You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
1356 lines
46 KiB
Fortran
1356 lines
46 KiB
Fortran
!!$
|
|
!!$
|
|
!!$ MLD2P4 version 1.1
|
|
!!$ MultiLevel Domain Decomposition Parallel Preconditioners Package
|
|
!!$ based on PSBLAS (Parallel Sparse BLAS version 2.3.1)
|
|
!!$
|
|
!!$ (C) Copyright 2008,2009
|
|
!!$
|
|
!!$ Salvatore Filippone University of Rome Tor Vergata
|
|
!!$ Alfredo Buttari CNRS-IRIT, Toulouse
|
|
!!$ Pasqua D'Ambra ICAR-CNR, Naples
|
|
!!$ Daniela di Serafino Second University of Naples
|
|
!!$
|
|
!!$ Redistribution and use in source and binary forms, with or without
|
|
!!$ modification, are permitted provided that the following conditions
|
|
!!$ are met:
|
|
!!$ 1. Redistributions of source code must retain the above copyright
|
|
!!$ notice, this list of conditions and the following disclaimer.
|
|
!!$ 2. Redistributions in binary form must reproduce the above copyright
|
|
!!$ notice, this list of conditions, and the following disclaimer in the
|
|
!!$ documentation and/or other materials provided with the distribution.
|
|
!!$ 3. The name of the MLD2P4 group or the names of its contributors may
|
|
!!$ not be used to endorse or promote products derived from this
|
|
!!$ software without specific written permission.
|
|
!!$
|
|
!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
|
!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
|
|
!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
|
|
!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
|
|
!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
|
|
!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
|
|
!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
|
!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
|
|
!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
|
|
!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
|
!!$ POSSIBILITY OF SUCH DAMAGE.
|
|
!!$
|
|
!!$
|
|
! File: mld_zmlprec_aply.f90
|
|
!
|
|
! Subroutine: mld_zmlprec_aply
|
|
! Version: complex
|
|
!
|
|
! This routine computes
|
|
!
|
|
! Y = beta*Y + alpha*op(M^(-1))*X,
|
|
! where
|
|
! - M is a multilevel domain decomposition (Schwarz) preconditioner associated
|
|
! to a certain matrix A and stored in p,
|
|
! - op(M^(-1)) is M^(-1) or its transpose, according to the value of trans,
|
|
! - X and Y are vectors,
|
|
! - alpha and beta are scalars.
|
|
!
|
|
! 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.
|
|
!
|
|
! A multilevel preconditioner is regarded as an array of 'one-level' data structures,
|
|
! each containing the part of the preconditioner associated to a certain level
|
|
! (for more details see the description of mld_Tonelev_type in mld_prec_type.f90).
|
|
! For each level ilev, the 'base preconditioner' K(ilev) is stored in
|
|
! p%precv(ilev)%prec
|
|
! 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 a general description of (parallel) multilevel 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.
|
|
! - K. Stuben,
|
|
! Algebraic Multigrid (AMG): An Introduction with Applications,
|
|
! GMD Report N. 70, 1999.
|
|
!
|
|
!
|
|
! Arguments:
|
|
! alpha - complex(psb_dpk_), input.
|
|
! The scalar alpha.
|
|
! p - type(mld_zprec_type), input.
|
|
! The multilevel preconditioner data structure containing the
|
|
! local part of the preconditioner to be applied.
|
|
! Note that nlev = size(p%precv) = number of levels.
|
|
! p%precv(ilev)%prec - type(psb_zbaseprec_type)
|
|
! The 'base preconditioner' for the current level
|
|
! p%precv(ilev)%ac - type(psb_zspmat_type)
|
|
! The local part of the matrix A(ilev).
|
|
! p%precv(ilev)%desc_ac - type(psb_desc_type).
|
|
! The communication descriptor associated to the sparse
|
|
! matrix A(ilev)
|
|
! p%precv(ilev)%map - type(psb_inter_desc_type)
|
|
! Stores the linear operators mapping level (ilev-1)
|
|
! to (ilev) and vice versa. These are the restriction
|
|
! and prolongation operators described in the sequel.
|
|
! p%precv(ilev)%iprcparm - integer, dimension(:), allocatable.
|
|
! The integer parameters defining the multilevel
|
|
! strategy
|
|
! p%precv(ilev)%rprcparm - real(psb_dpk_), dimension(:), allocatable.
|
|
! The real parameters defining the multilevel strategy
|
|
! p%precv(ilev)%mlia - integer, dimension(:), allocatable.
|
|
! The aggregation map (ilev-1) --> (ilev).
