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1440 lines
50 KiB
Fortran
1440 lines
50 KiB
Fortran
!!$
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!!$
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!!$ MLD2P4 version 1.0
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!!$ MultiLevel Domain Decomposition Parallel Preconditioners Package
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!!$ based on PSBLAS (Parallel Sparse BLAS version 2.2)
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!!$
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!!$ (C) Copyright 2008
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!!$
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!!$ Salvatore Filippone University of Rome Tor Vergata
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!!$ Alfredo Buttari University of Rome Tor Vergata
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!!$ Pasqua D'Ambra ICAR-CNR, Naples
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!!$ Daniela di Serafino Second University of Naples
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!!$
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!!$ Redistribution and use in source and binary forms, with or without
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!!$ modification, are permitted provided that the following conditions
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!!$ are met:
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!!$ 1. Redistributions of source code must retain the above copyright
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!!$ notice, this list of conditions and the following disclaimer.
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!!$ 2. Redistributions in binary form must reproduce the above copyright
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!!$ notice, this list of conditions, and the following disclaimer in the
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!!$ documentation and/or other materials provided with the distribution.
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!!$ 3. The name of the MLD2P4 group or the names of its contributors may
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!!$ not be used to endorse or promote products derived from this
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!!$ software without specific written permission.
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!!$
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!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
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!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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!!$ POSSIBILITY OF SUCH DAMAGE.
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!!$
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!!$
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! File: mld_cmlprec_aply.f90
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!
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! Subroutine: mld_cmlprec_aply
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! Version: complex
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!
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! This routine computes
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!
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! Y = beta*Y + alpha*op(M^(-1))*X,
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! where
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! - M is a multilevel domain decomposition (Schwarz) preconditioner associated
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! to a certain matrix A and stored in the array baseprecv,
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! - op(M^(-1)) is M^(-1) or its transpose, according to the value of trans,
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! - X and Y are vectors,
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! - alpha and beta are scalars.
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!
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! For each level we have as many submatrices as processes (except for the coarsest
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! level where we might have a replicated index space) and each process takes care
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! of one submatrix.
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!
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! The multilevel preconditioner M is regarded as an array of 'base preconditioners',
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! each representing the part of the preconditioner associated to a certain level.
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! For each level ilev, the base preconditioner K(ilev) is stored in baseprecv(ilev)
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! and is associated to a matrix A(ilev), obtained by 'tranferring' the original
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! matrix A (i.e. the matrix to be preconditioned) to the level ilev, through smoothed
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! aggregation.
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!
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! The levels are numbered in increasing order starting from the finest one, i.e.
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! level 1 is the finest level and A(1) is the matrix A.
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!
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! For a general description of (parallel) multilevel preconditioners see
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! - B.F. Smith, P.E. Bjorstad & W.D. Gropp,
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! Domain decomposition: parallel multilevel methods for elliptic partial
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! differential equations,
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! Cambridge University Press, 1996.
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! - K. Stuben,
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! Algebraic Multigrid (AMG): An Introduction with Applications,
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! GMD Report N. 70, 1999.
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!
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!
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! Arguments:
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! alpha - complex(psb_spk_), input.
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! The scalar alpha.
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! baseprecv - type(mld_cbaseprc_type), dimension(:), input.
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! The array of base preconditioner data structures containing the
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! local parts of the preconditioners to be applied at each level.
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! Note that nlev = size(baseprecv) = number of levels.
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! baseprecv(ilev)%av - type(psb_cspmat_type), dimension(:), allocatable(:).
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! The sparse matrices needed to apply the preconditioner
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! at level ilev.
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! baseprecv(ilev)%av(mld_l_pr_) - The L factor of the ILU factorization of the
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! local diagonal block of A(ilev).
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! baseprecv(ilev)%av(mld_u_pr_) - The U factor of the ILU factorization of the
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! local diagonal block of A(ilev), except its
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! diagonal entries (stored in baseprecv(ilev)%d).
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! baseprecv(ilev)%av(mld_ap_nd_) - The entries of the local part of A(ilev)
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! outside the diagonal block, for block-Jacobi
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! sweeps.
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! baseprecv(ilev)%av(mld_ac_) - The local part of the matrix A(ilev).
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! baseprecv(ilev)%av(mld_sm_pr_) - The smoothed prolongator.
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! It maps vectors (ilev) ---> (ilev-1).
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! baseprecv(ilev)%av(mld_sm_pr_t_) - The smoothed prolongator transpose.
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! It maps vectors (ilev-1) ---> (ilev).
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! baseprecv(ilev)%d - complex(psb_spk_), dimension(:), allocatable.
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! The diagonal entries of the U factor in the ILU
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! factorization of A(ilev).
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! baseprecv(ilev)%desc_data - type(psb_desc_type).
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! The communication descriptor associated to the base
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! preconditioner, i.e. to the sparse matrices needed
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! to apply the base preconditioner at the current level.
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! baseprecv(ilev)%desc_ac - type(psb_desc_type).
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! The communication descriptor associated to the sparse
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! matrix A(ilev), stored in baseprecv(ilev)%av(mld_ac_).
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! baseprecv(ilev)%iprcparm - integer, dimension(:), allocatable.
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! The integer parameters defining the base
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! preconditioner K(ilev).
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! baseprecv(ilev)%rprcparm - complex(psb_spk_), dimension(:), allocatable.
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! The real parameters defining the base preconditioner
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! K(ilev).
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! baseprecv(ilev)%perm - integer, dimension(:), allocatable.
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! The row and column permutations applied to the local
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! part of A(ilev) (defined only if baseprecv(ilev)%
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! iprcparm(mld_sub_ren_)>0).
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! baseprecv(ilev)%invperm - integer, dimension(:), allocatable.
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! The inverse of the permutation stored in
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! baseprecv(ilev)%perm.
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! baseprecv(ilev)%mlia - integer, dimension(:), allocatable.
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! The aggregation map (ilev-1) --> (ilev).
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! In case of non-smoothed aggregation, it is used
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! instead of mld_sm_pr_.
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! baseprecv(ilev)%nlaggr - integer, dimension(:), allocatable.
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! The number of aggregates (rows of A(ilev)) on the
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! various processes.
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! baseprecv(ilev)%base_a - type(psb_cspmat_type), pointer.
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! Pointer (really a pointer!) to the base matrix of
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! the current level, i.e. the local part of A(ilev);
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! so we have a unified treatment of residuals. We
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! need this to avoid passing explicitly the matrix
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! A(ilev) to the routine which applies the
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! preconditioner.
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! baseprecv(ilev)%base_desc - type(psb_desc_type), pointer.
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! Pointer to the communication descriptor associated
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! to the sparse matrix pointed by base_a.
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! baseprecv(ilev)%dorig - complex(psb_spk_), dimension(:), allocatable.
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! Diagonal entries of the matrix pointed by base_a.
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!
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! x - complex(psb_spk_), dimension(:), input.
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! The local part of the vector X.
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! beta - complex(psb_spk_), input.
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! The scalar beta.
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! y - complex(psb_spk_), dimension(:), input/output.
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! The local part of the vector Y.
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! desc_data - type(psb_desc_type), input.
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! The communication descriptor associated to the matrix to be
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! preconditioned.
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! trans - character, optional.
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! If trans='N','n' then op(M^(-1)) = M^(-1);
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! if trans='T','t' then op(M^(-1)) = M^(-T) (transpose of M^(-1)).
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! work - complex(psb_spk_), dimension (:), optional, target.
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! Workspace. Its size must be at least 4*psb_cd_get_local_cols(desc_data).
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! info - integer, output.
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! Error code.
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!
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! Note that when the LU factorization of the matrix A(ilev) is computed instead of
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! the ILU one, by using UMFPACK or SuperLU, the corresponding L and U factors
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! are stored in data structures provided by UMFPACK or SuperLU and pointed by
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! baseprecv(ilev)%iprcparm(mld_umf_ptr) or baseprecv(ilev)%iprcparm(mld_slu_ptr),
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! respectively.
