diff --git a/docs/html/userhtmlsu10.html b/docs/html/userhtmlsu10.html index 7492978d..a3b76328 100644 --- a/docs/html/userhtmlsu10.html +++ b/docs/html/userhtmlsu10.html @@ -10,7 +10,7 @@ -

[nextMethod hierarchy_build

-

-

call p%hierarchy_build(a,desc_a,info)
+

+

call p%hierarchy_build(a,desc_a,info)

-

This method builds the hierarchy of matrices and restriction/prolongation operators for the multilevel preconditioner p, according to the requirements made by the user class="cmr-12">through the methods init and set. -

Arguments

Arguments id="TBL-12-1">

a

type(psb_

a

type(psb_xspmat_type), intent(in).

The sparse matrix structure containing the local part of the matrix to be preconditioned. Note that ].

desc_a

type(psb_desc_type), intent(in)

desc_a

type(psb_desc_type), intent(in).

The communication descriptor of a. See the PSBLAS User’s Guide ].

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section 

-

[next] [up]

-

diff --git a/docs/html/userhtmlsu11.html b/docs/html/userhtmlsu11.html index da5b3709..e4e68ec7 100644 --- a/docs/html/userhtmlsu11.html +++ b/docs/html/userhtmlsu11.html @@ -10,7 +10,7 @@ -

[nextMethod smoothers_build

-

-

call p%smoothers_build(a,desc_a,p,info[,amold,vmold,imold])
+

+

call p%smoothers_build(a,desc_a,p,info[,amold,vmold,imold])

-

This method builds the smoothers and the coarsest-level solvers for the multilevel preconditioner p 5.3). -

Arguments

Arguments id="TBL-13-1"> @@ -168,7 +168,7 @@ class="td11">

a

type(psb_

a

type(psb_xspmat_type), intent(in).

The sparse matrix structure containing the local part of the matrix to be preconditioned. Note that ].

desc_a

type(psb_desc_type), intent(in)

desc_a

type(psb_desc_type), intent(in).

The communication descriptor of a. See the PSBLAS User’s Guide ].

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section 7 for details.

amold

class(psb_

amold

class(psb_x_base_sparse_mat), intent(in), optional.

The desired dynamic type for internal matrix components; this allows e.g. running on GPUs; it needs not be the same on all @@ -136,26 +136,26 @@ class="cmr-12">].

vmold

class(psb_

vmold

class(psb_x_base_vect_type), intent(in), optional.

The desired dynamic type for internal vector components; this allows e.g. running on GPUs.

imold

class(psb_i_base_vect_type), intent(in), optional

imold

class(psb_i_base_vect_type), intent(in), optional.

The desired dynamic type for internal integer vector components; this allows e.g. running on GPUs.

-

[next] [up]

-

diff --git a/docs/html/userhtmlsu12.html b/docs/html/userhtmlsu12.html index 33e34492..f6c1e8a6 100644 --- a/docs/html/userhtmlsu12.html +++ b/docs/html/userhtmlsu12.html @@ -10,7 +10,7 @@ -

[next5.5 Method build

-

-

call p%build(a,desc_a,info[,amold,vmold,imold])
+

+

call p%build(a,desc_a,info[,amold,vmold,imold])

-

This method builds the preconditioner p according to the requirements made by the and class="cmr-12">, whose nomenclature would however be somewhat unnatural when dealing with simple one-level preconditioners. -

Arguments

Arguments id="TBL-14-1">

a

type(psb_

a

type(psb_xspmat_type), intent(in).

The sparse matrix structure containing the local part of the matrix to be preconditioned. Note that ].

desc_a

type(psb_desc_type), intent(in)

desc_a

type(psb_desc_type), intent(in).

The communication descriptor of a. See the PSBLAS User’s Guide ].

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section 7 for details.

amold

class(psb_

amold

class(psb_x_base_sparse_mat), intent(in), optional.

The desired dynamic type for internal matrix components; this allows e.g. running on GPUs; it needs not be the same on all @@ -145,33 +145,33 @@ class="cmr-12">].

vmold

class(psb_

vmold

class(psb_x_base_vect_type), intent(in), optional.

The desired dynamic type for internal vector components; this allows e.g. running on GPUs.

imold

class(psb_i_base_vect_type), intent(in), optional

imold

class(psb_i_base_vect_type), intent(in), 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. @@ -179,7 +179,7 @@ class="cmr-12">The method can be used to build multilevel preconditioners too.