|
|
! p%precv(ilev)%nlaggr - integer, dimension(:), allocatable.
|
|
! The number of aggregates (rows of A(ilev)) on the
|
|
! various processes.
|
|
! p%precv(ilev)%base_a - type(psb_zspmat_type), pointer.
|
|
! Pointer (really a pointer!) to the base matrix of
|
|
! the current level, i.e. the local part of A(ilev);
|
|
! so we have a unified treatment of residuals. We
|
|
! need this to avoid passing explicitly the matrix
|
|
! A(ilev) to the routine which applies the
|
|
! preconditioner.
|
|
! p%precv(ilev)%base_desc - type(psb_desc_type), pointer.
|
|
! Pointer to the communication descriptor associated
|
|
! to the sparse matrix pointed by base_a.
|
|
!
|
|
! x - complex(psb_dpk_), dimension(:), input.
|
|
! The local part of the vector X.
|
|
! beta - complex(psb_dpk_), input.
|
|
! The scalar beta.
|
|
! y - complex(psb_dpk_), dimension(:), input/output.
|
|
! The local part of the vector Y.
|
|
! desc_data - type(psb_desc_type), input.
|
|
! The communication descriptor associated to the matrix to be
|
|
! preconditioned.
|
|
! trans - character, optional.
|
|
! If trans='N','n' then op(M^(-1)) = M^(-1);
|
|
! if trans='T','t' then op(M^(-1)) = M^(-T) (transpose of M^(-1)).
|
|
! work - complex(psb_dpk_), dimension (:), optional, target.
|
|
! Workspace. Its size must be at least 4*psb_cd_get_local_cols(desc_data).
|
|
! info - integer, output.
|
|
! Error code.
|
|
!
|
|
! Note that when the LU factorization of the matrix A(ilev) is computed instead of
|
|
! the ILU one, by using UMFPACK or SuperLU, the corresponding L and U factors
|
|
! are stored in data structures provided by UMFPACK or SuperLU and pointed by
|
|
! p%precv(ilev)%prec%iprcparm(mld_umf_ptr) or p%precv(ilev)%prec%iprcparm(mld_slu_ptr),
|
|
! respectively.
|
|
!
|
|
subroutine mld_zmlprec_aply(alpha,p,x,beta,y,desc_data,trans,work,info)
|
|
|
|
use psb_sparse_mod
|
|
use mld_inner_mod, mld_protect_name => mld_zmlprec_aply
|
|
|
|
implicit none
|
|
|
|
! Arguments
|
|
type(psb_desc_type),intent(in) :: desc_data
|
|
type(mld_zprec_type), intent(in) :: p
|
|
complex(psb_dpk_),intent(in) :: alpha,beta
|
|
complex(psb_dpk_),intent(in) :: x(:)
|
|
complex(psb_dpk_),intent(inout) :: y(:)
|
|
character, intent(in) :: trans
|
|
complex(psb_dpk_),target :: work(:)
|
|
integer, intent(out) :: info
|
|
|
|
! Local variables
|
|
integer :: ictxt, np, me, err_act
|
|
integer :: debug_level, debug_unit
|
|
character(len=20) :: name
|
|
character :: trans_
|
|
|
|
name = 'mld_zmlprec_aply'
|
|
info = psb_success_
|
|
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(p%precv)
|
|
|
|
trans_ = psb_toupper(trans)
|
|
|
|
select case(p%precv(2)%iprcparm(mld_ml_type_))
|
|
|
|
case(mld_no_ml_)
|
|
!
|
|
! No preconditioning, should not really get here
|
|
!
|
|
call psb_errpush(psb_err_internal_error_,name,a_err='mld_no_ml_ in mlprc_aply?')
|
|
goto 9999
|
|
|
|
case(mld_add_ml_)
|
|
!
|
|
! Additive multilevel
|
|
!
|
|
|
|
call add_ml_aply(alpha,p,x,beta,y,desc_data,trans_,work,info)
|
|
|
|
case(mld_mult_ml_)
|
|
!
|
|
! Multiplicative multilevel (multiplicative among the levels, additive inside
|
|
! each level)
|
|
!
|
|
! Pre/post-smoothing versions.
|
|
! Note that the transpose switches pre <-> post.
|
|
!
