[12] P. D’Ambra, S. Filippone and P. S. Vassilevski, BootCMatch: a software + package for bootstrap AMG based on graph weighted matching, ACM + Transactions on Mathematical Software, 44, (2018) 39:1–39:25. + + + +
++ [13] P., 2020, arXiv:2006.16147v3. - - -
[13][14] )
[14][15] SIAM Journal on Matrix Analysis and Applications, 20 (3), 1999, 7
[15][16] Software, 16 (1) 1990, 1–17.
[16][17] Transactions on Mathematical Software, 14 (1) 1988, 1–17.
[17][18] .
[18][19] . ACM Transactions on on Mathematical
Software, 38 (4), 2012, art. 23.
+
+
+
[19][20] Library for Parallel Linear Algebra Computation on Sparse Matric
class="cmr-12">, ACM
Transactions on Mathematical Software, 26 (4), 2000, 527–550.
-
-
-
[20][21] 2016, 23:501-518
[21][22] , MIT Press, 1998.
[22][23] Mathematical Software, 5 (3), 1979, 308–323.
[23][24] ACM Transactions on Mathematical Software, 29 (2), 2003, 110̵
[24][25] Numerical Linear Algebra with Applications, 15 (5), 2008, 473R
[25][26] , 2nd edition, SIAM,
2003.
[26][27] , Cambridge
University Press, 1996.
[27][28] Press, 1998.
[28][29] Oosterlee, Multigrid, Academic Press, 2001.
[29][30] editor, Proceedings of SuperComputing 2000, Dallas, 2000.
[30][31] Algebraic Multigrid by Smoothed
class="cmti-12">Aggregation for Second and Fourth Order Elliptic Problems
- [31] P. D’Ambra and P. S. Vassilevski, Adaptive AMG with coarsening based - on compatible weighted matching, Computing and Visualization in Science, - 16, (2013) 59–76. -
-- [32] P. D’Ambra, S. Filippone and P. S. Vassilevski, BootCMatch: a software - package for bootstrap AMG based on graph weighted matching, ACM - Transactions on Mathematical Software, 44, (2018) 39:1–39:25.
+class="cmr-12">(3) 1996, 179–196. diff --git a/docs/html/userhtmlse1.html b/docs/html/userhtmlse1.html index 5f8f1c19..5fed24a9 100644 --- a/docs/html/userhtmlse1.html +++ b/docs/html/userhtmlse1.html @@ -88,7 +88,7 @@ class="cmr-12">4, 2829]), to be used in the iterative solution of linear systems,| e | string | g | der | |
| No preconditioner | No preconditioner | ’NONE’ | ’ | Considered to use the PSBLAS Krylov solvers with no preconditioner. |
| Diagonal | Diagonal | ’DIAG’L1-JACOBI’ | ’ | Diagonal preconditioner. For any zero diagonal entry of the matrix to be preconditioned, the corresponding entry @@ -308,7 +308,7 @@ of the preconditioner is set to 1. |
| Gauss-Seidel | Gauss-Seidel | ’GS’L1-GS’ | ’ | Hybrid Gauss-Seidel (forward), that is, global block Jacobi with Gauss-Seidel as local solver. |
| Symmetrized Gauss-Seidel | Symmetrized Gauss-Seidel | ’FBGS’L1-FBGS’ | ’ | Symmetrized hybrid Gauss-Seidel, that is, forward Gauss-Seidel followed by backward Gauss-Seidel. |
| Block Jacobi | Block Jacobi | ’BJAC’L1-BJAC’ | ’ | Block-Jacobi with ILU(0) on the local blocks. |
| Additive Schwarz | Additive Schwarz | ’AS’ | ’ | Additive Schwarz (AS), with overlap 1 and ILU(0) on the local blocks. |
| Multilevel | Multilevel | ’ML’ | ’ | V-cycle with one hybrid forward Gauss-Seidel (GS) sweep as pre-smoother and one hybrid backward diff --git a/docs/html/userhtmlse6.html b/docs/html/userhtmlse6.html index cf4b33c9..b4614460 100644 --- a/docs/html/userhtmlse6.html +++ b/docs/html/userhtmlse6.html @@ -170,33 +170,33 @@ cellspacing="0" cellpadding="0" > |
smoother | smoother | class(amg_x_base_smoother_type) |
||
|
| The user-defined new smoother to be employed in the preconditioner. |
||
solver | solver | class(amg_x_base_solver_type) |
||
|
| The user-defined new solver to be employed in the preconditioner. |
PSBLAS error handling routines; for further details see the PSBLA [1718]. diff --git a/docs/html/userhtmlse9.html b/docs/html/userhtmlse9.html index 220606fb..21676acb 100644 --- a/docs/html/userhtmlse9.html +++ b/docs/html/userhtmlse9.html @@ -91,7 +91,7 @@ class="cmr-12">Trolling, insulting or derogatory comments, and personal or polit class="cmr-12">Public or private harassment
a
type(in).