[next] [up]

-

diff --git a/docs/html/userhtmlsu13.html b/docs/html/userhtmlsu13.html index 57ba9619..5610cce9 100644 --- a/docs/html/userhtmlsu13.html +++ b/docs/html/userhtmlsu13.html @@ -10,7 +10,7 @@ -

[next5.6 Method apply

-

-

call p%apply(x,y,desc_a,info [,trans,work])
+

+

call p%apply(x,y,desc_a,info [,trans,work])

-

This method computes y = is called within the PSBLAS method and hence it is completely transparent to the user. -

Arguments

Arguments id="TBL-15-1"> +class="td11">

trans

x

x

type(kind_parameter), dimension(:), intent(in)—.

The local part of the vector x. Note that , single/double class="cmr-12">precision version of AMG4PSBLAS under use.

y

y

type(kind_parameter), dimension(:), intent(out)—.

The local part of the vector y. Note that , single/double class="cmr-12">precision version of AMG4PSBLAS under use.

desc_a

type(psb_desc_type), intent(in)

desc_a

type(psb_desc_type), intent(in).

The communication descriptor associated to the matrix to be preconditioned.

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section 7 for details.

trans

character(len=1), optional, intent(in).

character(len=1), optional, intent(in).

If trans = ’N’,’n’ then 1).

work

work

type(kind_parameter), dimension(:), optional, target—.

Workspace. Its size should be at least 4 * psb_cd_get_local_ cols(desc_a) (see the PSBLAS User’s Guide). Note that

-

[next] [up]

-

diff --git a/docs/html/userhtmlsu14.html b/docs/html/userhtmlsu14.html index 2a3663dc..72622d87 100644 --- a/docs/html/userhtmlsu14.html +++ b/docs/html/userhtmlsu14.html @@ -10,7 +10,7 @@ -

[next5.7 Method free

-

-

call p%free(p,info)
+

+

call p%free(p,info)

-

This method deallocates the preconditioner data structure p. -

Arguments

Arguments id="TBL-16-1">

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section 

-

[next] [up]

-

diff --git a/docs/html/userhtmlsu15.html b/docs/html/userhtmlsu15.html index 1cab8c5f..96a6d2d1 100644 --- a/docs/html/userhtmlsu15.html +++ b/docs/html/userhtmlsu15.html @@ -10,7 +10,7 @@ -

[next5.8 Method descr

-

-

call p%descr(info, [iout, root, verbosity])
+

+

call p%descr(info, [iout, root, verbosity])

-

This method prints a description of the preconditioner p to the standard output or to a , or b class="cmr-12">, have been called. -

Arguments

Arguments id="TBL-17-1">

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section 7 for details.

iout

integer, intent(in), optional

iout

integer, intent(in), optional.

The id of the file where the preconditioner description will be printed; the default is the standard output.

root

integer, intent(in), optional

root

integer, intent(in), optional.

The id of the process where the preconditioner description will be printed; the default is psb_root_.

verbosity

integer, intent(in), optional

verbosity

integer, intent(in), optional.

The verbosity level of the description. Default value is 0. For values higher than 0, it prints out further information, e.g., for @@ -113,7 +113,7 @@ class="td11">

-

[next] [up]

-

diff --git a/docs/html/userhtmlsu16.html b/docs/html/userhtmlsu16.html index 1caabad5..945f8d98 100644 --- a/docs/html/userhtmlsu16.html +++ b/docs/html/userhtmlsu16.html @@ -10,7 +10,7 @@ -

[prev]

class="cmr-12">5.9 Auxiliary Methods -

Various functionalities are implemented as additional methods of the preconditioner object. -

+

5.9.1 Method: dump
-

-

call p%dump(info[,istart,iend,prefix,head,ac,rp,smoother,solver,global_num])
+

+

call p%dump(info[,istart,iend,prefix,head,ac,rp,smoother,solver,global_num])

-

Dump on file. -

Arguments

Arguments id="TBL-18-1">

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section 7 for details.

amold

class(psb_

amold

class(psb_x_base_sparse_mat), intent(in), optional.

The desired dynamic type for internal matrix components; this allows e.g. running on GPUs; it needs not be the same on all @@ -87,22 +87,22 @@ class="cmr-12">.