|
|
|
|
select case(p%precv(2)%iprcparm(mld_smoother_pos_))
|
|
|
|
case(mld_post_smooth_)
|
|
|
|
select case (trans_)
|
|
case('N')
|
|
call mlt_post_ml_aply(alpha,p,x,beta,y,desc_data,trans_,work,info)
|
|
case('T','C')
|
|
call mlt_pre_ml_aply(alpha,p,x,beta,y,desc_data,trans_,work,info)
|
|
case default
|
|
info = psb_err_internal_error_
|
|
call psb_errpush(info,name,a_err='invalid trans')
|
|
goto 9999
|
|
end select
|
|
|
|
case(mld_pre_smooth_)
|
|
|
|
select case (trans_)
|
|
case('N')
|
|
call mlt_pre_ml_aply(alpha,p,x,beta,y,desc_data,trans_,work,info)
|
|
case('T','C')
|
|
call mlt_post_ml_aply(alpha,p,x,beta,y,desc_data,trans_,work,info)
|
|
case default
|
|
info = psb_err_internal_error_
|
|
call psb_errpush(info,name,a_err='invalid trans')
|
|
goto 9999
|
|
end select
|
|
|
|
case(mld_twoside_smooth_)
|
|
|
|
call mlt_twoside_ml_aply(alpha,p,x,beta,y,desc_data,trans_,work,info)
|
|
|
|
case default
|
|
info = psb_err_from_subroutine_ai_
|
|
call psb_errpush(info,name,a_err='invalid smooth_pos',&
|
|
& i_Err=(/p%precv(2)%iprcparm(mld_smoother_pos_),0,0,0,0/))
|
|
goto 9999
|
|
|
|
end select
|
|
|
|
case default
|
|
info = psb_err_from_subroutine_ai_
|
|
call psb_errpush(info,name,a_err='invalid mltype',&
|
|
& i_Err=(/p%precv(2)%iprcparm(mld_ml_type_),0,0,0,0/))
|
|
goto 9999
|
|
|
|
end select
|
|
|
|
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
|
|
|
|
contains
|
|
!
|
|
! Subroutine: add_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 an additive multilevel domain decomposition (Schwarz) preconditioner
|
|
! associated to a certain matrix A and stored in p,
|
|
! - 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 is regarded as an array of 'one-level' data structures,
|
|
! each containing the part of the preconditioner associated to a certain level
|
|
! (for more details see the description of mld_Tonelev_type in mld_prec_type.f90).
|
|
! For each level ilev, the 'base preconditioner' K(ilev) is stored in
|
|
! p%precv(ilev)%prec
|
|
! 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_zmlprec_aply.
|
|
!
|
|
! A sketch of the algorithm implemented in this routine is provided below.
|
|
! (P(ilev) denotes the smoothed prolongator from level ilev to level
|
|
! ilev-1, while PT(ilev) 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
|
|
! Y(1) = (K(1)^(-1))*X(1)
|
|
!
|
|
! 2. DO ilev=2,nlev
|
|
!
|
|
! ! Transfer X(ilev-1) to the next coarser level.
|
|
! X(ilev) = PT(ilev)*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) = P(ilev+1)*Y(ilev+1)
|
|
!
|
|
! ENDDO
|
|
!
|
|
! 4. Yext = beta*Yext + alpha*Y(1)
|
|
!
|
|
subroutine add_ml_aply(alpha,p,x,beta,y,desc_data,trans,work,info)
|
|
|
|
implicit none
|
|
|
|
! Arguments
|
|
type(psb_desc_type),intent(in) :: desc_data
|
|
type(mld_zprec_type), intent(in) :: p
|
|
complex(psb_dpk_),intent(in) :: alpha,beta
|
|
complex(psb_dpk_),intent(in) :: x(:)
|
|
complex(psb_dpk_),intent(inout) :: y(:)
|
|
character, intent(in) :: trans
|
|
complex(psb_dpk_),target :: work(:)
|
|
integer, intent(out) :: info
|
|
|
|
! Local variables
|
|
integer :: ictxt,np,me,i, nr2l,nc2l,err_act
|
|
integer :: debug_level, debug_unit
|
|
integer :: nlev, ilev
|
|
character(len=20) :: name
|
|
|
|
type psb_mlprec_wrk_type
|
|
complex(psb_dpk_), allocatable :: tx(:),ty(:),x2l(:),y2l(:)
|
|
end type psb_mlprec_wrk_type
|
|
type(psb_mlprec_wrk_type), allocatable :: mlprec_wrk(:)
|
|
|
|
name = 'add_ml_aply'
|
|
info = psb_success_
|
|
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(p%precv)
|
|
|
|
nlev = size(p%precv)
|
|
allocate(mlprec_wrk(nlev),stat=info)
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_from_subroutine_,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 /= psb_success_) then
|
|
info=psb_err_alloc_request_
|
|
call psb_errpush(info,name,i_err=(/size(x)+size(y),0,0,0,0/),&
|
|
& a_err='complex(psb_dpk_)')
|
|
goto 9999
|
|
end if
|
|
|
|
mlprec_wrk(1)%x2l(:) = x(:)
|
|
mlprec_wrk(1)%y2l(:) = zzero
|
|
|
|
call mld_baseprec_aply(alpha,p%precv(1)%prec,x,beta,y,&
|
|
& p%precv(1)%base_desc,trans,work,info)
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_from_subroutine_,name,a_err='baseprec_aply')
|
|
goto 9999
|
|
end if
|
|
!