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!
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subroutine mld_cmlprec_aply(alpha,baseprecv,x,beta,y,desc_data,trans,work,info)
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use psb_base_mod
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use mld_inner_mod, mld_protect_name => mld_cmlprec_aply
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implicit none
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! Arguments
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type(psb_desc_type),intent(in) :: desc_data
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type(mld_cbaseprc_type), intent(in) :: baseprecv(:)
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complex(psb_spk_),intent(in) :: alpha,beta
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complex(psb_spk_),intent(in) :: x(:)
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complex(psb_spk_),intent(inout) :: y(:)
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character, intent(in) :: trans
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complex(psb_spk_),target :: work(:)
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integer, intent(out) :: info
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! Local variables
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integer :: ictxt, np, me, err_act
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integer :: debug_level, debug_unit
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character(len=20) :: name
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character :: trans_
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name = 'mld_cmlprec_aply'
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info = 0
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call psb_erractionsave(err_act)
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debug_unit = psb_get_debug_unit()
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debug_level = psb_get_debug_level()
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ictxt = psb_cd_get_context(desc_data)
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call psb_info(ictxt, me, np)
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if (debug_level >= psb_debug_inner_) &
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& write(debug_unit,*) me,' ',trim(name),&
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& ' Entry ', size(baseprecv)
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trans_ = psb_toupper(trans)
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select case(baseprecv(2)%iprcparm(mld_ml_type_))
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case(mld_no_ml_)
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!
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! No preconditioning, should not really get here
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!
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call psb_errpush(4001,name,a_err='mld_no_ml_ in mlprc_aply?')
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goto 9999
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case(mld_add_ml_)
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!
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! Additive multilevel
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!
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call add_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans_,work,info)
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case(mld_mult_ml_)
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!
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! Multiplicative multilevel (multiplicative among the levels, additive inside
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! each level)
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!
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! Pre/post-smoothing versions.
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! Note that the transpose switches pre <-> post.
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!
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select case(baseprecv(2)%iprcparm(mld_smooth_pos_))
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case(mld_post_smooth_)
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select case (trans_)
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case('N')
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call mlt_post_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans_,work,info)
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case('T','C')
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call mlt_pre_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans_,work,info)
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case default
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info = 4001
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call psb_errpush(info,name,a_err='invalid trans')
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goto 9999
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end select
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case(mld_pre_smooth_)
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select case (trans_)
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case('N')
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call mlt_pre_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans_,work,info)
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case('T','C')
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call mlt_post_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans_,work,info)
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case default
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info = 4001
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call psb_errpush(info,name,a_err='invalid trans')
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goto 9999
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end select
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case(mld_twoside_smooth_)
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call mlt_twoside_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans_,work,info)
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case default
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info = 4013
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call psb_errpush(info,name,a_err='invalid smooth_pos',&
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& i_Err=(/baseprecv(2)%iprcparm(mld_smooth_pos_),0,0,0,0/))
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goto 9999
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end select
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case default
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info = 4013
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call psb_errpush(info,name,a_err='invalid mltype',&
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& i_Err=(/baseprecv(2)%iprcparm(mld_ml_type_),0,0,0,0/))
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goto 9999
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end select
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call psb_erractionrestore(err_act)
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return
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9999 continue
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call psb_erractionrestore(err_act)
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if (err_act.eq.psb_act_abort_) then
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call psb_error()
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return
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end if
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return
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contains
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!
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! Subroutine: add_ml_aply
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! Version: complex
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! Note: internal subroutine of mld_dmlprec_aply.
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!
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! This routine computes
|
|
!
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! Y = beta*Y + alpha*op(M^(-1))*X,
|
|
! where
|
|
! - M is an additive multilevel domain decomposition (Schwarz) preconditioner
|
|
! associated to a certain matrix A and stored in the array baseprecv,
|
|
! - op(M^(-1)) is M^(-1) or its (conjugate) transpose, according to
|
|
! the value of trans,
|
|
! - X and Y are vectors,
|
|
! - alpha and beta are scalars.
|
|
!
|
|
! The preconditioner M is additive both through the levels and inside each
|
|
! level.
|
|
!
|
|
! For each level we have as many submatrices as processes (except for the coarsest
|
|
! level where we might have a replicated index space) and each process takes care
|
|
! of one submatrix.
|
|
!
|
|
! The multilevel preconditioner M is regarded as an array of 'base preconditioners',
|
|
! each representing the part of the preconditioner associated to a certain level.
|
|
! For each level ilev, the base preconditioner K(ilev) is stored in baseprecv(ilev)
|
|
! and is associated to a matrix A(ilev), obtained by 'tranferring' the original
|
|
! matrix A (i.e. the matrix to be preconditioned) to the level ilev, through smoothed
|
|
! aggregation.
|
|
!
|
|
! The levels are numbered in increasing order starting from the finest one, i.e.
|
|
! level 1 is the finest level and A(1) is the matrix A.
|
|
!
|
|
! For details on the additive multilevel Schwarz preconditioner see the
|
|
! Algorithm 3.1.1 in the book:
|
|
! B.F. Smith, P.E. Bjorstad & W.D. Gropp,
|
|
! Domain decomposition: parallel multilevel methods for elliptic partial
|
|
! differential equations, Cambridge University Press, 1996.
|
|
!
|
|
! For a description of the arguments see mld_dmlprec_aply.
|
|
!
|
|
! A sketch of the algorithm implemented in this routine is provided below
|
|
! (AV(ilev; sm_pr_) denotes the smoothed prolongator from level ilev to
|
|
! level ilev-1, while AV(ilev; sm_pr_t_) denotes its transpose, i.e. the
|
|
! corresponding restriction operator from level ilev-1 to level ilev).
|
|
!
|
|
! 1. ! Apply the base preconditioner at level 1.
|
|
! ! The sum over the subdomains is carried out in the
|
|
! ! application of K(1).
|
|
! X(1) = Xest
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! Y(1) = (K(1)^(-1))*X(1)
|
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!
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! 2. DO ilev=2,nlev
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|
!
|
|
! ! Transfer X(ilev-1) to the next coarser level.
|
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! X(ilev) = AV(ilev; sm_pr_t_)*X(ilev-1)
|
|
!
|
|
! ! Apply the base preconditioner at the current level.
|
|
! ! The sum over the subdomains is carried out in the
|
|
! ! application of K(ilev).
|
|
! Y(ilev) = (K(ilev)^(-1))*X(ilev)
|
|
!
|
|
! ENDDO
|
|
!
|
|
! 3. DO ilev=nlev-1,1,-1
|
|
!
|
|
! ! Transfer Y(ilev+1) to the next finer level.
|
|
! Y(ilev) = AV(ilev+1; sm_pr_)*Y(ilev+1)
|
|
!
|
|
! ENDDO
|
|
!
|
|
! 4. Yext = beta*Yext + alpha*Y(1)
|
|
!