The sparse matrix structure containing the local part of the matrix , single/double precision version of AMG4PSBLAS class="cmr-12">under use. See the PSBLAS User’s Guide for details [1718].
desc_a
type(in).
The communication descriptor of a. See the PSBLAS User’s Guide class="cmr-12">for details [1718].
info
integer,out).
Error code. If no error, 0 is returned. See Section 7 for details.
amold
class( optional.
The desired dynamic type for internal matrix components; this allows e.g. running on GPUs; it needs not be the same class="cmr-12">processes. See the PSBLAS User’s Guide for details [1718].
vmold
class( optional.
The desired dynamic type for internal vector components; this allows e.g. running on GPUs.
imold
class( optional.
The desired dynamic type for internal integer vector components; this allows e.g. running on GPUs.
a
type(in).
The sparse matrix structure containing the local part of the matrix , single/double precision version of AMG4PSBLAS class="cmr-12">under use. See the PSBLAS User’s Guide for details [1718].
desc_a
type(in).
The communication descriptor of a. See the PSBLAS User’s Guide class="cmr-12">for details [1718].
info
integer,out).
Error code. If no error, 0 is returned. See Section 7 for details.
amold
class( optional.
The desired dynamic type for internal matrix components; this allows e.g. running on GPUs; it needs not be the same class="cmr-12">processes. See the PSBLAS User’s Guide for details [1718].
vmold
class( optional.
The desired dynamic type for internal vector components; this allows e.g. running on GPUs.
imold
class( optional.
The desired dynamic type for internal integer vector components; this allows e.g. running on GPUs.
The method can be used to build multilevel preconditioners too. diff --git a/docs/html/userhtmlsu12.html b/docs/html/userhtmlsu12.html index 6643e608..2689d6c3 100644 --- a/docs/html/userhtmlsu12.html +++ b/docs/html/userhtmlsu12.html @@ -96,9 +96,9 @@ cellspacing="0" cellpadding="0" >
x
type(kind_parameter), dimension(:), intent(in)—.
The local part of the vector x, single/double precision version of AMG4PSBLAS under use.
y
type(kind_parameter), dimension(:), intent(out)—.
The local part of the vector y, single/double precision version of AMG4PSBLAS under use.
desc_a
type(in).
The communication descriptor associated to the matrix to be preconditioned.
info
integer,out).
Error code. If no error, 0 is returned. See Section 7 for details.
trans
character((in).
If trans -1).
work
type(kind_parameter), dimension(:), optional, target—.
Workspace. Its size should be at least 4, single/double precision version of AMG4PSBLAS under use.
info
integer,out).
Error code. If no error, 0 is returned. See Section for details.
info
integer,out).
Error code. If no error, 0 is returned. See Section 7 for details.
iout
integer, optional.
The id of the file where the preconditioner description will be printed; the default is the standard output.
root
integer, optional.
The id of the process where the preconditioner description will be printed; the default is psb_root_.
verbosity
integer, optional.
The verbosity level of the description. Default value is 0. For a distributed multilevel preconditioner the size of the coarsematrices on every process.
info
integer,out).
Error code. If no error, 0 is returned. See Section 7 for details.
amold
class( optional.
The desired dynamic type for internal matrix components; this allows e.g. running on GPUs; it needs not be the same class="cmr-12">processes. See the PSBLAS User’s Guide for details [1718].
pout
type(out).
The copy of the preconditioner data structure. Note that x , single/double precision version of AMG4PSBLAS under use.
info
integer,out).
Error code. If no error, 0 is returned. See Section 7 for details.
global
logical, optional.
Whether the global or local preconditioner memory occupatio is false..
info
integer,out).
Error code. If no error, 0 is returned. See Section 7 for details.
vmold
class( optional.
The desired dynamic type for internal vector components; this allows e.g. running on GPUs.
info
integer,out).
Error code. If no error, 0 is returned. See Section 7 for details.
The part of the code dealing with reading and assembling the sparse matrix and the right-hand side vector and the deallocation of the relevant data structured, performed +class="cmr-12">right-hand side vector and the deallocation of the relevant data structures, performed through the PSBLAS routines for sparse matrix and vector management, is not the use of the PSBLAS routines, see the PSBLAS User’s Guide class="cmr-12"> [1718].