|
|
! STEP 2
|
|
!
|
|
! For each level except the finest one ...
|
|
!
|
|
do ilev = 2, nlev
|
|
nc2l = psb_cd_get_local_cols(p%precv(ilev)%base_desc)
|
|
nr2l = psb_cd_get_local_rows(p%precv(ilev)%base_desc)
|
|
allocate(mlprec_wrk(ilev)%x2l(nc2l),mlprec_wrk(ilev)%y2l(nc2l),&
|
|
& stat=info)
|
|
if (info /= psb_success_) then
|
|
info=psb_err_alloc_request_
|
|
call psb_errpush(info,name,i_err=(/2*nc2l,0,0,0,0/),&
|
|
& a_err='complex(psb_dpk_)')
|
|
goto 9999
|
|
end if
|
|
|
|
! Apply the prolongator transpose, i.e. the restriction
|
|
call psb_map_X2Y(zone,mlprec_wrk(ilev-1)%x2l,&
|
|
& zzero,mlprec_wrk(ilev)%x2l,&
|
|
& p%precv(ilev)%map,info,work=work)
|
|
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_internal_error_,name,a_err='Error during restriction')
|
|
goto 9999
|
|
end if
|
|
|
|
!
|
|
! Apply the base preconditioner
|
|
!
|
|
call mld_baseprec_aply(zone,p%precv(ilev)%prec,&
|
|
& mlprec_wrk(ilev)%x2l,zzero,mlprec_wrk(ilev)%y2l,&
|
|
& p%precv(ilev)%base_desc,trans,work,info)
|
|
|
|
enddo
|
|
|
|
!
|
|
! STEP 3
|
|
!
|
|
! For each level except the finest one ...
|
|
!
|
|
do ilev =nlev,2,-1
|
|
|
|
nc2l = psb_cd_get_local_cols(p%precv(ilev)%base_desc)
|
|
nr2l = psb_cd_get_local_rows(p%precv(ilev)%base_desc)
|
|
|
|
!
|
|
! Apply the prolongator
|
|
!
|
|
call psb_map_Y2X(zone,mlprec_wrk(ilev)%y2l,&
|
|
& zone,mlprec_wrk(ilev-1)%y2l,&
|
|
& p%precv(ilev)%map,info,work=work)
|
|
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_internal_error_,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,zone,y,p%precv(1)%base_desc,info)
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_internal_error_,name,a_err='Error on final update')
|
|
goto 9999
|
|
end if
|
|
|
|
deallocate(mlprec_wrk,stat=info)
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_alloc_dealloc_,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_zmlprec_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 p%precv,
|
|
! - 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 is regarded as an array of 'one-level' data structures,
|
|
! each containing the part of the preconditioner associated to a certain level
|
|
! (for more details see the description of mld_Tonelev_type in mld_prec_type.f90).
|
|
! For each level ilev, the 'base preconditioner' K(ilev) is stored in
|
|
! p%precv(ilev)%prec
|
|
! 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_zmlprec_aply.
|
|
!
|
|
! A sketch of the algorithm implemented in this routine is provided below.
|
|
! (P(ilev) denotes the smoothed prolongator from level ilev to level
|
|
! ilev-1, while PT(ilev) 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) = PT(ilev)*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) + P(ilev+1)*Y(ilev+1)
|
|
!
|
|
! ENDDO
|
|
!
|
|
! 6. Yext = beta*Yext + alpha*Y(1)
|
|
!
|
|
!
|
|
subroutine mlt_pre_ml_aply(alpha,p,x,beta,y,desc_data,trans,work,info)
|
|
|
|
implicit none
|
|
|
|
! Arguments
|
|
type(psb_desc_type),intent(in) :: desc_data
|
|
type(mld_zprec_type), intent(in) :: p
|
|
complex(psb_dpk_),intent(in) :: alpha,beta
|
|
complex(psb_dpk_),intent(in) :: x(:)
|
|
complex(psb_dpk_),intent(inout) :: y(:)
|
|
character, intent(in) :: trans
|
|
complex(psb_dpk_),target :: work(:)
|
|
integer, intent(out) :: info
|
|
|
|
! Local variables
|
|
integer :: ictxt,np,me,i, nr2l,nc2l,err_act
|
|
integer :: debug_level, debug_unit
|
|
integer :: nlev, ilev
|
|
character(len=20) :: name
|
|
|
|
type psb_mlprec_wrk_type
|
|
complex(psb_dpk_), 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 = psb_success_
|
|
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(p%precv)
|
|
|
|
nlev = size(p%precv)
|
|
allocate(mlprec_wrk(nlev),stat=info)
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_from_subroutine_,name,a_err='Allocate')
|
|
goto 9999
|
|
end if
|
|
|
|
!