|
|
subroutine add_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans,work,info)
|
|
|
|
implicit none
|
|
|
|
! Arguments
|
|
type(psb_desc_type),intent(in) :: desc_data
|
|
type(mld_cbaseprc_type), intent(in) :: baseprecv(:)
|
|
complex(psb_spk_),intent(in) :: alpha,beta
|
|
complex(psb_spk_),intent(in) :: x(:)
|
|
complex(psb_spk_),intent(inout) :: y(:)
|
|
character, intent(in) :: trans
|
|
complex(psb_spk_),target :: work(:)
|
|
integer, intent(out) :: info
|
|
|
|
! Local variables
|
|
integer :: n_row,n_col
|
|
integer :: ictxt,np,me,i, nr2l,nc2l,err_act
|
|
integer :: debug_level, debug_unit
|
|
integer :: ismth, nlev, ilev, icm
|
|
character(len=20) :: name
|
|
|
|
type psb_mlprec_wrk_type
|
|
complex(psb_spk_), allocatable :: tx(:),ty(:),x2l(:),y2l(:)
|
|
end type psb_mlprec_wrk_type
|
|
type(psb_mlprec_wrk_type), allocatable :: mlprec_wrk(:)
|
|
|
|
name = 'add_ml_aply'
|
|
info = 0
|
|
call psb_erractionsave(err_act)
|
|
debug_unit = psb_get_debug_unit()
|
|
debug_level = psb_get_debug_level()
|
|
|
|
ictxt = psb_cd_get_context(desc_data)
|
|
call psb_info(ictxt, me, np)
|
|
|
|
if (debug_level >= psb_debug_inner_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' Entry ', size(baseprecv)
|
|
|
|
nlev = size(baseprecv)
|
|
allocate(mlprec_wrk(nlev),stat=info)
|
|
if (info /= 0) then
|
|
call psb_errpush(4010,name,a_err='Allocate')
|
|
goto 9999
|
|
end if
|
|
|
|
!
|
|
! STEP 1
|
|
!
|
|
! Apply the base preconditioner at the finest level
|
|
!
|
|
allocate(mlprec_wrk(1)%x2l(size(x)),mlprec_wrk(1)%y2l(size(y)), stat=info)
|
|
if (info /= 0) then
|
|
info=4025
|
|
call psb_errpush(info,name,i_err=(/size(x)+size(y),0,0,0,0/),&
|
|
& a_err='complex(psb_spk_)')
|
|
goto 9999
|
|
end if
|
|
|
|
mlprec_wrk(1)%x2l(:) = x(:)
|
|
mlprec_wrk(1)%y2l(:) = czero
|
|
|
|
|
|
call mld_baseprec_aply(alpha,baseprecv(1),x,beta,y,&
|
|
& baseprecv(1)%base_desc,trans,work,info)
|
|
if (info /=0) then
|
|
call psb_errpush(4010,name,a_err='baseprec_aply')
|
|
goto 9999
|
|
end if
|
|
!
|
|
! STEP 2
|
|
!
|
|
! For each level except the finest one ...
|
|
!
|
|
do ilev = 2, nlev
|
|
n_row = psb_cd_get_local_rows(baseprecv(ilev-1)%base_desc)
|
|
n_col = psb_cd_get_local_cols(baseprecv(ilev-1)%base_desc)
|
|
nc2l = psb_cd_get_local_cols(baseprecv(ilev)%base_desc)
|
|
nr2l = psb_cd_get_local_rows(baseprecv(ilev)%base_desc)
|
|
allocate(mlprec_wrk(ilev)%x2l(nc2l),mlprec_wrk(ilev)%y2l(nc2l),&
|
|
& stat=info)
|
|
if (info /= 0) then
|
|
info=4025
|
|
call psb_errpush(info,name,i_err=(/2*(nc2l+max(n_row,n_col)),0,0,0,0/),&
|
|
& a_err='complex(psb_spk_)')
|
|
goto 9999
|
|
end if
|
|
|
|
ismth = baseprecv(ilev)%iprcparm(mld_aggr_kind_)
|
|
icm = baseprecv(ilev)%iprcparm(mld_coarse_mat_)
|
|
|
|
! Apply prolongator transpose, i.e. restriction
|
|
call psb_forward_map(cone,mlprec_wrk(ilev-1)%x2l,&
|
|
& czero,mlprec_wrk(ilev)%x2l,&
|
|
& baseprecv(ilev)%map_desc,info,work=work)
|
|
|
|
|
|
if (info /=0) then
|
|
call psb_errpush(4001,name,a_err='Error during restriction')
|
|
goto 9999
|
|
end if
|
|
|
|
|
|
if (icm == mld_repl_mat_) then
|
|
call psb_sum(ictxt,mlprec_wrk(ilev)%x2l(1:nr2l))
|
|
else if (icm /= mld_distr_mat_) then
|
|
info = 4013
|
|
call psb_errpush(info,name,a_err='invalid mld_coarse_mat_',&
|
|
& i_Err=(/icm,0,0,0,0/))
|
|
goto 9999
|
|
endif
|
|
|
|
!
|
|
! Apply the base preconditioner
|
|
!
|
|
call mld_baseprec_aply(cone,baseprecv(ilev),&
|
|
& mlprec_wrk(ilev)%x2l,czero,mlprec_wrk(ilev)%y2l,&
|
|
& baseprecv(ilev)%base_desc,trans,work,info)
|
|
|
|
enddo
|
|
|
|
!
|
|
! STEP 3
|
|
!
|
|
! For each level except the finest one ...
|
|
!
|
|
do ilev =nlev,2,-1
|
|
|
|
n_row = psb_cd_get_local_rows(baseprecv(ilev-1)%base_desc)
|
|
n_col = psb_cd_get_local_cols(baseprecv(ilev-1)%base_desc)
|
|
nc2l = psb_cd_get_local_cols(baseprecv(ilev)%base_desc)
|
|
nr2l = psb_cd_get_local_rows(baseprecv(ilev)%base_desc)
|
|
ismth = baseprecv(ilev)%iprcparm(mld_aggr_kind_)
|
|
icm = baseprecv(ilev)%iprcparm(mld_coarse_mat_)
|
|
|
|
!
|
|
! Apply prolongator
|
|
!
|
|
call psb_backward_map(cone,mlprec_wrk(ilev)%y2l,&
|
|
& cone,mlprec_wrk(ilev-1)%y2l,&
|
|
& baseprecv(ilev)%map_desc,info,work=work)
|
|
|
|
if (info /=0) then
|
|
call psb_errpush(4001,name,a_err='Error during prolongation')
|
|
goto 9999
|
|
end if
|
|
end do
|
|
|
|
!
|
|
! STEP 4
|
|
!
|
|
! Compute the output vector Y
|
|
!
|
|
call psb_geaxpby(alpha,mlprec_wrk(1)%y2l,cone,y,baseprecv(1)%base_desc,info)
|
|
if (info /= 0) then
|
|
call psb_errpush(4001,name,a_err='Error on final update')
|
|
goto 9999
|
|
end if
|
|
|
|
deallocate(mlprec_wrk,stat=info)
|
|
if (info /= 0) then
|
|
call psb_errpush(4000,name)
|
|
goto 9999
|
|
end if
|
|
|
|
call psb_erractionrestore(err_act)
|
|
return
|
|
|
|
9999 continue
|
|
call psb_erractionrestore(err_act)
|
|
if (err_act.eq.psb_act_abort_) then
|
|
call psb_error()
|
|
return
|
|
end if
|
|
return
|
|
|
|
end subroutine add_ml_aply
|
|
!
|
|
! Subroutine: mlt_pre_ml_aply
|
|
! Version: complex
|
|
! Note: internal subroutine of mld_dmlprec_aply.
|
|
!
|
|
! This routine computes
|
|
!
|
|
! Y = beta*Y + alpha*op(M^(-1))*X,
|
|
! where
|
|
! - M is a hybrid multilevel domain decomposition (Schwarz) preconditioner
|
|
! associated to a certain matrix A and stored in the array baseprecv,
|
|
! - op(M^(-1)) is M^(-1) or its (conjugate) transpose, according to
|
|
! the value of trans,
|
|
! - X and Y are vectors,
|
|
! - alpha and beta are scalars.
|
|
!
|
|
! The preconditioner M is hybrid in the sense that it is multiplicative through the
|
|
! levels and additive inside a level; pre-smoothing only is applied at each level.
|
|
!
|
|
! For each level we have as many submatrices as processes (except for the coarsest
|
|
! level where we might have a replicated index space) and each process takes care
|
|
! of one submatrix.
|
|
!
|
|
! The multilevel preconditioner M is regarded as an array of 'base preconditioners',
|
|
! each representing the part of the preconditioner associated to a certain level.
