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533 lines
15 KiB
Fortran
533 lines
15 KiB
Fortran
!
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module psb_d_pde3d_mod
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use psb_base_mod, only : psb_dpk_, psb_ipk_, psb_desc_type,&
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& psb_dspmat_type, psb_d_vect_type, dzero,&
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& psb_d_base_sparse_mat, psb_d_base_vect_type, psb_i_base_vect_type
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interface
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function d_func_3d(x,y,z) result(val)
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import :: psb_dpk_
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real(psb_dpk_), intent(in) :: x,y,z
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real(psb_dpk_) :: val
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end function d_func_3d
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end interface
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interface psb_gen_pde3d
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module procedure psb_d_gen_pde3d
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end interface psb_gen_pde3d
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contains
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function d_null_func_3d(x,y,z) result(val)
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real(psb_dpk_), intent(in) :: x,y,z
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real(psb_dpk_) :: val
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val = dzero
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end function d_null_func_3d
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!
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! subroutine to allocate and fill in the coefficient matrix and
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! the rhs.
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!
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subroutine psb_d_gen_pde3d(ictxt,idim,a,bv,xv,desc_a,afmt,&
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& a1,a2,a3,b1,b2,b3,c,g,info,f,amold,vmold,imold,nrl,iv)
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use psb_base_mod
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!
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! Discretizes the partial differential equation
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!
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! a1 dd(u) a2 dd(u) a3 dd(u) b1 d(u) b2 d(u) b3 d(u)
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! - ------ - ------ - ------ + ----- + ------ + ------ + c u = f
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! dxdx dydy dzdz dx dy dz
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!
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! with Dirichlet boundary conditions
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! u = g
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!
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! on the unit cube 0<=x,y,z<=1.
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!
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!
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! Note that if b1=b2=b3=c=0., the PDE is the Laplace equation.
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!
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implicit none
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procedure(d_func_3d) :: b1,b2,b3,c,a1,a2,a3,g
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integer(psb_ipk_) :: idim
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type(psb_dspmat_type) :: a
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type(psb_d_vect_type) :: xv,bv
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type(psb_desc_type) :: desc_a
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integer(psb_ipk_) :: ictxt, info
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character(len=*) :: afmt
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procedure(d_func_3d), optional :: f
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class(psb_d_base_sparse_mat), optional :: amold
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class(psb_d_base_vect_type), optional :: vmold
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class(psb_i_base_vect_type), optional :: imold
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integer(psb_ipk_), optional :: nrl,iv(:)
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! Local variables.
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integer(psb_ipk_), parameter :: nb=20
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type(psb_d_csc_sparse_mat) :: acsc
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type(psb_d_coo_sparse_mat) :: acoo
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type(psb_d_csr_sparse_mat) :: acsr
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real(psb_dpk_) :: zt(nb),x,y,z
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integer(psb_ipk_) :: m,n,nnz,glob_row,nlr,i,ii,ib,k
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integer(psb_ipk_) :: ix,iy,iz,ia,indx_owner
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integer(psb_ipk_) :: np, iam, nr, nt
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integer(psb_ipk_) :: icoeff
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integer(psb_ipk_), allocatable :: irow(:),icol(:),myidx(:)
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real(psb_dpk_), allocatable :: val(:)
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! deltah dimension of each grid cell
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! deltat discretization time
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real(psb_dpk_) :: deltah, sqdeltah, deltah2
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real(psb_dpk_), parameter :: rhs=0.d0,one=1.d0,zero=0.d0
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real(psb_dpk_) :: t0, t1, t2, t3, tasb, talc, ttot, tgen, tcdasb
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integer(psb_ipk_) :: err_act
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procedure(d_func_3d), pointer :: f_
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character(len=20) :: name, ch_err,tmpfmt
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info = psb_success_
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name = 'create_matrix'
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call psb_erractionsave(err_act)
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call psb_info(ictxt, iam, np)
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if (present(f)) then
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f_ => f
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else
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f_ => d_null_func_3d
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end if
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deltah = 1.d0/(idim+2)
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sqdeltah = deltah*deltah
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deltah2 = 2.d0* deltah
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! initialize array descriptor and sparse matrix storage. provide an
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! estimate of the number of non zeroes
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m = idim*idim*idim
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n = m
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nnz = ((n*9)/(np))
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if(iam == psb_root_) write(psb_out_unit,'("Generating Matrix (size=",i0,")...")')n
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if (.not.present(iv)) then
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if (present(nrl)) then
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nr = nrl
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else
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!
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! Using a simple BLOCK distribution.
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!