-

+

5.9.2 Method: clone
-

-

call p%clone(pout,info)
+

+

call p%clone(pout,info)

-

Create a (deep) copy of the preconditioner object. -

Arguments

Arguments id="TBL-19-1">

pout

type(amg_

pout

type(amg_xprec_type), intent(out).

The copy of the preconditioner data structure. Note that x must @@ -129,13 +129,13 @@ class="cmr-12">, single/double precision class="cmr-12">version of AMG4PSBLAS under use.

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section for details.

-

+

5.9.3 Method: sizeof
-

-

sz = p%sizeof([global])
+

+

sz = p%sizeof([global])

Method: sizeof id="TBL-20-1">

global

logical, optional

global

logical, optional.

Whether the global or local preconditioner memory occupation is desired. Default: .false..

Return memory footprint in bytes. -

+

5.9.4 Method: allocate_wrk
-

-

call p%allocate_wrk(info[, vmold])
+

+

call p%allocate_wrk(info[, vmold])

-

Allocate internal work vectors. Each application of the preconditioner uses a number of work vectors which are allocated internally as necessary; therefore allocation and @@ -216,7 +216,7 @@ class="cmr-12">taken care of based on the dynamic type of the argument to the apply method. -

Arguments

Arguments id="TBL-21-1">

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section 7 for details.

vmold

class(psb_

vmold

class(psb_x_base_vect_type), intent(in), optional.

The desired dynamic type for internal vector components; this allows e.g. running on GPUs.

-

+

5.9.5 Method: free_wrk
-

-

call p%free_wrk(info)
+

+

call p%free_wrk(info)

-

Deallocate internal work vectors. -

Arguments

Arguments id="TBL-22-1">

info

integer, intent(out)

info

integer, intent(out).

Error code. If no error, 0 is returned. See Section  7-89. For example, the block-Jacobi smoother using ILU(0) on the blocks is obtained by combining the block-Jacobi smoother object with the ILU(0) solver @@ -319,6 +319,47 @@ class="cmr-12">). class="newline" />

Remark 3. The polynomial-accelerated smoother described in Tables 7 and 9 +redefines a sweep or iteration as corresponding to the degree of the polynomial used. +Consequently, the ’SMOOTHER_SWEEPS’ option is overridden by the ’POLY_DEGREE’ +option. This smoother is paired with a base smoother object, whose iterations are +accelerated using the specified polynomial smoothing technique. By default, the + + + +ℓ1-Jacobi smoother serves as the base smoother, offering theoretical guarantees on the +resulting convergence factor [15, 27]. Alternative combinations are experimental and +lack established guarantees.
+

Remark 4. Many of the coarsest-level solvers apply to a specific coarsest-matrix layout; therefore, setting the solver after the layout may change the layout to either @@ -326,10 +367,7 @@ class="cmr-12">layout; therefore, setting the solver after the layout may change class="cmr-12">distributed or replicated. Similarly, setting the layout after the solver may change the solver. - - - -

More precisely, UMFPACK and SuperLU require the coarsest-level matrix to be replicated, while SuperLUsingle Gauss-Seidel sweep, respectively, which are very poor solvers. -

On the other hand, the distributed layout can be used with any solver but UMFPACK and SuperLU; therefore, if any of these two solvers has already been @@ -376,13 +414,13 @@ class="cmr-12">_Dist or KRM have been class="cmr-12">previously set, the coarsest-level solver is changed to the default sequential solver. -

In a parallel setting with many cores, we suggest to the users to change the default coarsest solver for using the KRM choice, i.e. a parallel distributed iterative solution of the coarsest system based on Krylov methods. -

Remark 4. The argument idx can be used to allow finer control for those solvers; @@ -402,7 +440,7 @@ class="cmr-12">. -

@@ -410,7 +448,7 @@ class="cmr-12">.
-

+

-

@@ -508,7 +546,7 @@ applied.
-

+

@@ -522,7 +560,7 @@ id="TBL-5-4">

@@ -756,7 +794,7 @@ class="content">Parameters defining the aggregation algorithm.

@@ -764,7 +802,7 @@ class="content">Parameters defining the aggregation algorithm.

+

what

what

dtype

val

val

deault

cots

’ML_CYCLE’ +class="td11">

’ML_CYCLE’

character(len=*) +class="td11">

character(len=*)

’VCYCLE’ -

’WCYCLE’ -

’KCYCLE’ -

’ADD’ +class="td11">

’VCYCLE’ +

’WCYCLE’ +

’KCYCLE’ +

’ADD’

’VCYCLE’ +class="td11">

’VCYCLE’

Multilevel cycle: V-cycle, W-cycle, K-cycle, +class="td11">

Multilevel cycle: V-cycle, W-cycle, K-cycle, and additive composition.