|
|
! For each level ilev, the base preconditioner K(ilev) is stored in baseprecv(ilev)
|
|
! and is associated to a matrix A(ilev), obtained by 'tranferring' the original
|
|
! matrix A (i.e. the matrix to be preconditioned) to the level ilev, through smoothed
|
|
! aggregation.
|
|
!
|
|
! The levels are numbered in increasing order starting from the finest one, i.e.
|
|
! level 1 is the finest level and A(1) is the matrix A.
|
|
!
|
|
! For details on the pre-smoothed hybrid multiplicative multilevel Schwarz
|
|
! preconditioner, see the Algorithm 3.2.1 in the book:
|
|
! B.F. Smith, P.E. Bjorstad & W.D. Gropp,
|
|
! Domain decomposition: parallel multilevel methods for elliptic partial
|
|
! differential equations, Cambridge University Press, 1996.
|
|
!
|
|
! For a description of the arguments see mld_dmlprec_aply.
|
|
!
|
|
! A sketch of the algorithm implemented in this routine is provided below
|
|
! (AV(ilev; sm_pr_) denotes the smoothed prolongator from level ilev to
|
|
! level ilev-1, while AV(ilev; sm_pr_t_) denotes its transpose, i.e. the
|
|
! corresponding restriction operator from level ilev-1 to level ilev).
|
|
!
|
|
! 1. X(1) = Xext
|
|
!
|
|
! 2. ! Apply the base preconditioner at the finest level.
|
|
! Y(1) = (K(1)^(-1))*X(1)
|
|
!
|
|
! 3. ! Compute the residual at the finest level.
|
|
! TX(1) = X(1) - A(1)*Y(1)
|
|
!
|
|
! 4. DO ilev=2, nlev
|
|
!
|
|
! ! Transfer the residual to the current (coarser) level.
|
|
! X(ilev) = AV(ilev; sm_pr_t_)*TX(ilev-1)
|
|
!
|
|
! ! Apply the base preconditioner at the current level.
|
|
! ! The sum over the subdomains is carried out in the
|
|
! ! application of K(ilev).
|
|
! Y(ilev) = (K(ilev)^(-1))*X(ilev)
|
|
!
|
|
! ! Compute the residual at the current level (except at
|
|
! ! the coarsest level).
|
|
! IF (ilev < nlev)
|
|
! TX(ilev) = (X(ilev)-A(ilev)*Y(ilev))
|
|
!
|
|
! ENDDO
|
|
!
|
|
! 5. DO ilev=nlev-1,1,-1
|
|
!
|
|
! ! Transfer Y(ilev+1) to the next finer level
|
|
! Y(ilev) = Y(ilev) + AV(ilev+1; sm_pr_)*Y(ilev+1)
|
|
!
|
|
! ENDDO
|
|
!
|
|
! 6. Yext = beta*Yext + alpha*Y(1)
|
|
!
|
|
!
|
|
subroutine mlt_pre_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans,work,info)
|
|
|
|
implicit none
|
|
|
|
! Arguments
|
|
type(psb_desc_type),intent(in) :: desc_data
|
|
type(mld_cbaseprc_type), intent(in) :: baseprecv(:)
|
|
complex(psb_spk_),intent(in) :: alpha,beta
|
|
complex(psb_spk_),intent(in) :: x(:)
|
|
complex(psb_spk_),intent(inout) :: y(:)
|
|
character, intent(in) :: trans
|
|
complex(psb_spk_),target :: work(:)
|
|
integer, intent(out) :: info
|
|
|
|
! Local variables
|
|
integer :: n_row,n_col
|
|
integer :: ictxt,np,me,i, nr2l,nc2l,err_act
|
|
integer :: debug_level, debug_unit
|
|
integer :: ismth, nlev, ilev, icm
|
|
character(len=20) :: name
|
|
|
|
type psb_mlprec_wrk_type
|
|
complex(psb_spk_), allocatable :: tx(:),ty(:),x2l(:),y2l(:)
|
|
end type psb_mlprec_wrk_type
|
|
type(psb_mlprec_wrk_type), allocatable :: mlprec_wrk(:)
|
|
|
|
name = 'mlt_pre_ml_aply'
|
|
info = 0
|
|
call psb_erractionsave(err_act)
|
|
debug_unit = psb_get_debug_unit()
|
|
debug_level = psb_get_debug_level()
|
|
|
|
ictxt = psb_cd_get_context(desc_data)
|
|
call psb_info(ictxt, me, np)
|
|
|
|
if (debug_level >= psb_debug_inner_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' Entry ', size(baseprecv)
|
|
|
|
nlev = size(baseprecv)
|
|
allocate(mlprec_wrk(nlev),stat=info)
|
|
if (info /= 0) then
|
|
call psb_errpush(4010,name,a_err='Allocate')
|
|
goto 9999
|
|
end if
|
|
|
|
!
|
|
! STEP 1
|
|
!
|
|
! Copy the input vector X
|
|
!
|
|
n_col = psb_cd_get_local_cols(desc_data)
|
|
nc2l = psb_cd_get_local_cols(baseprecv(1)%base_desc)
|
|
|
|
allocate(mlprec_wrk(1)%x2l(nc2l),mlprec_wrk(1)%y2l(nc2l), &
|
|
& mlprec_wrk(1)%tx(nc2l), stat=info)
|
|
if (info /= 0) then
|
|
info=4025
|
|
call psb_errpush(info,name,i_err=(/4*nc2l,0,0,0,0/),&
|
|
& a_err='complex(psb_spk_)')
|
|
goto 9999
|
|
end if
|
|
|
|
mlprec_wrk(1)%x2l(:) = x
|
|
!
|
|
! STEP 2
|
|
!
|
|
! Apply the base preconditioner at the finest level
|
|
!
|
|
call mld_baseprec_aply(cone,baseprecv(1),mlprec_wrk(1)%x2l,&
|
|
& czero,mlprec_wrk(1)%y2l,baseprecv(1)%base_desc,&
|
|
& trans,work,info)
|
|
if (info /=0) then
|
|
call psb_errpush(4010,name,a_err=' baseprec_aply')
|
|
goto 9999
|
|
end if
|
|
|
|
!
|
|
! STEP 3
|
|
!
|
|
! Compute the residual at the finest level
|
|
!
|
|
mlprec_wrk(1)%tx = mlprec_wrk(1)%x2l
|
|
|
|
call psb_spmm(-cone,baseprecv(1)%base_a,mlprec_wrk(1)%y2l,&
|
|
& cone,mlprec_wrk(1)%tx,baseprecv(1)%base_desc,info,&
|
|
& work=work,trans=trans)
|
|
if (info /=0) then
|
|
call psb_errpush(4001,name,a_err=' fine level residual')
|
|
goto 9999
|
|
end if
|
|
|
|
!
|
|
! STEP 4
|
|
!
|
|
! For each level but the finest one ...
|
|
!
|
|
do ilev = 2, nlev
|
|
|
|
n_row = psb_cd_get_local_rows(baseprecv(ilev-1)%base_desc)
|
|
n_col = psb_cd_get_local_cols(baseprecv(ilev-1)%base_desc)
|
|
nc2l = psb_cd_get_local_cols(baseprecv(ilev)%base_desc)
|
|
nr2l = psb_cd_get_local_rows(baseprecv(ilev)%base_desc)
|
|
ismth = baseprecv(ilev)%iprcparm(mld_aggr_kind_)
|
|
icm = baseprecv(ilev)%iprcparm(mld_coarse_mat_)
|
|
|
|
allocate(mlprec_wrk(ilev)%tx(nc2l),mlprec_wrk(ilev)%y2l(nc2l),&
|
|
& mlprec_wrk(ilev)%x2l(nc2l), stat=info)
|
|
if (info /= 0) then
|
|
info=4025
|
|
call psb_errpush(info,name,i_err=(/4*nc2l,0,0,0,0/),&
|
|
& a_err='complex(psb_spk_)')
|
|
goto 9999
|
|
end if
|
|
|
|
! Apply prolongator transpose, i.e. restriction
|
|
call psb_forward_map(cone,mlprec_wrk(ilev-1)%tx,&
|
|
& czero,mlprec_wrk(ilev)%x2l,&
|
|
& baseprecv(ilev)%map_desc,info,work=work)
|
|
|
|
if (info /=0) then
|
|
call psb_errpush(4001,name,a_err='Error during restriction')
|
|
goto 9999
|
|
end if
|
|
|
|
if (icm ==mld_repl_mat_) then
|
|
call psb_sum(ictxt,mlprec_wrk(ilev)%x2l(1:nr2l))
|
|
else if (icm /= mld_distr_mat_) then
|
|
info = 4013
|
|
call psb_errpush(info,name,a_err='invalid mld_coarse_mat_',&
|
|
& i_Err=(/icm,0,0,0,0/))
|
|
goto 9999
|
|
endif
|
|
|
|
!