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nt = (m+np-1)/np
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nr = max(0,min(nt,m-(iam*nt)))
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end if
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nt = nr
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call psb_sum(ictxt,nt)
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if (nt /= m) then
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write(psb_err_unit,*) iam, 'Initialization error ',nr,nt,m
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info = -1
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call psb_barrier(ictxt)
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call psb_abort(ictxt)
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return
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end if
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else
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if (size(iv) /= m) then
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write(psb_err_unit,*) iam, 'Initialization error IV',size(iv),m
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info = -1
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call psb_barrier(ictxt)
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call psb_abort(ictxt)
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return
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end if
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end if
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call psb_barrier(ictxt)
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t0 = psb_wtime()
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if (present(iv)) then
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call psb_cdall(ictxt,desc_a,info,vg=iv)
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else
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call psb_cdall(ictxt,desc_a,info,nl=nr)
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end if
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if (info == psb_success_) call psb_spall(a,desc_a,info,nnz=nnz)
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! define rhs from boundary conditions; also build initial guess
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if (info == psb_success_) call psb_geall(xv,desc_a,info)
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if (info == psb_success_) call psb_geall(bv,desc_a,info)
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call psb_barrier(ictxt)
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talc = psb_wtime()-t0
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_
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ch_err='allocation rout.'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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! we build an auxiliary matrix consisting of one row at a
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! time; just a small matrix. might be extended to generate
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! a bunch of rows per call.
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!
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allocate(val(20*nb),irow(20*nb),&
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&icol(20*nb),stat=info)
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if (info /= psb_success_ ) then
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info=psb_err_alloc_dealloc_
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call psb_errpush(info,name)
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goto 9999
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endif
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myidx = desc_a%get_global_indices()
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nlr = size(myidx)
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! loop over rows belonging to current process in a block
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! distribution.
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call psb_barrier(ictxt)
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t1 = psb_wtime()
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do ii=1, nlr,nb
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ib = min(nb,nlr-ii+1)
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icoeff = 1
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do k=1,ib
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i=ii+k-1
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! local matrix pointer
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glob_row=myidx(i)
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! compute gridpoint coordinates
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if (mod(glob_row,(idim*idim)) == 0) then
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ix = glob_row/(idim*idim)
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else
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ix = glob_row/(idim*idim)+1
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endif
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if (mod((glob_row-(ix-1)*idim*idim),idim) == 0) then
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iy = (glob_row-(ix-1)*idim*idim)/idim
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else
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iy = (glob_row-(ix-1)*idim*idim)/idim+1
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endif
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iz = glob_row-(ix-1)*idim*idim-(iy-1)*idim
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! x, y, x coordinates
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x = (ix-1)*deltah
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y = (iy-1)*deltah
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z = (iz-1)*deltah
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zt(k) = f_(x,y,z)
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! internal point: build discretization
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!
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! term depending on (x-1,y,z)
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!
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val(icoeff) = -a1(x,y,z)/sqdeltah-b1(x,y,z)/deltah2
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if (ix == 1) then
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zt(k) = g(dzero,y,z)*(-val(icoeff)) + zt(k)
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else
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icol(icoeff) = (ix-2)*idim*idim+(iy-1)*idim+(iz)
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irow(icoeff) = glob_row
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icoeff = icoeff+1
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endif
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! term depending on (x,y-1,z)
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val(icoeff) = -a2(x,y,z)/sqdeltah-b2(x,y,z)/deltah2
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if (iy == 1) then
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zt(k) = g(x,dzero,z)*(-val(icoeff)) + zt(k)
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else
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icol(icoeff) = (ix-1)*idim*idim+(iy-2)*idim+(iz)
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irow(icoeff) = glob_row
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icoeff = icoeff+1
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endif
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! term depending on (x,y,z-1)
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val(icoeff)=-a3(x,y,z)/sqdeltah-b3(x,y,z)/deltah2
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if (iz == 1) then
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zt(k) = g(x,y,dzero)*(-val(icoeff)) + zt(k)
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else
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icol(icoeff) = (ix-1)*idim*idim+(iy-1)*idim+(iz-1)
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irow(icoeff) = glob_row
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icoeff = icoeff+1
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endif
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! term depending on (x,y,z)
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val(icoeff)=2.d0*(a1(x,y,z)+a2(x,y,z)+a3(x,y,z))/sqdeltah &
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& + c(x,y,z)
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icol(icoeff) = (ix-1)*idim*idim+(iy-1)*idim+(iz)
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irow(icoeff) = glob_row
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icoeff = icoeff+1
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! term depending on (x,y,z+1)
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val(icoeff)=-a3(x,y,z)/sqdeltah+b3(x,y,z)/deltah2
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if (iz == idim) then
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zt(k) = g(x,y,done)*(-val(icoeff)) + zt(k)
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else
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icol(icoeff) = (ix-1)*idim*idim+(iy-1)*idim+(iz+1)
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irow(icoeff) = glob_row
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icoeff = icoeff+1
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endif
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! term depending on (x,y+1,z)
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val(icoeff)=-a2(x,y,z)/sqdeltah+b2(x,y,z)/deltah2