2 shows how to set a V-cycle preconditioner which applies 1 block-Jacobi sweep as pre- and +class="cmr-12">how to set a V-cycle preconditioner which applies 1 block-Jacobi sweep as pre- post-smoother, and solves the coarsest-level system with 8 block-Jacobi sweeps. Note +class="cmr-12">and post-smoother, and solves the coarsest-level system with 8 block-Jacobi that the ILU(0) factorization (plus triangular solve) is used as local solver for the +class="cmr-12">sweeps. Note that the ILU(0) factorization (plus triangular solve) is used as block-Jacobi sweeps, since this is the default associated with block-Jacobi +class="cmr-12">local solver for the block-Jacobi sweeps, since this is the default associated and set bywith block-Jacobi and set by P%init. Furthermore, specifying block-Jacobi as coarsest-level +class="cmr-12">. Furthermore, specifying block-Jacobi as solver implies that the coarsest-level matrix is distributed among the processes. +class="cmr-12">coarsest-level solver implies that the coarsest-level matrix is distributed among Figurethe processes. Figure 3 shows how to set a W-cycle preconditioner using the Coarsening +class="cmr-12">shows how to set a W-cycle preconditioner using the based on Compatible Weighted Matching. It applies 2 hybrid Gauss-Seidel +class="cmr-12">Coarsening based on Compatible Weighted Matching, aggregates of size at sweeps as pre- and post-smoother, and solves the coarsest-level system with the +class="cmr-12">most 8 and smoothed prolongators. It applies 2 hybrid Gauss-Seidel sweeps as multifrontal LU factorization implemented in MUMPS. It is specified that the +class="cmr-12">pre- and post-smoother, and solves the coarsest-level system with the parallel coarsest-level matrix is distributed, since MUMPS can be used on both replicated and +class="cmr-12">flexible Conjugate Gradient method (KRM) coupled with the block-Jacobi distributed matrices, and by default it is used on replicated ones. The code +class="cmr-12">preconditioner having ILU(0) on the blocks. Default parameters are used for stopping fragments shown in Figurescriterion of the coarsest solver. Note that, also in this case, specifying KRM as +coarsest-level solver implies that the coarsest-level matrix is distributed among the +processes. +
The code fragments shown in Figures 2 and 3 are included in the example program file -amg_dexample_ml.f90 too. DA CORREGGERE NEL CODICE ESEMPIO +class="cmr-12">are included in the example program 3 -
file amg_dexample_ml.f90 too. +
Finally, Figure nonsymmetric. The corresponding example program is available in t
amg_dexample_1lev.f90.
- For all the previous preconditioners, example programs where the sparse matrix
and the right-hand side are generated by discretizing a PDE with Dirichlet
@@ -276,7 +280,7 @@ class="cmr-12">.
+
+
contxt type(in). The communication context. ptype character(in) . The type of preconditioner. Its values are specified in Table 1. Note that strings are case insensitive. info integer,out). Error code. If no error, 0 is returned. See Section 7 for details. what character(len=*). The parameter to be set. It can be specified through its name; the
8. val integer or in). The value of the parameter to be set. The list of allowed values and
len=*), it is also treated as case insensitive. info integer,out). Error code. If no error, 0 is returned. See Section 7 for details. ilev integer,in). For the multilevel preconditioner, the level at which the
8). ilmax integer,in). For the multilevel preconditioner, when both ilev The levels are numbered in increasing order starting from the fin
one, i.e., level 1 is the finest level. pos character(in). Whether the other arguments apply only to the pre-smoother
not concern the smoothers,
class="cmtt-12">pos is ignored. idx integer,in). An auxiliary input argument that can be passed to the underlying
what val dfault cnts ’ML_CYCLE ’VCYCLE’
’ADD’ ’VCYCLE’ Multilevel cycle: V-cycle, W-cycle, K-cycle,
and additive composition. ’CYCLE_SWEEPS’ integer Any integer
number ≥ 1 1 1 Number of multilevel cycles. what val dfault cnts ’MIN_COARSE_SIZE_PER_PROCESS’ integer Any number
> 0 200 200 Coarse size threshold per process. The
aggregation stops if the global number of
variables of the computed coarsest matrix
@@ -723,17 +723,17 @@ multiplied by the number of processes
(see Note). ’MIN_COARSE_SIZE’ integer Any number
> 0 -1 -1 Coarse size threshold. The aggregation
stops if the global number of variables
of the computed coarsest matrix is lower
@@ -746,17 +746,17 @@ class="cmtt-10x-x-109">MIN_COARSE_SIZE_PER_PROCESS’. ’MIN_CR_RATIO’ real Any number
> 1 1.5 1.5 Minimum coarsening
ratio. The aggregation stops if the ratio
between the global matrix dimensions at
@@ -764,23 +764,23 @@ two consecutive levels is lower than or
equal to this threshold (see Note). ’MAX_LEVS’ integer Any integer
number > 1 20 20 Maximum number of levels. The
aggregation stops if the number of levels
reaches this value (see Note). ’PAR_AGGR_ALG ’DEC’,
’SYMDEC’,
’COUPLED’ ’DEC’ Parallel aggregation algorithm.