|
|
! Apply the base preconditioner
|
|
!
|
|
call mld_baseprec_aply(cone,baseprecv(ilev),mlprec_wrk(ilev)%x2l,&
|
|
& czero,mlprec_wrk(ilev)%y2l,baseprecv(ilev)%base_desc,trans,work,info)
|
|
|
|
!
|
|
! Compute the residual (at all levels but the coarsest one)
|
|
!
|
|
if (ilev < nlev) then
|
|
mlprec_wrk(ilev)%tx = mlprec_wrk(ilev)%x2l
|
|
if (info == 0) call psb_spmm(-cone,baseprecv(ilev)%base_a,&
|
|
& mlprec_wrk(ilev)%y2l,cone,mlprec_wrk(ilev)%tx,&
|
|
& baseprecv(ilev)%base_desc,info,work=work,trans=trans)
|
|
endif
|
|
if (info /=0) then
|
|
call psb_errpush(4001,name,a_err='Error on up sweep residual')
|
|
goto 9999
|
|
end if
|
|
enddo
|
|
|
|
!
|
|
! STEP 5
|
|
!
|
|
! For each level but the coarsest one ...
|
|
!
|
|
do ilev = nlev-1, 1, -1
|
|
|
|
ismth = baseprecv(ilev+1)%iprcparm(mld_aggr_kind_)
|
|
n_row = psb_cd_get_local_rows(baseprecv(ilev)%base_desc)
|
|
|
|
!
|
|
! Apply prolongator
|
|
!
|
|
call psb_backward_map(cone,mlprec_wrk(ilev+1)%y2l,&
|
|
& cone,mlprec_wrk(ilev)%y2l,&
|
|
& baseprecv(ilev+1)%map_desc,info,work=work)
|
|
|
|
if (info /=0) then
|
|
call psb_errpush(4001,name,a_err='Error during prolongation')
|
|
goto 9999
|
|
end if
|
|
enddo
|
|
|
|
!
|
|
! STEP 6
|
|
!
|
|
! Compute the output vector Y
|
|
!
|
|
call psb_geaxpby(alpha,mlprec_wrk(1)%y2l,beta,y,&
|
|
& baseprecv(1)%base_desc,info)
|
|
if (info /=0) then
|
|
call psb_errpush(4001,name,a_err='Error on final update')
|
|
goto 9999
|
|
end if
|
|
|
|
deallocate(mlprec_wrk,stat=info)
|
|
if (info /= 0) then
|
|
call psb_errpush(4000,name)
|
|
goto 9999
|
|
end if
|
|
|
|
call psb_erractionrestore(err_act)
|
|
return
|
|
|
|
9999 continue
|
|
call psb_erractionrestore(err_act)
|
|
if (err_act.eq.psb_act_abort_) then
|
|
call psb_error()
|
|
return
|
|
end if
|
|
return
|
|
end subroutine mlt_pre_ml_aply
|
|
!
|
|
! Subroutine: mlt_post_ml_aply
|
|
! Version: complex
|
|
! Note: internal subroutine of mld_dmlprec_aply.
|
|
!
|
|
! This routine computes
|
|
!
|
|
! Y = beta*Y + alpha*op(M^(-1))*X,
|
|
! where
|
|
! - M is a hybrid multilevel domain decomposition (Schwarz) preconditioner
|
|
! associated to a certain matrix A and stored in the array baseprecv,
|
|
! - op(M^(-1)) is M^(-1) or its (conjugate) transpose, according to
|
|
! the value of trans,
|
|
! - X and Y are vectors,
|
|
! - alpha and beta are scalars.
|
|
!
|
|
! The preconditioner M is hybrid in the sense that it is multiplicative through the
|
|
! levels and additive inside a level; post-smoothing only is applied at each level.
|
|
!
|
|
! For each level we have as many submatrices as processes (except for the coarsest
|
|
! level where we might have a replicated index space) and each process takes care
|
|
! of one submatrix.
|
|
!
|
|
! The multilevel preconditioner M is regarded as an array of 'base preconditioners',
|
|
! each representing the part of the preconditioner associated to a certain level.
|
|
! For each level ilev, the base preconditioner K(ilev) is stored in baseprecv(ilev)
|
|
! and is associated to a matrix A(ilev), obtained by 'tranferring' the original
|
|
! matrix A (i.e. the matrix to be preconditioned) to the level ilev, through smoothed
|
|
! aggregation.
|
|
!
|
|
! The levels are numbered in increasing order starting from the finest one, i.e.
|
|
! level 1 is the finest level and A(1) is the matrix A.
|
|
!
|
|
! For details on hybrid multiplicative multilevel Schwarz preconditioners, see
|
|
! B.F. Smith, P.E. Bjorstad & W.D. Gropp,
|
|
! Domain decomposition: parallel multilevel methods for elliptic partial
|
|
! differential equations, Cambridge University Press, 1996.
|
|
!
|
|
! For a description of the arguments see mld_dmlprec_aply.
|
|
!
|
|
! A sketch of the algorithm implemented in this routine is provided below.
|
|
! (AV(ilev; sm_pr_) denotes the smoothed prolongator from level ilev to
|
|
! level ilev-1, while AV(ilev; sm_pr_t_) denotes its transpose, i.e. the
|
|
! corresponding restriction operator from level ilev-1 to level ilev).
|
|
!
|
|
! 1. X(1) = Xext
|
|
!
|
|
! 2. DO ilev=2, nlev
|
|
!
|
|
! ! Transfer X(ilev-1) to the next coarser level.
|
|
! X(ilev) = AV(ilev; sm_pr_t_)*X(ilev-1)
|
|
!
|
|
! ENDDO
|
|
!
|
|
! 3.! Apply the preconditioner at the coarsest level.
|
|
! Y(nlev) = (K(nlev)^(-1))*X(nlev)
|
|
!
|
|
! 4. DO ilev=nlev-1,1,-1
|
|
!
|
|
! ! Transfer Y(ilev+1) to the next finer level.
|
|
! Y(ilev) = AV(ilev+1; sm_pr_)*Y(ilev+1)
|
|
!
|
|
! ! Compute the residual at the current level and apply to it the
|
|
! ! base preconditioner. The sum over the subdomains is carried out
|
|
! ! in the application of K(ilev).
|
|
! Y(ilev) = Y(ilev) + (K(ilev)^(-1))*(X(ilev)-A(ilev)*Y(ilev))
|
|
!
|
|
! ENDDO
|
|
!
|
|
! 5. Yext = beta*Yext + alpha*Y(1)
|
|
!
|
|
!