|
|
! STEP 1
|
|
!
|
|
! Copy the input vector X
|
|
!
|
|
nc2l = psb_cd_get_local_cols(p%precv(1)%base_desc)
|
|
|
|
allocate(mlprec_wrk(1)%x2l(nc2l),mlprec_wrk(1)%y2l(nc2l), &
|
|
& mlprec_wrk(1)%tx(nc2l), stat=info)
|
|
if (info /= psb_success_) then
|
|
info=psb_err_alloc_request_
|
|
call psb_errpush(info,name,i_err=(/4*nc2l,0,0,0,0/),&
|
|
& a_err='complex(psb_dpk_)')
|
|
goto 9999
|
|
end if
|
|
|
|
mlprec_wrk(1)%x2l(:) = x
|
|
!
|
|
! STEP 2
|
|
!
|
|
! Apply the base preconditioner at the finest level
|
|
!
|
|
call mld_baseprec_aply(zone,p%precv(1)%prec,mlprec_wrk(1)%x2l,&
|
|
& zzero,mlprec_wrk(1)%y2l,p%precv(1)%base_desc,&
|
|
& trans,work,info)
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_from_subroutine_,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(-zone,p%precv(1)%base_a,mlprec_wrk(1)%y2l,&
|
|
& zone,mlprec_wrk(1)%tx,p%precv(1)%base_desc,info,&
|
|
& work=work,trans=trans)
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_internal_error_,name,a_err=' fine level residual')
|
|
goto 9999
|
|
end if
|
|
|
|
!
|
|
! STEP 4
|
|
!
|
|
! For each level but the finest one ...
|
|
!
|
|
do ilev = 2, nlev
|
|
|
|
nc2l = psb_cd_get_local_cols(p%precv(ilev)%base_desc)
|
|
nr2l = psb_cd_get_local_rows(p%precv(ilev)%base_desc)
|
|
|
|
allocate(mlprec_wrk(ilev)%tx(nc2l),mlprec_wrk(ilev)%y2l(nc2l),&
|
|
& mlprec_wrk(ilev)%x2l(nc2l), stat=info)
|
|
if (info /= psb_success_) then
|
|
info=psb_err_alloc_request_
|
|
call psb_errpush(info,name,i_err=(/4*nc2l,0,0,0,0/),&
|
|
& a_err='complex(psb_dpk_)')
|
|
goto 9999
|
|
end if
|
|
|
|
! Apply the prolongator transpose, i.e. the restriction
|
|
call psb_map_X2Y(zone,mlprec_wrk(ilev-1)%tx,&
|
|
& zzero,mlprec_wrk(ilev)%x2l,&
|
|
& p%precv(ilev)%map,info,work=work)
|
|
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_internal_error_,name,a_err='Error during restriction')
|
|
goto 9999
|
|
end if
|
|
|
|
!
|
|
! Apply the base preconditioner
|
|
!
|
|
call mld_baseprec_aply(zone,p%precv(ilev)%prec,mlprec_wrk(ilev)%x2l,&
|
|
& zzero,mlprec_wrk(ilev)%y2l,p%precv(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 == psb_success_) call psb_spmm(-zone,p%precv(ilev)%base_a,&
|
|
& mlprec_wrk(ilev)%y2l,zone,mlprec_wrk(ilev)%tx,&
|
|
& p%precv(ilev)%base_desc,info,work=work,trans=trans)
|
|
endif
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_internal_error_,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
|
|
!
|
|
! Apply the prolongator
|
|
!
|
|
call psb_map_Y2X(zone,mlprec_wrk(ilev+1)%y2l,&
|
|
& zone,mlprec_wrk(ilev)%y2l,&
|
|
& p%precv(ilev+1)%map,info,work=work)
|
|
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_internal_error_,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,&
|
|
& p%precv(1)%base_desc,info)
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_internal_error_,name,a_err='Error on final update')
|
|
goto 9999
|
|
end if
|
|
|
|
deallocate(mlprec_wrk,stat=info)
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_alloc_dealloc_,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_zmlprec_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 p%precv,
|
|
! - 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 is regarded as an array of 'one-level' data structures,
|
|
! each containing the part of the preconditioner associated to a certain level
|
|
! (for more details see the description of mld_Tonelev_type in mld_prec_type.f90).
