[2][3] S. Filippone, Sparse approximate inverse preconditioners on high performance GPU platforms, Comput. Math. Appl. +class="cmr-12">, Comput. Math. Appl., 71 (2016), no.71, (2016), no. 3, 693–711.
[3][4] , Computing, 63, 1999, 233–263.
[4][5] , SIAM, 2000.
[5][6] Extending class="cmti-12">PSBLAS to Build Parallel Schwarz Preconditioners, in J. Dongarra, + + + K. Madsen, J.State of the Art in Scientific Computing, Lecture Notes in Comput Springer, 2005, 593–602.
- - -[6][7] Computing, 18 (3) 2007, 223–239.
[7][8] (2), 1999, 792–797.
[8][9] Pothen, Distributed-memory parallel algorithms for matching and coloring, in PCO11 New Trends in Parallel Computing and Optimization, +class="cmr-12">, in PCO’11 New Trends in Parallel Computing and Optimization, IEEE International Symposium on Parallel and Distributed Processing Workshops, IEEE CS, 2011.
- [9][10] 57 (11-12), 2007, 1181-1196.
[10][11] , ACM Trans. Math. Softw., 37(3), 2010, art. 30.
[11][12] on compatible weighted matching, Computing and Visualization in Science, 16, (2013) 59–76. + + +
[12][13] package for bootstrap AMG based on graph weighted matchi class="cmr-12">, ACM Transactions on Mathematical Software, 44, (2018) 39:1–39:25. - - -
[13][14] .
[14][15] )
[15][16] SIAM Journal on Matrix Analysis and Applications, 20 (3), 1999, 7
[16][17] Software, 16 (1) 1990, 1–17.
[17][18] Transactions on Mathematical Software, 14 (1) 1988, 1–17.
[18][19] S. Filippone, P. D’Ambra, M. Colajanni, Using a Parallel Library of
+ Sparse Linear Algebra in a Fluid Dynamics Application Code on Linux
+ Clusters, in Proc. of ParCo 2001, Parallel Computing, Advances and Current
+ Issues, 2002.
+
+
+
+
+ [20] .
[19][21] . ACM Transactions on on Mathematical Software, 38 (4), 2012, art. 23. - - -
[20][22] Transactions on Mathematical Software, 26 (4), 2000, 527–55
[21][23] 2016, 23:501-518
[22][24] , MIT Press, 1998.
[23][25] Mathematical Software, 5 (3), 1979, 308–323.
[24][26] Distributed-memory Sparse Direct Solver for Unsymmetric Linear S class="cmr-12">, ACM Transactions on Mathematical Software, 29 (2), 2003, 110–140. + + +
[25][27] Numerical Linear Algebra with Applications, 15 (5), 2008, 473R
[26][28] , 2nd edition, SIAM, 2003.
- - -[27][29] University Press, 1996.
[28][30] Press, 1998.
[29][31] Oosterlee, Multigrid, Academic Press, 2001.
[30][32] editor, Proceedings of SuperComputing 2000, Dallas, 2000.
[31][33] ) provides parallel Algebraic MultiGrid (AMG) preconditioners (se class="cmr-12">e.g., [45, 2931]), 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 [1820]. 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 [1820].
desc_a
type(in).
The communication descriptor of a. See the PSBLAS User’s Guide class="cmr-12">for details [1820].
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 [1820].
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 [1820].
desc_a
type(in).
The communication descriptor of a. See the PSBLAS User’s Guide class="cmr-12">for details [1820].
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 [1820].
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 4a36f3b8..8f1f65bf 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 [1820].
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.
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’,
’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 [31],
+href="userhtmlli5.html#XVANEK_MANDEL_BREZINA">33],
and the one by Gratton et al [21]. The
+href="userhtmlli5.html#XGrHeJi:16">23]. The
coupled aggregation is based on a parallel
version of the half-approximate matching
implemented in the MatchBox-P software
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
@@ -1230,7 +1230,7 @@ UMFPACK and SuperLU_Dist are available only in
double precision. ’COARSE_SUBSOLVE ’ILU’
’AINV’ See Note. See Note. Solver for the diagonal blocks of the coarsest
matrix, in case the block Jacobi solver is chosen
as coarsest-level solver: ILU(t); note
that approximate inverses are specifically suited
for GPUs since they do not employ triangular
system solve kernels, see [2]. Note that UMFPACK
+href="userhtmlli5.html#XBERTACCINIFILIPPONE">3]. Note that UMFPACK
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. ’KRM_METHOD ’CG’
’RGMRES’ ’FCG’ A string that defines the iterative method to
be used. CG the Conjugate Gradient method;
@@ -1671,11 +1671,11 @@ with restarting; RGMRES the Generalized
Minimal Residual method with restarting.
Refer to the PSBLAS guide [18] for further
+href="userhtmlli5.html#XPSBLASGUIDE">20] for further
information. ’KRM_KPREC Table 1 ’BJAC’ The one-level
preconditioners from the Table 1 can be used
for the coarse Krylov solver. ’KRM_SUB_SOLVE Table 5 ’ILU’ Solver for the diagonal blocks of the coarsest
matrix preconditioner, in case the block Jacobi
solver is chosen
@@ -1739,7 +1739,7 @@ The same caveat from Table 5 applies here. ’KRM_GLOBAL ’TRUE’,
’FALSE’ ’FALSE’ Choose between a global Krylov solver, all
unknowns on a single node, or a distributed
one. The default choice is the distributed
solver. ’KRM_EPS Real < 1 10-6 The stopping tolerance. ’KRM_IRST’ integer Integer
≥ 1 30 30 An integer specifying the restart parameter.
This is employed for the BiCGSTABL or RGMRES
methods, otherwise it is ignored. ’KRM_ISTOPC’ integer Integers
-1,2,3 2 2 If 1 then the method uses the normwise
backward error in the infinity norm; if 3
the relative residual reduction in the 2-norm is
used instead; refer to the PSBLAS [18] guide
+href="userhtmlli5.html#XPSBLASGUIDE">20] guide
for the details. ’KRM_ITMAX’ integer Integer
≥ 1 40 40 The maximum number of iterations to
perform. ’KRM_ITRACE’ integer Integer
≥ 0 -1 -1 If > 0 print out
an informational message about convergence
@@ -1861,23 +1861,23 @@ class="cmtt-10x-x-109">’ iterations. If = 0 print a
message in case of convergence failure. ’KRM_FILLIN’ integer Integer
≥ 0 0 0 Fill-in level p of the ILU factorizations and
first fill-in for the approximate inverses. 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
triangular system solve kernels, see [23]. See
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 [1820]. desc_a type(in). The communication descriptor of a. See the PSBLAS User’s Guide
class="cmr-12">for details [1820]. info integer,out). Error code. If no error, 0 is returned. See Section 7 for details. 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 > 0 integer > 0 real) character=*) ’ ’ character=*) 1 ’ character=*) 5 ’ character=*) ’ ’ real) < 1 6 integer ≥ 1 integer integer ≥ 1 integer ≥ 0 integer ≥ 0 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