|
|
subroutine mlt_post_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans,work,info)
|
|
|
|
implicit none
|
|
|
|
! Arguments
|
|
type(psb_desc_type),intent(in) :: desc_data
|
|
type(mld_cbaseprc_type), intent(in) :: baseprecv(:)
|
|
complex(psb_spk_),intent(in) :: alpha,beta
|
|
complex(psb_spk_),intent(in) :: x(:)
|
|
complex(psb_spk_),intent(inout) :: y(:)
|
|
character, intent(in) :: trans
|
|
complex(psb_spk_),target :: work(:)
|
|
integer, intent(out) :: info
|
|
|
|
! Local variables
|
|
integer :: n_row,n_col
|
|
integer :: ictxt,np,me,i, nr2l,nc2l,err_act
|
|
integer :: debug_level, debug_unit
|
|
integer :: ismth, nlev, ilev, icm
|
|
character(len=20) :: name
|
|
|
|
type psb_mlprec_wrk_type
|
|
complex(psb_spk_), allocatable :: tx(:),ty(:),x2l(:),y2l(:)
|
|
end type psb_mlprec_wrk_type
|
|
type(psb_mlprec_wrk_type), allocatable :: mlprec_wrk(:)
|
|
|
|
name = 'mlt_post_ml_aply'
|
|
info = 0
|
|
call psb_erractionsave(err_act)
|
|
debug_unit = psb_get_debug_unit()
|
|
debug_level = psb_get_debug_level()
|
|
|
|
ictxt = psb_cd_get_context(desc_data)
|
|
call psb_info(ictxt, me, np)
|
|
|
|
if (debug_level >= psb_debug_inner_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' Entry ', size(baseprecv)
|
|
|
|
nlev = size(baseprecv)
|
|
allocate(mlprec_wrk(nlev),stat=info)
|
|
if (info /= 0) then
|
|
call psb_errpush(4010,name,a_err='Allocate')
|
|
goto 9999
|
|
end if
|
|
|
|
!
|
|
! STEP 1
|
|
!
|
|
! Copy the input vector X
|
|
!
|
|
if (debug_level >= psb_debug_inner_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' desc_data status',allocated(desc_data%matrix_data)
|
|
|
|
n_col = psb_cd_get_local_cols(desc_data)
|
|
nc2l = psb_cd_get_local_cols(baseprecv(1)%base_desc)
|
|
|
|
allocate(mlprec_wrk(1)%x2l(nc2l),mlprec_wrk(1)%y2l(nc2l), &
|
|
& mlprec_wrk(1)%tx(nc2l), stat=info)
|
|
|
|
call psb_geaxpby(cone,x,czero,mlprec_wrk(1)%tx,&
|
|
& baseprecv(1)%base_desc,info)
|
|
call psb_geaxpby(cone,x,czero,mlprec_wrk(1)%x2l,&
|
|
& baseprecv(1)%base_desc,info)
|
|
|
|
!
|
|
! STEP 2
|
|
!
|
|
! For each level but the finest one ...
|
|
!
|
|
do ilev=2, nlev
|
|
|
|
n_row = psb_cd_get_local_rows(baseprecv(ilev-1)%base_desc)
|
|
n_col = psb_cd_get_local_cols(baseprecv(ilev-1)%base_desc)
|
|
nc2l = psb_cd_get_local_cols(baseprecv(ilev)%base_desc)
|
|
nr2l = psb_cd_get_local_rows(baseprecv(ilev)%base_desc)
|
|
ismth = baseprecv(ilev)%iprcparm(mld_aggr_kind_)
|
|
icm = baseprecv(ilev)%iprcparm(mld_coarse_mat_)
|
|
|
|
if (debug_level >= psb_debug_inner_) &
|
|
& write(debug_unit,*) me,' ',trim(name), &
|
|
& ' starting up sweep ',&
|
|
& ilev,allocated(baseprecv(ilev)%iprcparm),n_row,n_col,&
|
|
& nc2l, nr2l,ismth
|
|
|
|
allocate(mlprec_wrk(ilev)%tx(nc2l),mlprec_wrk(ilev)%y2l(nc2l),&
|
|
& mlprec_wrk(ilev)%x2l(nc2l), stat=info)
|
|
|
|
if (info /= 0) then
|
|
info=4025
|
|
call psb_errpush(info,name,i_err=(/4*nc2l,0,0,0,0/),&
|
|
& a_err='complex(psb_spk_)')
|
|
goto 9999
|
|
end if
|
|
|
|
! Apply prolongator transpose, i.e. restriction
|
|
call psb_forward_map(cone,mlprec_wrk(ilev-1)%x2l,&
|
|
& czero,mlprec_wrk(ilev)%x2l,&
|
|
& baseprecv(ilev)%map_desc,info,work=work)
|
|
|
|
if (info /=0) then
|
|
call psb_errpush(4001,name,a_err='Error during restriction')
|
|
goto 9999
|
|
end if
|
|
|
|
if (icm == mld_repl_mat_) Then
|
|
call psb_sum(ictxt,mlprec_wrk(ilev)%x2l(1:nr2l))
|
|
else if (icm /= mld_distr_mat_) Then
|
|
info = 4013
|
|
call psb_errpush(info,name,a_err='invalid mld_coarse_mat_',&
|
|
& i_Err=(/icm,0,0,0,0/))
|
|
goto 9999
|
|
endif
|
|
|
|
!
|
|
! update x2l
|
|
!
|
|
call psb_geaxpby(cone,mlprec_wrk(ilev)%x2l,czero,mlprec_wrk(ilev)%tx,&
|
|
& baseprecv(ilev)%base_desc,info)
|
|
if (info /= 0) then
|
|
call psb_errpush(4001,name,a_err='Error in update')
|
|
goto 9999
|
|
end if
|
|
|
|
if (debug_level >= psb_debug_inner_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' done up sweep ', ilev
|
|
|
|
enddo
|
|
|
|
!
|
|
! STEP 3
|
|
!
|
|
! Apply the base preconditioner at the coarsest level
|
|
!
|
|
call mld_baseprec_aply(cone,baseprecv(nlev),mlprec_wrk(nlev)%x2l, &
|
|
& czero, mlprec_wrk(nlev)%y2l,baseprecv(nlev)%base_desc,trans,work,info)
|
|
if (info /=0) then
|
|
call psb_errpush(4010,name,a_err='baseprec_aply')
|
|
goto 9999
|
|
end if
|
|
|
|
if (debug_level >= psb_debug_inner_) write(debug_unit,*) &
|
|
& me,' ',trim(name), ' done baseprec_aply ', nlev
|
|
|
|
!
|
|
! STEP 4
|
|
!
|
|
! For each level but the coarsest one ...
|
|
!
|
|
do ilev=nlev-1, 1, -1
|
|
|
|
if (debug_level >= psb_debug_inner_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' starting down sweep',ilev
|
|
|
|
ismth = baseprecv(ilev+1)%iprcparm(mld_aggr_kind_)
|
|
n_row = psb_cd_get_local_rows(baseprecv(ilev)%base_desc)
|
|
|
|
!
|
|
! Apply prolongator
|
|
!
|
|
call psb_backward_map(cone,mlprec_wrk(ilev+1)%y2l,&
|
|
& czero,mlprec_wrk(ilev)%y2l,&
|
|
& baseprecv(ilev+1)%map_desc,info,work=work)
|
|
|
|
if (info /=0) then
|
|
call psb_errpush(4001,name,a_err='Error during prolongation')
|
|
goto 9999
|
|
end if
|
|
|
|
!
|
|
! Compute the residual
|
|
!
|
|
call psb_spmm(-cone,baseprecv(ilev)%base_a,mlprec_wrk(ilev)%y2l,&
|
|
& cone,mlprec_wrk(ilev)%tx,baseprecv(ilev)%base_desc,info,&
|
|
& work=work,trans=trans)
|
|
|
|
!
|
|
! Apply the base preconditioner
|
|
!
|
|
if (info == 0) call mld_baseprec_aply(cone,baseprecv(ilev),mlprec_wrk(ilev)%tx,&
|
|
& cone,mlprec_wrk(ilev)%y2l,baseprecv(ilev)%base_desc,trans,work,info)
|
|
if (info /=0) then
|
|
call psb_errpush(4001,name,a_err=' spmm/baseprec_aply')
|
|
goto 9999
|
|
end if
|
|
|
|
if (debug_level >= psb_debug_inner_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' done down sweep',ilev
|
|
enddo
|
|
|
|
!