|
|
! For each level ilev, the 'base preconditioner' K(ilev) is stored in
|
|
! p%precv(ilev)%prec
|
|
! 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_zmlprec_aply.
|
|
!
|
|
! A sketch of the algorithm implemented in this routine is provided below.
|
|
! (P(ilev) denotes the smoothed prolongator from level ilev to level
|
|
! ilev-1, while PT(ilev) 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) = PT(ilev)*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) = P(ilev+1)*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,p,x,beta,y,desc_data,trans,work,info)
|
|
|
|
implicit none
|
|
|
|
! Arguments
|
|
type(psb_desc_type),intent(in) :: desc_data
|
|
type(mld_zprec_type), intent(in) :: p
|
|
complex(psb_dpk_),intent(in) :: alpha,beta
|
|
complex(psb_dpk_),intent(in) :: x(:)
|
|
complex(psb_dpk_),intent(inout) :: y(:)
|
|
character, intent(in) :: trans
|
|
complex(psb_dpk_),target :: work(:)
|
|
integer, intent(out) :: info
|
|
|
|
! Local variables
|
|
integer :: ictxt,np,me,i, nr2l,nc2l,err_act
|
|
integer :: debug_level, debug_unit
|
|
integer :: nlev, ilev
|
|
character(len=20) :: name
|
|
|
|
type psb_mlprec_wrk_type
|
|
complex(psb_dpk_), 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 = psb_success_
|
|
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(p%precv)
|
|
|
|
nlev = size(p%precv)
|
|
allocate(mlprec_wrk(nlev),stat=info)
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_from_subroutine_,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)
|
|
|
|
nc2l = psb_cd_get_local_cols(p%precv(1)%base_desc)
|
|
|
|
allocate(mlprec_wrk(1)%x2l(nc2l),mlprec_wrk(1)%y2l(nc2l), &
|
|
& mlprec_wrk(1)%tx(nc2l), stat=info)
|
|
if (info /= psb_success_) then
|
|
info=psb_err_alloc_request_
|
|
call psb_errpush(info,name,i_err=(/4*nc2l,0,0,0,0/),&
|
|
& a_err='complex(psb_dpk_)')
|
|
goto 9999
|
|
end if
|
|
|
|
call psb_geaxpby(zone,x,zzero,mlprec_wrk(1)%tx,&
|
|
& p%precv(1)%base_desc,info)
|
|
call psb_geaxpby(zone,x,zzero,mlprec_wrk(1)%x2l,&
|
|
& p%precv(1)%base_desc,info)
|
|
|
|
!
|
|
! STEP 2
|
|
!
|
|
! For each level but the finest one ...
|
|
!
|
|
do ilev=2, nlev
|
|
|
|
nc2l = psb_cd_get_local_cols(p%precv(ilev)%base_desc)
|
|
nr2l = psb_cd_get_local_rows(p%precv(ilev)%base_desc)
|
|
|
|
if (debug_level >= psb_debug_inner_) &
|
|
& write(debug_unit,*) me,' ',trim(name), &
|
|
& ' starting up sweep ',&
|
|
& ilev,allocated(p%precv(ilev)%iprcparm),nc2l, nr2l
|
|
|
|
allocate(mlprec_wrk(ilev)%tx(nc2l),mlprec_wrk(ilev)%y2l(nc2l),&
|
|
& mlprec_wrk(ilev)%x2l(nc2l), stat=info)
|
|
|
|
if (info /= psb_success_) then
|
|
info=psb_err_alloc_request_
|
|
call psb_errpush(info,name,i_err=(/4*nc2l,0,0,0,0/),&
|
|
& a_err='complex(psb_dpk_)')
|
|
goto 9999
|
|
end if
|
|
|
|
! Apply the prolongator transpose, i.e. the restriction
|
|
call psb_map_X2Y(zone,mlprec_wrk(ilev-1)%x2l,&
|
|
& zzero,mlprec_wrk(ilev)%x2l,&
|
|
& p%precv(ilev)%map,info,work=work)
|
|
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_internal_error_,name,a_err='Error during restriction')
|
|
goto 9999
|
|
end if
|
|
|
|
!
|
|
! update x2l
|
|
!