’CYCLE_SWEEPS’ +class="td11">

’CYCLE_SWEEPS’

integer +class="td11">

integer

Any integer -

number

Any integer +

number ≥ 1

1 +class="td11">

1

Number of multilevel cycles. +class="td11">

Number of multilevel cycles.

what

what

dtype

val

val

deault

cots

’MIN_COARSE_SIZE_PER_PROCESS’ +class="td11">

’MIN_COARSE_SIZE_PER_PROCESS’

integer +class="td11">

integer

Any number -

Any number +

> 0

200 +class="td11">

200

Coarse size threshold per process. The +class="td11">

Coarse size threshold per process. The aggregation stops if the global number of variables of the computed coarsest matrix is lower than or equal to this threshold @@ -575,17 +613,17 @@ class="td11">

Coarse size threshold per pr

’MIN_COARSE_SIZE’ +class="td11">

’MIN_COARSE_SIZE’

integer +class="td11">

integer

Any number -

Any number +

> 0

-1 +class="td11">

-1

Coarse size threshold. The aggregation +class="td11">

Coarse size threshold. The aggregation stops if the global number of variables of the computed coarsest matrix is lower than or equal @@ -596,17 +634,17 @@ class="td11">

Coarse size threshold. The a

’MIN_CR_RATIO’ +class="td11">

’MIN_CR_RATIO’

real +class="td11">

real

Any number -

Any number +

> 1

1.5 +class="td11">

1.5

Minimum coarsening +class="td11">

Minimum coarsening ratio. The aggregation stops if the ratio between the global matrix dimensions at two consecutive levels is lower than or @@ -615,39 +653,39 @@ class="td11">

Minimum

’MAX_LEVS’ +class="td11">

’MAX_LEVS’

integer +class="td11">

integer

Any integer -

number

Any integer +

number > 1

20 +class="td11">

20

Maximum number of levels. The +class="td11">

Maximum number of levels. The aggregation stops if the number of levels reaches this value (see Note).

’PAR_AGGR_ALG’ +class="td11">

’PAR_AGGR_ALG’

character(len=*) +class="td11">

character(len=*)

’DEC’, ’SYMDEC’, ’COUPLED’

’DEC’

Parallel aggregation algorithm. -

the SYMDEC option applies decoupled +class="td11">

Parallel aggregation algorithm. +

the SYMDEC option applies decoupled aggregation to the sparsity pattern of A + T .

’AGGR_TYPE’ +class="td11">

’AGGR_TYPE’

character(len=*) +class="td11">

character(len=*)

’SOC1’, +class="td11">

’SOC1’, ’SOC2’, ’MATCHBOXP’

’SOC1’ +class="td11">

’SOC1’

Type of aggregation algorithm: currently, +class="td11">

Type of aggregation algorithm: currently, for the decoupled aggregation we implement two measures of strength of connection, the @@ -684,12 +722,12 @@ href="userhtmlli5.html#XMatchBoxP">9].

’AGGR_SIZE’ +class="td11">

’AGGR_SIZE’

integer +class="td11">

integer

Any integer -

power of 2, +class="td11">

Any integer +

power of 2, with aggr_size ≥ 2

4 +class="td11">

4

Maximum size of aggregates when the +class="td11">

Maximum size of aggregates when the coupled aggregation based on matching is applied. For aggressive coarsening with size of aggregate larger than 8 @@ -712,16 +750,16 @@ class="cmtt-10x-x-109">’MATCHBOXP’

’AGGR_PROL’ +class="td11">

’AGGR_PROL’

character(len=*) +class="td11">

character(len=*)

’SMOOTHED’, +class="td11">

’SMOOTHED’, ’UNSMOOTHED’

’SMOOTHED’ +class="td11">

’SMOOTHED’

Prolongator used by the aggregation +class="td11">

Prolongator used by the aggregation algorithm: smoothed or unsmoothed (i.e., tentative prolongator).

Parameters defining the aggregation algorithm (continued).

@@ -899,7 +937,7 @@ class="content">Parameters defining the aggregation algorithm (continued). -

+

@@ -913,7 +951,7 @@ id="TBL-7-4">

+class="td11">

The stopping tolerance.