|
|
! STEP 5
|
|
!
|
|
! Compute the output vector Y
|
|
!
|
|
call psb_geaxpby(alpha,mlprec_wrk(1)%y2l,beta,y,baseprecv(1)%base_desc,info)
|
|
|
|
if (info /=0) then
|
|
call psb_errpush(4001,name,a_err=' Final update')
|
|
goto 9999
|
|
end if
|
|
|
|
|
|
|
|
deallocate(mlprec_wrk,stat=info)
|
|
if (info /= 0) then
|
|
call psb_errpush(4000,name)
|
|
goto 9999
|
|
end if
|
|
|
|
call psb_erractionrestore(err_act)
|
|
return
|
|
|
|
9999 continue
|
|
call psb_erractionrestore(err_act)
|
|
if (err_act.eq.psb_act_abort_) then
|
|
call psb_error()
|
|
return
|
|
end if
|
|
return
|
|
end subroutine mlt_post_ml_aply
|
|
!
|
|
! Subroutine: mlt_twoside_ml_aply
|
|
! Version: complex
|
|
! Note: internal subroutine of mld_dmlprec_aply.
|
|
!
|
|
! This routine computes
|
|
!
|
|
! Y = beta*Y + alpha*op(M^(-1))*X,
|
|
! where
|
|
! - M is a symmetrized hybrid multilevel domain decomposition (Schwarz)
|
|
! preconditioner associated to a certain matrix A and stored in the array
|
|
! baseprecv,
|
|
! - op(M^(-1)) is M^(-1) or its (conjugate) transpose, according to
|
|
! the value of trans,
|
|
! - X and Y are vectors,
|
|
! - alpha and beta are scalars.
|
|
!
|
|
! The preconditioner M is hybrid in the sense that it is multiplicative through
|
|
! the levels and additive inside a level; it is symmetrized since pre-smoothing
|
|
! and post-smoothing are applied at each level.
|
|
!
|
|
! For each level we have as many submatrices as processes (except for the coarsest
|
|
! level where we might have a replicated index space) and each process takes care
|
|
! of one submatrix.
|
|
!
|
|
! The multilevel preconditioner M is regarded as an array of 'base preconditioners',
|
|
! each representing the part of the preconditioner associated to a certain level.
|
|
! For each level ilev, the base preconditioner K(ilev) is stored in baseprecv(ilev)
|
|
! and is associated to a matrix A(ilev), obtained by 'tranferring' the original
|
|
! matrix A (i.e. the matrix to be preconditioned) to the level ilev, through smoothed
|
|
! aggregation.
|
|
!
|
|
! The levels are numbered in increasing order starting from the finest one, i.e.
|
|
! level 1 is the finest level and A(1) is the matrix A.
|
|
!
|
|
! For details on the symmetrized hybrid multiplicative multilevel Schwarz
|
|
! preconditioner, see the Algorithm 3.2.2 of the book:
|
|
! B.F. Smith, P.E. Bjorstad & W.D. Gropp,
|
|
! Domain decomposition: parallel multilevel methods for elliptic partial
|
|
! differential equations, Cambridge University Press, 1996.
|
|
!
|
|
! For a description of the arguments see mld_dmlprec_aply.
|
|
!
|
|
! A sketch of the algorithm implemented in this routine is provided below.
|
|
! (AV(ilev; sm_pr_) denotes the smoothed prolongator from level ilev to
|
|
! level ilev-1, while AV(ilev; sm_pr_t_) denotes its transpose, i.e. the
|
|
! corresponding restriction operator from level ilev-1 to level ilev).
|
|
!
|
|
! 1. X(1) = Xext
|
|
!
|
|
! 2. ! Apply the base peconditioner at the finest level
|
|
! Y(1) = (K(1)^(-1))*X(1)
|
|
!
|
|
! 3. ! Compute the residual at the finest level
|
|
! TX(1) = X(1) - A(1)*Y(1)
|
|
!
|
|
! 4. DO ilev=2, nlev
|
|
!
|
|
! ! Transfer the residual to the current (coarser) level
|
|
! X(ilev) = AV(ilev; sm_pr_t)*TX(ilev-1)
|
|
!
|
|
! ! Apply the base preconditioner at the current level.
|
|
! ! The sum over the subdomains is carried out in the
|
|
! ! application of K(ilev)
|
|
! Y(ilev) = (K(ilev)^(-1))*X(ilev)
|
|
!
|
|
! ! Compute the residual at the current level
|
|
! TX(ilev) = (X(ilev)-A(ilev)*Y(ilev))
|
|
!
|
|
! ENDDO
|
|
!
|
|
! 5. DO ilev=NLEV-1,1,-1
|
|
!
|
|
! ! Transfer Y(ilev+1) to the next finer level
|
|
! Y(ilev) = Y(ilev) + AV(ilev+1; sm_pr_)*Y(ilev+1)
|
|
!
|
|
! ! Compute the residual at the current level and apply to it the
|
|
! ! base preconditioner. The sum over the subdomains is carried out
|
|
! ! in the application of K(ilev)
|
|
! Y(ilev) = Y(ilev) + (K(ilev)**(-1))*(X(ilev)-A(ilev)*Y(ilev))
|
|
!
|
|
! ENDDO
|
|
!
|
|
! 6. Yext = beta*Yext + alpha*Y(1)
|
|
!
|
|
subroutine mlt_twoside_ml_aply(alpha,baseprecv,x,beta,y,desc_data,trans,work,info)
|
|
|
|
implicit none
|
|
|
|
! Arguments
|
|
type(psb_desc_type),intent(in) :: desc_data
|
|
type(mld_cbaseprc_type), intent(in) :: baseprecv(:)
|
|
complex(psb_spk_),intent(in) :: alpha,beta
|
|
complex(psb_spk_),intent(in) :: x(:)
|
|
complex(psb_spk_),intent(inout) :: y(:)
|
|
character, intent(in) :: trans
|
|
complex(psb_spk_),target :: work(:)
|
|
integer, intent(out) :: info
|
|
|
|
! Local variables
|
|
integer :: n_row,n_col
|
|
integer :: ictxt,np,me,i, nr2l,nc2l,err_act
|
|
integer :: debug_level, debug_unit
|
|
integer :: ismth, nlev, ilev, icm
|
|
character(len=20) :: name
|
|
|
|
type psb_mlprec_wrk_type
|
|
complex(psb_spk_), allocatable :: tx(:),ty(:),x2l(:),y2l(:)
|
|
end type psb_mlprec_wrk_type
|
|
type(psb_mlprec_wrk_type), allocatable :: mlprec_wrk(:)
|
|
|
|
name = 'mlt_twoside_ml_aply'
|
|
info = 0
|
|
call psb_erractionsave(err_act)
|
|
debug_unit = psb_get_debug_unit()
|
|
debug_level = psb_get_debug_level()
|
|
|
|
ictxt = psb_cd_get_context(desc_data)
|
|
call psb_info(ictxt, me, np)
|
|
|
|
if (debug_level >= psb_debug_inner_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' Entry ', size(baseprecv)
|
|
|
|
nlev = size(baseprecv)
|
|
allocate(mlprec_wrk(nlev),stat=info)
|
|
if (info /= 0) then
|
|
call psb_errpush(4010,name,a_err='Allocate')
|
|
goto 9999
|
|
end if
|
|
|
|
! STEP 1
|
|
!
|
|
! Copy the input vector X
|
|
!