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if (iy == idim) then
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zt(k) = g(x,done,z)*(-val(icoeff)) + zt(k)
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else
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icol(icoeff) = (ix-1)*idim*idim+(iy)*idim+(iz)
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irow(icoeff) = glob_row
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icoeff = icoeff+1
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endif
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! term depending on (x+1,y,z)
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val(icoeff)=-a1(x,y,z)/sqdeltah+b1(x,y,z)/deltah2
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if (ix==idim) then
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zt(k) = g(done,y,z)*(-val(icoeff)) + zt(k)
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else
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icol(icoeff) = (ix)*idim*idim+(iy-1)*idim+(iz)
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irow(icoeff) = glob_row
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icoeff = icoeff+1
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endif
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end do
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call psb_spins(icoeff-1,irow,icol,val,a,desc_a,info)
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if(info /= psb_success_) exit
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call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),bv,desc_a,info)
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if(info /= psb_success_) exit
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zt(:)=0.d0
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call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),xv,desc_a,info)
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if(info /= psb_success_) exit
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end do
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tgen = psb_wtime()-t1
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if(info /= psb_success_) then
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info=psb_err_from_subroutine_
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ch_err='insert rout.'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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deallocate(val,irow,icol)
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call psb_barrier(ictxt)
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t1 = psb_wtime()
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call psb_cdasb(desc_a,info,mold=imold)
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tcdasb = psb_wtime()-t1
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call psb_barrier(ictxt)
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t1 = psb_wtime()
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if (info == psb_success_) then
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if (present(amold)) then
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call psb_spasb(a,desc_a,info,dupl=psb_dupl_err_,mold=amold)
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else
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call psb_spasb(a,desc_a,info,dupl=psb_dupl_err_,afmt=afmt)
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end if
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end if
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call psb_barrier(ictxt)
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if(info /= psb_success_) then
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info=psb_err_from_subroutine_
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ch_err='asb rout.'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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if (info == psb_success_) call psb_geasb(xv,desc_a,info,mold=vmold)
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if (info == psb_success_) call psb_geasb(bv,desc_a,info,mold=vmold)
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if(info /= psb_success_) then
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info=psb_err_from_subroutine_
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ch_err='asb rout.'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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tasb = psb_wtime()-t1
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call psb_barrier(ictxt)
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ttot = psb_wtime() - t0
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call psb_amx(ictxt,talc)
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call psb_amx(ictxt,tgen)
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call psb_amx(ictxt,tasb)
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call psb_amx(ictxt,ttot)
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if(iam == psb_root_) then
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tmpfmt = a%get_fmt()
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write(psb_out_unit,'("The matrix has been generated and assembled in ",a3," format.")')&
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& tmpfmt
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write(psb_out_unit,'("-allocation time : ",es12.5)') talc
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write(psb_out_unit,'("-coeff. gen. time : ",es12.5)') tgen
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write(psb_out_unit,'("-desc asbly time : ",es12.5)') tcdasb
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write(psb_out_unit,'("- mat asbly time : ",es12.5)') tasb
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write(psb_out_unit,'("-total time : ",es12.5)') ttot
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end if
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call psb_erractionrestore(err_act)
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return
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9999 call psb_error_handler(ictxt,err_act)
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return
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end subroutine psb_d_gen_pde3d
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end module psb_d_pde3d_mod
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program d_matgen
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use psb_base_mod
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use psb_util_mod
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use psb_d_pde3d_mod
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use psb_d_xyz_mat_mod
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implicit none
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! input parameters
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character(len=20) :: kmethd, ptype
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character(len=5) :: afmt
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integer(psb_ipk_) :: idim
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! miscellaneous
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real(psb_dpk_), parameter :: one = 1.d0
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real(psb_dpk_) :: t1, t2, tprec
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! sparse matrix and preconditioner
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type(psb_dspmat_type) :: a
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! type(psb_dprec_type) :: prec
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! descriptor
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type(psb_desc_type) :: desc_a
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! dense matrices
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type(psb_d_vect_type) :: b, x
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! blacs parameters
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integer(psb_ipk_) :: ictxt, iam, np
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! solver parameters
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integer(psb_ipk_) :: iter, itmax,itrace, istopc, irst
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integer(psb_long_int_k_) :: amatsize, precsize, descsize
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real(psb_dpk_) :: err, eps
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type(psb_d_csr_sparse_mat) :: acsr
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type(psb_d_xyz_sparse_mat) :: axyz
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! other variables
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integer(psb_ipk_) :: info, err_act
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character(len=20) :: name,ch_err
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info=psb_success_
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call psb_init(ictxt)
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call psb_info(ictxt,iam,np)
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if (iam < 0) then
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! This should not happen, but just in case
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call psb_exit(ictxt)
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stop
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endif
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if(psb_get_errstatus() /= 0) goto 9999
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call psb_set_errverbosity(itwo)
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!