|
|
call psb_geaxpby(zone,mlprec_wrk(ilev)%x2l,zzero,mlprec_wrk(ilev)%tx,&
|
|
& p%precv(ilev)%base_desc,info)
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_internal_error_,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(zone,p%precv(nlev)%prec,mlprec_wrk(nlev)%x2l, &
|
|
& zzero, mlprec_wrk(nlev)%y2l,p%precv(nlev)%base_desc,trans,work,info)
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_from_subroutine_,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
|
|
|
|
!
|
|
! Apply the prolongator
|
|
!
|
|
call psb_map_Y2X(zone,mlprec_wrk(ilev+1)%y2l,&
|
|
& zzero,mlprec_wrk(ilev)%y2l,&
|
|
& p%precv(ilev+1)%map,info,work=work)
|
|
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_internal_error_,name,a_err='Error during prolongation')
|
|
goto 9999
|
|
end if
|
|
|
|
!
|
|
! Compute the residual
|
|
!
|
|
call psb_spmm(-zone,p%precv(ilev)%base_a,mlprec_wrk(ilev)%y2l,&
|
|
& zone,mlprec_wrk(ilev)%tx,p%precv(ilev)%base_desc,info,&
|
|
& work=work,trans=trans)
|
|
|
|
!
|
|
! Apply the base preconditioner
|
|
!
|
|
if (info == psb_success_) call mld_baseprec_aply(zone,p%precv(ilev)%prec,&
|
|
& mlprec_wrk(ilev)%tx,zone,mlprec_wrk(ilev)%y2l,p%precv(ilev)%base_desc,&
|
|
&trans,work,info)
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_internal_error_,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,p%precv(1)%base_desc,info)
|
|
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_internal_error_,name,a_err=' Final update')
|
|
goto 9999
|
|
end if
|
|
|
|
|
|
|
|
deallocate(mlprec_wrk,stat=info)
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_alloc_dealloc_,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_zmlprec_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
|
|
! p%precv,
|
|
! - 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 is regarded as an array of 'one-level' data structures,
|
|
! each containing the part of the preconditioner associated to a certain level
|
|
! (for more details see the description of mld_Tonelev_type in mld_prec_type.f90).
|
|
! For each level ilev, the 'base preconditioner' K(ilev) is stored in
|
|
! p%precv(ilev)%prec
|
|
! 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_zmlprec_aply.
|
|
!
|
|
! A sketch of the algorithm implemented in this routine is provided below.
|
|
! (P(ilev) denotes the smoothed prolongator from level ilev to level
|
|
! ilev-1, while PT(ilev) 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) = PT(ilev)*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 for ilev=nlev)
|
|
! if(ilev < nlev)then
|
|
! TX(ilev) = (X(ilev)-A(ilev)*Y(ilev))
|
|
! endif
|
|
!
|
|
! ENDDO
|
|
!
|
|
! 5. DO ilev=NLEV-1,1,-1
|
|
!
|
|
! ! Transfer Y(ilev+1) to the next finer level
|
|
! Y(ilev) = Y(ilev) + P(ilev+1)*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,p,x,beta,y,desc_data,trans,work,info)
|
|
|
|
implicit none
|
|
|
|
! Arguments
|
|
type(psb_desc_type),intent(in) :: desc_data
|
|
type(mld_zprec_type), intent(in) :: p
|
|
complex(psb_dpk_),intent(in) :: alpha,beta
|
|
complex(psb_dpk_),intent(in) :: x(:)
|
|
complex(psb_dpk_),intent(inout) :: y(:)
|
|
character, intent(in) :: trans
|
|
complex(psb_dpk_),target :: work(:)
|
|
integer, intent(out) :: info
|
|
|
|
! Local variables
|
|
integer :: ictxt,np,me,i, nr2l,nc2l,err_act
|
|
integer :: debug_level, debug_unit
|
|
integer :: nlev, ilev
|
|
character(len=20) :: name
|
|
|
|
type psb_mlprec_wrk_type
|
|
complex(psb_dpk_), 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 = psb_success_
|
|
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(p%precv)
|
|
|
|
nlev = size(p%precv)
|
|
allocate(mlprec_wrk(nlev),stat=info)
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_from_subroutine_,name,a_err='Allocate')
|
|
goto 9999
|
|
end if
|
|
|
|
! STEP 1
|
|
!
|
|
! Copy the input vector X
|
|
!
|
|
nc2l = psb_cd_get_local_cols(p%precv(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 /= psb_success_) then
|
|
info=psb_err_alloc_request_
|
|
call psb_errpush(info,name,i_err=(/4*nc2l,0,0,0,0/),&
|
|
& a_err='complex(psb_dpk_)')
|
|
goto 9999
|
|
end if
|
|
|
|
call psb_geaxpby(zone,x,zzero,mlprec_wrk(1)%x2l,&
|
|
& p%precv(1)%base_desc,info)
|
|
call psb_geaxpby(zone,x,zzero,mlprec_wrk(1)%tx,&
|
|
& p%precv(1)%base_desc,info)
|
|
|
|
!