the SYMDEC option applies decoupled
@@ -808,7 +808,7 @@ class="cmmi-10x-x-109">AT . ’AGGR_TYPE ’SOC1’ ’SOC1’,
’’,
’MATCHBOXP’ ’SOC1’ Type of aggregation algorithm: currently,
for the
decoupled aggregation we implement two
measures of strength of connection, the
one by Vaněk, Mandel and Brezina [30],
+href="userhtmlli5.html#XVANEK_MANDEL_BREZINA">31],
and the one by Gratton et al [20]. The
+href="userhtmlli5.html#XGrHeJi:16">21]. The
coupled aggregation is based on a parallel
version of the half-approximate matching
implemented in the MatchBox-P software
@@ -849,13 +849,13 @@ package [8]. ’AGGR_SIZE’ integer Any integer
power of 2,
with
@@ -863,8 +863,8 @@ with
class="cmtt-10x-x-109">aggr_size ≥
-2 4 4 Maximum size of aggregates when the
coupled aggregation based on matching
is applied. For aggressive coarsening
@@ -876,7 +876,7 @@ and ’MATCHBOXP’ ’AGGR_PROL ’SMOOTHED’,
’UNSMOOTHED’ ’SMOOTHED’ Prolongator used by the aggregation
algorithm: smoothed or unsmoothed (i.e.,
tentative prolongator). what val dfault cnts ’AGGR_ORD ’NATURAL’
’DEGREE’ ’NATURAL’ Initial ordering of indices for
the decoupled aggregation algorithm:
either natural ordering or sorted by
@@ -1009,7 +1009,7 @@ descending degrees of the nodes in the
matrix graph. ’AGGR_THRESH Any real
number ∈
[0,1] 0.01 0.01 The threshold θ in the strength of
connection algorithm. See also the note
at the bottom of this table. ’AGGR_FILTER ’FILTER’
’NOFILTER’ ’NOFILTER’ Matrix used in computing the smoothed
prolongator: filtered or unfiltered. what val dfault cnts ’COARSE_MAT ’DIST’
’REPL’ ’REPL’ Coarsest matrix layout: distributed among the
processes or replicated on each of them. ’COARSE_SOLVE ’MUMPS’
’KRM’ See Note. See Note. Solver used at the coarsest level: sequential
LU from MUMPS, UMFPACK, or SuperLU
(plus triangular solve); distributed LU from
@@ -1208,7 +1208,7 @@ MUMPS or SuperLU_Dist (plus triangular solve);
point-Jacobi, hybrid Gauss-Seidel or block-Jacobi
and related ℓ1-versions; Krylov Method (Flexible
+class="cmr-8">1-versions; Krylov Method (flexible
Conjugate Gradient) coupled with the block-Jacobi
preconditioner with ILU(0) on the blocks. Note
that
’COARSE_SUBSOLVE ’ILU’
’AINV’ See Note. Solver for the diagonal blocks of the coarse matrix,
-in case the block Jacobi solver is chosen as
-coarsest-level solver: ILU(p), ILU(p,t), MILU(’ See Note. Solver for the diagonal blocks of the coarsest
+matrix, in case the block Jacobi solver is chosen
+as coarsest-level solver: ILU(p), ILU(p,t), MILU(p),
LU from MUMPS, SuperLU or UMFPACK
(plus triangular solve), Approximate Inverses
@@ -1303,29 +1303,29 @@ and SuperLU_Dist are available only in double
precision. what val dfault cts ’COARSE_SWEEPS’ integer Any
integer
number >
-0 10 10 Number of sweeps when JACOBI, GS or BJAC is
chosen as coarsest-level solver. ’COARSE_FILLIN’ integer Any
integer
number ≥
-0 0 0 Fill-in level p of the ILU factorizations and first
fill-in for the approximate inverses. ’COARSE_ILUTHRS Any real
number ≥
-0 0 0 Drop tolerance t in the ILU(p,t) factorization and
first drop-tolerance for the approximate inverses. what val dfault cnts ’BJAC_STOP ’FALSE’
’TRUE’ ’FALSE’ Select whether to use a stopping criterion for the
Block-Jacobi method used as a coarse solver. ’BJAC_TRACE ’FALSE’
’TRUE’ ’FALSE’ Select whether to print a trace for the calculated
residual for the Block-Jacobi method used as a
coarse solver. ’BJAC_ITRACE’ integer Any
integer >
-0 -1 -1 Number of iterations after which a trace is to be
printed. ’BJAC_RESCHECK’ integer Any
integer >
-0 -1 -1 Number of iterations after which a residual is to
be calculated. ’BJAC_STOPTOL Any real
< 1 0 0 Tolerance for the stopping criterion on the
residual. what val dfault cnts ’SMOOTHER_TYPE ’JACOBI’L1-FBGS’ ’FBGS’ Type of smoother used in the multilevel
-point-Jacobi and Additive Schwarz.