@@ -1561,7 +1599,7 @@ class="content">Additional parameters defining the solver at the coarsest level. -

@@ -1569,7 +1607,7 @@ class="content">Additional parameters defining the solver at the coarsest level.
-

+

what

what

dtype

val

val

deault

cots

’AGGR_ORD’ +class="td11">

’AGGR_ORD’

character(len=*) +class="td11">

character(len=*)

’NATURAL’ -

’DEGREE’

’NATURAL’

Initial ordering of indices for +class="td11">

Initial ordering of indices for the decoupled aggregation algorithm: either natural ordering or sorted by descending degrees of the nodes in the @@ -829,19 +867,19 @@ class="td11">

Initial ordering of ind

’AGGR_THRESH’ +class="td11">

’AGGR_THRESH’

real(kind_parameter) +class="td11">

real(kind_parameter)

Any real -

number 

Any real +

number ∈ [0,1]

0.01 +class="td11">

0.01

The threshold

The threshold θ in the strength of connection algorithm. See also the note at the bottom of this table. @@ -849,19 +887,19 @@ class="cmmi-10x-x-109">θ in the strength of

’AGGR_FILTER’ +class="td11">

’AGGR_FILTER’

character(len=*) +class="td11">

character(len=*)

’FILTER’ -

’NOFILTER’

’NOFILTER’

Matrix used in computing the smoothed +class="td11">

Matrix used in computing the smoothed prolongator: filtered or unfiltered.

what

what

dtype

val

val

deault

cots

’COARSE_MAT’ +class="td11">

’COARSE_MAT’

character(len=*) +class="td11">

character(len=*)

’DIST’ -

’REPL’ +class="td11">

’DIST’ +

’REPL’

’REPL’ +class="td11">

’REPL’

Coarsest matrix layout: distributed among the +class="td11">

Coarsest matrix layout: distributed among the processes or replicated on each of them.

’COARSE_SOLVE’ +class="td11">

’COARSE_SOLVE’

character(len=*) +class="td11">

character(len=*)

’MUMPS’ -

’UMF’ -

’SLU’ -

’SLUDIST’ -

’ILU’ -

’JACOBI’ -

’GS’ -

’BJAC’ -

’KRM’ -

’L1-JACOBI’ -

’L1-BJAC’ -

’L1-FBGS’ +class="td11">

’MUMPS’ +

’UMF’ +

’SLU’ +

’SLUDIST’ +

’ILU’ +

’JACOBI’ +

’GS’ +

’BJAC’ +

’KRM’ +

’L1-JACOBI’ +

’L1-BJAC’ +

’L1-FBGS’

See Note. +class="td11">

See Note.

Solver used at the coarsest level: sequential +class="td11">

Solver used at the coarsest level: sequential LU from MUMPS, UMFPACK, or SuperLU (plus triangular solve); distributed LU from MUMPS or SuperLU_Dist (plus triangular solve); @@ -1004,30 +1042,30 @@ class="cmtt-10x-x-109">MUMPS can be used with either a replicated or a distributed matrix. When any of the previous solvers is specified, the matrix layout is set to a default value which allows the use - of the solver (see Remark 3, p. 24). Note also that + of the solver (see Remark 4, p. 21). Note also that UMFPACK and SuperLU_Dist are available only in double precision.

’COARSE_SUBSOLVE’ +class="td11">

’COARSE_SUBSOLVE’

character(len=*) +class="td11">

character(len=*)

’ILU’ -

’ILUT’ -

’MILU’ -

’MUMPS’ -

’SLU’ -

’UMF’ -

’INVT’ -

’INVK’ -

’AINV’ +class="td11">

’ILU’ +

’ILUT’ +

’MILU’ +

’MUMPS’ +

’SLU’ +

’UMF’ +

’INVT’ +

’INVK’ +

’AINV’

See Note. +class="td11">

See Note.

Solver for the diagonal blocks of the coarsest +class="td11">

Solver for the diagonal blocks of the coarsest matrix, in case the block Jacobi solver is chosen as coarsest-level solver: ILU(p), ILU(ILU otherwise.

what

what

dtype

val

val

deault

cos

’COARSE_SWEEPS’ +class="td11">

’COARSE_SWEEPS’

integer +class="td11">

integer

Any +class="td11">

Any integer -

number

number > 0

10 +class="td11">

10

Number of sweeps when JACOBI, GS or BJAC is +class="td11">

Number of sweeps when JACOBI, GS or BJAC is chosen as coarsest-level solver.