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! get parameters
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!
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call get_parms(ictxt,idim)
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!
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! allocate and fill in the coefficient matrix, rhs and initial guess
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!
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call psb_barrier(ictxt)
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t1 = psb_wtime()
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if (.true.) then
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call psb_gen_pde3d(ictxt,idim,a,b,x,desc_a,afmt,&
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& a1,a2,a3,b1,b2,b3,c,g,info,amold=acsr)
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else if (.false.) then
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call psb_gen_pde3d(ictxt,idim,a,b,x,desc_a,afmt,&
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& a1,a2,a3,b1,b2,b3,c,g,info,amold=axyz)
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end if
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call psb_barrier(ictxt)
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t2 = psb_wtime() - t1
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call psb_exit(ictxt)
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stop
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9999 call psb_error(ictxt)
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stop
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contains
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!
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! get iteration parameters from standard input
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!
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subroutine get_parms(ictxt,idim)
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integer(psb_ipk_) :: ictxt
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integer(psb_ipk_) :: idim
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integer(psb_ipk_) :: np, iam
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integer(psb_ipk_) :: intbuf(10), ip
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call psb_info(ictxt, iam, np)
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read(psb_inp_unit,*) idim
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return
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end subroutine get_parms
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!
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! print an error message
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!
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subroutine pr_usage(iout)
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integer(psb_ipk_) :: iout
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|
write(iout,*)'incorrect parameter(s) found'
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|
write(iout,*)' usage: pde90 methd prec dim &
|
|
&[istop itmax itrace]'
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|
write(iout,*)' where:'
|
|
write(iout,*)' methd: cgstab cgs rgmres bicgstabl'
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|
write(iout,*)' prec : bjac diag none'
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|
write(iout,*)' dim number of points along each axis'
|
|
write(iout,*)' the size of the resulting linear '
|
|
write(iout,*)' system is dim**3'
|
|
write(iout,*)' istop stopping criterion 1, 2 '
|
|
write(iout,*)' itmax maximum number of iterations [500] '
|
|
write(iout,*)' itrace <=0 (no tracing, default) or '
|
|
write(iout,*)' >= 1 do tracing every itrace'
|
|
write(iout,*)' iterations '
|
|
end subroutine pr_usage
|
|
|
|
!
|
|
! functions parametrizing the differential equation
|
|
!
|
|
function b1(x,y,z)
|
|
use psb_base_mod, only : psb_dpk_
|
|
real(psb_dpk_) :: b1
|
|
real(psb_dpk_), intent(in) :: x,y,z
|
|
b1=1.d0/sqrt(3.d0)
|
|
end function b1
|
|
function b2(x,y,z)
|
|
use psb_base_mod, only : psb_dpk_
|
|
real(psb_dpk_) :: b2
|
|
real(psb_dpk_), intent(in) :: x,y,z
|
|
b2=1.d0/sqrt(3.d0)
|
|
end function b2
|
|
function b3(x,y,z)
|
|
use psb_base_mod, only : psb_dpk_
|
|
real(psb_dpk_) :: b3
|
|
real(psb_dpk_), intent(in) :: x,y,z
|
|
b3=1.d0/sqrt(3.d0)
|
|
end function b3
|
|
function c(x,y,z)
|
|
use psb_base_mod, only : psb_dpk_
|
|
real(psb_dpk_) :: c
|
|
real(psb_dpk_), intent(in) :: x,y,z
|
|
c=0.d0
|
|
end function c
|
|
function a1(x,y,z)
|
|
use psb_base_mod, only : psb_dpk_
|
|
real(psb_dpk_) :: a1
|
|
real(psb_dpk_), intent(in) :: x,y,z
|
|
a1=1.d0/80
|
|
end function a1
|
|
function a2(x,y,z)
|
|
use psb_base_mod, only : psb_dpk_
|
|
real(psb_dpk_) :: a2
|
|
real(psb_dpk_), intent(in) :: x,y,z
|
|
a2=1.d0/80
|
|
end function a2
|
|
function a3(x,y,z)
|
|
use psb_base_mod, only : psb_dpk_
|
|
real(psb_dpk_) :: a3
|
|
real(psb_dpk_), intent(in) :: x,y,z
|
|
a3=1.d0/80
|
|
end function a3
|
|
function g(x,y,z)
|
|
use psb_base_mod, only : psb_dpk_, done
|
|
real(psb_dpk_) :: g
|
|
real(psb_dpk_), intent(in) :: x,y,z
|
|
g = dzero
|
|
if (x == done) then
|
|
g = done
|
|
else if (x == dzero) then
|
|
g = exp(y**2-z**2)
|
|
end if
|
|
end function g
|
|
|
|
end program d_matgen
|