1,LL) k2 = ln(2,LL) ! dfac = qa(LL) dfac = (csu(LL)*ux + snu(LL)*uy) * Au(LL) dfluxfac(1,LL) = max(dfac,0d0) dfluxfac(2,LL) = min(dfac,0d0) end do ! initialize matrix entries aC = 0d0 ipoint = 0 irow = 0 do kk=1,Ndxi ! x-component irow = irow+1 ! shift between x-component and y-component ishift = 1+nd(kk)%lnx ! diagonal entry x-component ipoint = ipoint+1 ipointdiag = ipoint ! check numbering if ( jC(ipointdiag).ne.irow ) then call qnerror('fillsystem_advec: numbering error', ' ', ' ') goto 1234 end if if ( jC(ipointdiag+ishift).ne.irow+1 ) then call qnerror('fillsystem_advec: numbering error', ' ', ' ') goto 1234 end if ! off-diagonals do i=1,nd(kk)%lnx ipoint = ipoint+1 LL = nd(kk)%ln(i) idir = 0 ! to kk if ( LL.lt.0 ) then idir = 1 ! from kk LL = -LL end if ! check numbering if ( jC(ipoint).ne.(ln(1,LL)+ln(2,LL)-kk-1)*2+1 ) then call qnerror('fillsystem_advec: numbering error', ' ', ' ') goto 1234 end if if ( jC(ipoint+ishift).ne.(ln(1,LL)+ln(2,LL)-kk-1)*2+2 ) then call qnerror('fillsystem_advec: numbering error', ' ', ' ') end if ! x-component aC(ipoint) = aC(ipoint) + (idir*dfluxfac(2,LL) - (1-idir)*dfluxfac(1,LL))/vol1(kk) ac(ipointdiag) = aC(ipointdiag) + (idir*dfluxfac(1,LL) - (1-idir)*dfluxfac(2,LL))/vol1(kk) ! y-component aC(ipoint +ishift) = aC(ipoint +ishift) + (idir*dfluxfac(2,LL) - (1-idir)*dfluxfac(1,LL))/vol1(kk) ac(ipointdiag+ishift) = aC(ipointdiag+ishift) + (idir*dfluxfac(1,LL) - (1-idir)*dfluxfac(2,LL))/vol1(kk) end do ! shift to y-component ipoint = ipoint+ishift irow = irow+1 end do ! boundaries: apply homogeneous Neumann condition (copy from inside) do kk=Ndxi+1,Ndx irow = irow+1 LL = iabs(nd(kk)%ln(1)) ! only one flowlink attached to boundary flownode kkother = ln(1,LL) + ln(2,LL) - kk ! ln(2,LL) ! x-component irowother = (kkother-1)*2+1 do i=iC(irowother),iC(irowother+1)-1 ipoint = ipoint+1 aC(ipoint) = aC(i) end do ! y-component irow = irow+1 irowother = (kkother-1)*2+2 do i=iC(irowother),iC(irowother+1)-1 ipoint = ipoint+1 aC(ipoint) = aC(i) end do end do if ( jaoutput.eq.1 ) then call writematrix('C.m', 2*Ndx, iC, jC, aC, 'A_C') end if ierror = 0 1234 continue ! if ( allocated(dfluxfac) ) deallocate(dfluxfac) return end subroutine fillsystem_advec !> output matrix in CRS format to file subroutine writeMatrix(FNAM, N, ia, ja, a, VARNAM) implicit none character(len=*), intent(in) :: FNAM !< filename integer, intent(in) :: N !< number of rows integer, dimension(N+1), intent(in) :: ia integer, dimension(ia(N+1)-1), intent(in) :: ja double precision, dimension(ia(N+1)-1), intent(in) :: a !< matrix in CRS format character(len=*), intent(in) :: VARNAM !< variable name integer :: irow, icol, j open(1234,file=trim(FNAM)) write(1234,"('dum = [')") do irow=1,N do j=ia(irow),ia(irow+1)-1 icol = ja(j) write(1234,"(2I7,E20.10)") irow, icol, a(j) end do end do write(1234,"('];')") write(1234,"(A16, '=sparse(dum(:,1), dum(:,2), dum(:,3));')") VARNAM ! write rhs ! write(1234,"('rhs = [')") ! do irow=1,solver%numrows ! write(1234,"(E15.5)") solver%rhs(irow) ! end do ! write(1234,"('];')") close(1234) end subroutine writeMatrix