|
|
! STEP 2
|
|
!
|
|
! Apply the base preconditioner at the finest level
|
|
!
|
|
call mld_baseprec_aply(zone,p%precv(1)%prec,mlprec_wrk(1)%x2l,&
|
|
& zzero,mlprec_wrk(1)%y2l,p%precv(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 == psb_success_) call psb_spmm(-zone,p%precv(1)%base_a,mlprec_wrk(1)%y2l,&
|
|
& zone,mlprec_wrk(1)%ty,p%precv(1)%base_desc,info,&
|
|
& work=work,trans=trans)
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_from_subroutine_,name,a_err='Fine level baseprec/residual')
|
|
goto 9999
|
|
end if
|
|
|
|
!
|
|
! STEP 4
|
|
!
|
|
! For each level but the finest one ...
|
|
!
|
|
do ilev = 2, nlev
|
|
|
|
nc2l = psb_cd_get_local_cols(p%precv(ilev)%base_desc)
|
|
nr2l = psb_cd_get_local_rows(p%precv(ilev)%base_desc)
|
|
|
|
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 /= psb_success_) then
|
|
info=psb_err_alloc_request_
|
|
call psb_errpush(info,name,i_err=(/4*nc2l,0,0,0,0/),&
|
|
& a_err='complex(psb_dpk_)')
|
|
goto 9999
|
|
end if
|
|
|
|
! Apply the prolongator transpose, i.e. the restriction
|
|
call psb_map_X2Y(zone,mlprec_wrk(ilev-1)%ty,&
|
|
& zzero,mlprec_wrk(ilev)%x2l,&
|
|
& p%precv(ilev)%map,info,work=work)
|
|
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_internal_error_,name,a_err='Error during restriction')
|
|
goto 9999
|
|
end if
|
|
|
|
call psb_geaxpby(zone,mlprec_wrk(ilev)%x2l,zzero,mlprec_wrk(ilev)%tx,&
|
|
& p%precv(ilev)%base_desc,info)
|
|
!
|
|
! Apply the base preconditioner
|
|
!
|
|
if (info == psb_success_) call mld_baseprec_aply(zone,p%precv(ilev)%prec,&
|
|
& mlprec_wrk(ilev)%x2l,zzero,mlprec_wrk(ilev)%y2l,&
|
|
&p%precv(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 == psb_success_) call psb_spmm(-zone,p%precv(ilev)%base_a,&
|
|
& mlprec_wrk(ilev)%y2l,zone,mlprec_wrk(ilev)%ty,&
|
|
& p%precv(ilev)%base_desc,info,work=work,trans=trans)
|
|
endif
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_internal_error_,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
|
|
|
|
!
|
|
! Apply the prolongator
|
|
!
|
|
call psb_map_Y2X(zone,mlprec_wrk(ilev+1)%y2l,&
|
|
& zone,mlprec_wrk(ilev)%y2l,&
|
|
& p%precv(ilev+1)%map,info,work=work)
|
|
|
|
if (info /= psb_success_ ) then
|
|
call psb_errpush(psb_err_internal_error_,name,a_err='Error during restriction')
|
|
goto 9999
|
|
end if
|
|
|
|
!
|
|
! Compute the residual
|
|
!
|
|
call psb_spmm(-zone,p%precv(ilev)%base_a,mlprec_wrk(ilev)%y2l,&
|
|
& zone,mlprec_wrk(ilev)%tx,p%precv(ilev)%base_desc,info,&
|
|
& work=work,trans=trans)
|
|
!
|
|
! Apply the base preconditioner
|
|
!
|
|
if (info == psb_success_) call mld_baseprec_aply(zone,p%precv(ilev)%prec,mlprec_wrk(ilev)%tx,&
|
|
& zone,mlprec_wrk(ilev)%y2l,p%precv(ilev)%base_desc, trans, work,info)
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_internal_error_,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,&
|
|
& p%precv(1)%base_desc,info)
|
|
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_internal_error_,name,a_err='Error final update')
|
|
goto 9999
|
|
end if
|
|
|
|
|
|
|
|
deallocate(mlprec_wrk,stat=info)
|
|
if (info /= psb_success_) then
|
|
call psb_errpush(psb_err_alloc_dealloc_,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_zmlprec_aply
|
|
|