|
|
n_col = psb_cd_get_local_cols(desc_data)
|
|
nc2l = psb_cd_get_local_cols(baseprecv(1)%base_desc)
|
|
|
|
allocate(mlprec_wrk(1)%x2l(nc2l),mlprec_wrk(1)%y2l(nc2l), &
|
|
& mlprec_wrk(1)%ty(nc2l), mlprec_wrk(1)%tx(nc2l), stat=info)
|
|
|
|
if (info /= 0) then
|
|
info=4025
|
|
call psb_errpush(info,name,i_err=(/4*nc2l,0,0,0,0/),&
|
|
& a_err='complex(psb_spk_)')
|
|
goto 9999
|
|
end if
|
|
|
|
call psb_geaxpby(cone,x,czero,mlprec_wrk(1)%x2l,&
|
|
& baseprecv(1)%base_desc,info)
|
|
call psb_geaxpby(cone,x,czero,mlprec_wrk(1)%tx,&
|
|
& baseprecv(1)%base_desc,info)
|
|
|
|
!
|
|
! STEP 2
|
|
!
|
|
! Apply the base preconditioner at the finest level
|
|
!
|
|
call mld_baseprec_aply(cone,baseprecv(1),mlprec_wrk(1)%x2l,&
|
|
& czero,mlprec_wrk(1)%y2l,baseprecv(1)%base_desc,&
|
|
& trans,work,info)
|
|
!
|
|
! STEP 3
|
|
!
|
|
! Compute the residual at the finest level
|
|
!
|
|
mlprec_wrk(1)%ty = mlprec_wrk(1)%x2l
|
|
if (info == 0) call psb_spmm(-cone,baseprecv(1)%base_a,mlprec_wrk(1)%y2l,&
|
|
& cone,mlprec_wrk(1)%ty,baseprecv(1)%base_desc,info,&
|
|
& work=work,trans=trans)
|
|
if (info /=0) then
|
|
call psb_errpush(4010,name,a_err='Fine level baseprec/residual')
|
|
goto 9999
|
|
end if
|
|
|
|
!
|
|
! STEP 4
|
|
!
|
|
! For each level but the finest one ...
|
|
!
|
|
do ilev = 2, nlev
|
|
|
|
n_row = psb_cd_get_local_rows(baseprecv(ilev-1)%base_desc)
|
|
n_col = psb_cd_get_local_cols(baseprecv(ilev-1)%base_desc)
|
|
nc2l = psb_cd_get_local_cols(baseprecv(ilev)%base_desc)
|
|
nr2l = psb_cd_get_local_rows(baseprecv(ilev)%base_desc)
|
|
ismth = baseprecv(ilev)%iprcparm(mld_aggr_kind_)
|
|
icm = baseprecv(ilev)%iprcparm(mld_coarse_mat_)
|
|
allocate(mlprec_wrk(ilev)%tx(nc2l),mlprec_wrk(ilev)%ty(nc2l),&
|
|
& mlprec_wrk(ilev)%y2l(nc2l),mlprec_wrk(ilev)%x2l(nc2l), stat=info)
|
|
|
|
if (info /= 0) then
|
|
info=4025
|
|
call psb_errpush(info,name,i_err=(/4*nc2l,0,0,0,0/),&
|
|
& a_err='complex(psb_spk_)')
|
|
goto 9999
|
|
end if
|
|
|
|
! Apply prolongator transpose, i.e. restriction
|
|
call psb_forward_map(cone,mlprec_wrk(ilev-1)%ty,&
|
|
& czero,mlprec_wrk(ilev)%x2l,&
|
|
& baseprecv(ilev)%map_desc,info,work=work)
|
|
|
|
if (info /=0) then
|
|
call psb_errpush(4001,name,a_err='Error during restriction')
|
|
goto 9999
|
|
end if
|
|
|
|
if (icm == mld_repl_mat_) then
|
|
call psb_sum(ictxt,mlprec_wrk(ilev)%x2l(1:nr2l))
|
|
else if (icm /= mld_distr_mat_) then
|
|
info = 4013
|
|
call psb_errpush(info,name,a_err='invalid mld_coarse_mat_',&
|
|
& i_Err=(/icm,0,0,0,0/))
|
|
goto 9999
|
|
endif
|
|
|
|
call psb_geaxpby(cone,mlprec_wrk(ilev)%x2l,czero,mlprec_wrk(ilev)%tx,&
|
|
& baseprecv(ilev)%base_desc,info)
|
|
!
|
|
! Apply the base preconditioner
|
|
!
|
|
if (info == 0) call mld_baseprec_aply(cone,baseprecv(ilev),&
|
|
& mlprec_wrk(ilev)%x2l,czero,mlprec_wrk(ilev)%y2l,&
|
|
&baseprecv(ilev)%base_desc,trans,work,info)
|
|
!
|
|
! Compute the residual (at all levels but the coarsest one)
|
|
!
|
|
if(ilev < nlev) then
|
|
mlprec_wrk(ilev)%ty = mlprec_wrk(ilev)%x2l
|
|
if (info == 0) call psb_spmm(-cone,baseprecv(ilev)%base_a,&
|
|
& mlprec_wrk(ilev)%y2l,cone,mlprec_wrk(ilev)%ty,&
|
|
& baseprecv(ilev)%base_desc,info,work=work,trans=trans)
|
|
endif
|
|
if (info /=0) then
|
|
call psb_errpush(4001,name,a_err='baseprec_aply/residual')
|
|
goto 9999
|
|
end if
|
|
|
|
enddo
|
|
|
|
!
|
|
! STEP 5
|
|
!
|
|
! For each level but the coarsest one ...
|
|
!
|
|
do ilev=nlev-1, 1, -1
|
|
|
|
ismth = baseprecv(ilev+1)%iprcparm(mld_aggr_kind_)
|
|
n_row = psb_cd_get_local_rows(baseprecv(ilev)%base_desc)
|
|
|
|
!
|
|
! Apply prolongator
|
|
!
|
|
call psb_backward_map(cone,mlprec_wrk(ilev+1)%y2l,&
|
|
& cone,mlprec_wrk(ilev)%y2l,&
|
|
& baseprecv(ilev+1)%map_desc,info,work=work)
|
|
|
|
if (info /=0 ) then
|
|
call psb_errpush(4001,name,a_err='Error during restriction')
|
|
goto 9999
|
|
end if
|
|
|
|
!
|
|
! Compute the residual
|
|
!
|
|
call psb_spmm(-cone,baseprecv(ilev)%base_a,mlprec_wrk(ilev)%y2l,&
|
|
& cone,mlprec_wrk(ilev)%tx,baseprecv(ilev)%base_desc,info,&
|
|
& work=work,trans=trans)
|
|
!
|
|
! Apply the base preconditioner
|
|
!
|
|
if (info == 0) call mld_baseprec_aply(cone,baseprecv(ilev),mlprec_wrk(ilev)%tx,&
|
|
& cone,mlprec_wrk(ilev)%y2l,baseprecv(ilev)%base_desc, trans, work,info)
|
|
if (info /= 0) then
|
|
call psb_errpush(4001,name,a_err='Error: residual/baseprec_aply')
|
|
goto 9999
|
|
end if
|
|
enddo
|
|
|
|
!
|
|
! STEP 6
|
|
!
|
|
! Compute the output vector Y
|
|
!
|
|
call psb_geaxpby(alpha,mlprec_wrk(1)%y2l,beta,y,&
|
|
& baseprecv(1)%base_desc,info)
|
|
|
|
if (info /= 0) then
|
|
call psb_errpush(4001,name,a_err='Error final update')
|
|
goto 9999
|
|
end if
|
|
|
|
|
|
|
|
deallocate(mlprec_wrk,stat=info)
|
|
if (info /= 0) then
|
|
call psb_errpush(4000,name)
|
|
goto 9999
|
|
end if
|
|
|
|
call psb_erractionrestore(err_act)
|
|
return
|
|
|
|
9999 continue
|
|
call psb_erractionrestore(err_act)
|
|
if (err_act.eq.psb_act_abort_) then
|
|
call psb_error()
|
|
return
|
|
end if
|
|
return
|
|
end subroutine mlt_twoside_ml_aply
|
|
|
|
end subroutine mld_cmlprec_aply
|
|
|