class="cmr-10">It is ignored by one-level preconditioners. ’SUB_SOLVE ’JACOBI’
’AINV’ GS and and Additive Schwarz
one-level
preconditioners The local solver to be used with the
. See
class="cmr-10">Note for details on hybrid Gauss-Seidel. ’SMOOTHER_SWEEPS’ integer Any integer
number ≥ 0 1 Number of sweeps of the smoother or
,
class="cmr-10">respectively. ’SUB_OVR’ integer Any integer
number ≥ 0 1 Number of overlap layers, for Additive
Schwarz only. what val dfault cnts ’SUB_RESTR ’HALO’
’NONE’ ’HALO’ Type of restriction operator, for Additive
classical Addditive Schwarz smoother and
class="cmr-10">its RAS variant. ’SUB_PROL ’SUM’
’NONE’ ’NONE’ Type of prolongation operator, for Additive
’ for its RAS variant. ’SUB_FILLIN’ integer Any integer
number ≥ 0 0 Fill-in level p of the incomplete LU
class="cmr-10">factorizations. ’SUB_ILUTHRS Any real
number ≥ 0 0 Drop tolerance t )
class="cmr-10">factorization. ’MUMPS_LOC_GLOB ’LOCAL_SOLVER’
’GLOBAL_SOLVER’ ’GLOBAL_SOLVER’ Whether MUMPS should be used as a
only on the part of the matrix local to each
class="cmr-10">process. ’MUMPS_IPAR_ENTRY’ integer Any integer
number 0 Set an entry in the MUMPS integer control
optional
class="cmr-10">argument. ’MUMPS_RPAR_ENTRY’ real Any real number 0 Set an entry in the MUMPS real control
optional
class="cmr-10">argument. a type(in). The sparse matrix structure containing the local part of the matrix
, single/double precision version of AMG4PSBLAS
class="cmr-12">under use. See the PSBLAS User’s Guide for details [1718]. desc_a type(in). The communication descriptor of a. See the PSBLAS User’s Guide
class="cmr-12">for details [1718]. info integer,out). Error code. If no error, 0 is returned. See Section 7 for details.
! build a V-cycle preconditioner with 1 block-Jacobi sweep (with
@@ -298,7 +302,7 @@ class="cmr-12">.
call P%smoothers_build(A,desc_A,info)
... ...
! set RAS with overlap 2 and ILU(0) on the local blocks
@@ -365,7 +370,7 @@ on weighted matching
! solve Ax=b with preconditioned BiCGSTAB
call psb_krylov(’BICGSTAB’,A,P,b,x,tol,desc_A,info)
contxt ptype info what info ilev ilmax pos idx a type e val t character=*) ’ ’ integer ≥ 1
a type e val t integer > 0 integer > 0 real > 1 integer > 1 character=*) ’COUPLED’ ’DEC’ character=*) ’ integer character=*) ’ ’ a type e val t character=*) ’DEGREE’ ’NATURAL’ real) ,1] character=*) ’NOFILTER’ ’NOFILTER’
a type e val t character=*) ’ ’ character=*) ’ character=*) a type e val t integer integer real)
a type e val t character=*) ’ ’ character=*) ’ ’ integer integer real) < 1
a type e val t character=*) ’ ’ character=*) ’ preconditioners integer 0 1 integer 0 1
a type e val t character=*) ’ ’ character=*) ’ ’ integer 0 0 real) 0 0 character=*) ’ ’ integer number 0 real Any real number 0
a desc_a info