’COARSE_FILLIN’ +class="td11">

’COARSE_FILLIN’

integer +class="td11">

integer

Any +class="td11">

Any integer -

number

number ≥ 0

0 +class="td11">

0

Fill-in level

Fill-in level p of the ILU factorizations and first fill-in for the approximate inverses.

’COARSE_ILUTHRS’ +class="td11">

’COARSE_ILUTHRS’

real(kind_parameter) +class="td11">

real(kind_parameter)

Any real -

number

Any real +

number ≥ 0

0 +class="td11">

0

Drop tolerance

Drop tolerance t in the ILU(p,t) factorization and first drop-tolerance for the approximate inverses. @@ -1192,7 +1230,7 @@ class="content">Parameters defining the solver at the coarsest level (continued) -

@@ -1200,7 +1238,7 @@ class="content">Parameters defining the solver at the coarsest level (continued)
-

+

@@ -1214,7 +1252,7 @@ id="TBL-8-4">

what

what

dtype

val

val

deault

cots

’BJAC_STOP’ +class="td11">

’BJAC_STOP’

character(len=*) +class="td11">

character(len=*)

’FALSE’ -

’TRUE’ +class="td11">

’FALSE’ +

’TRUE’

’FALSE’ +class="td11">

’FALSE’

Select whether to use a stopping criterion for +class="td11">

Select whether to use a stopping criterion for the Block-Jacobi method used as a coarse solver.

’BJAC_TRACE’ +class="td11">

’BJAC_TRACE’

character(len=*) +class="td11">

character(len=*)

’FALSE’ -

’TRUE’ +class="td11">

’FALSE’ +

’TRUE’

’FALSE’ +class="td11">

’FALSE’

Select whether to print a trace for the +class="td11">

Select whether to print a trace for the calculated residual for the Block-Jacobi method used as a coarse solver.

’BJAC_ITRACE’ +class="td11">

’BJAC_ITRACE’

integer +class="td11">

integer

Any integer -

Any integer +

> 0

-1 +class="td11">

-1

Number of iterations after which a trace is to +class="td11">

Number of iterations after which a trace is to be printed.

’BJAC_RESCHECK’ +class="td11">

’BJAC_RESCHECK’

integer +class="td11">

integer

Any integer -

Any integer +

> 0

-1 +class="td11">

-1

Number of iterations after which a residual is +class="td11">

Number of iterations after which a residual is to be calculated.

’BJAC_STOPTOL’ +class="td11">

’BJAC_STOPTOL’

real(kind_parameter) +class="td11">

real(kind_parameter)

Any real -

Any real +

< 1

0 +class="td11">

0

Tolerance for the stopping criterion on the +class="td11">

Tolerance for the stopping criterion on the residual.

’KRM_METHOD’ +class="td11">

’KRM_METHOD’

character(len=*) +class="td11">

character(len=*)

’CG’ -

’FCG’ -

’CGS’ -

’CGR’ -

’BICG’ -

’BICGSTAB’ -

’BICGSTABL’ -

’RGMRES’ +class="td11">

’CG’ +

’FCG’ +

’CGS’ +

’CGR’ +

’BICG’ +

’BICGSTAB’ +

’BICGSTABL’ +

’RGMRES’

’FCG’ +class="td11">

’FCG’

A string that defines the iterative method to +class="td11">

A string that defines the iterative method to be used when employing a Krylov method ’KRM’ as a coarse solver. CG the Conjugate @@ -1372,16 +1410,16 @@ href="userhtmlli5.html#XPSBLASGUIDE">21] for further

’KRM_KPREC’ +class="td11">

’KRM_KPREC’

character(len=*) +class="td11">

character(len=*)

Table 

Table 1

’BJAC’ +class="td11">

’BJAC’

The one-level +class="td11">

The one-level preconditioners from the Table 1 can be used for the coarse Krylov solver. @@ -1389,16 +1427,16 @@ href="userhtmlse4.html#x14-13015r1">1 can be

’KRM_SUB_SOLVE’ +class="td11">

’KRM_SUB_SOLVE’

character(len=*) +class="td11">

character(len=*)

Table 

Table 5

’ILU’ +class="td11">

’ILU’

Solver for the diagonal blocks of the coarsest +class="td11">

Solver for the diagonal blocks of the coarsest matrix preconditioner, in case the block Jacobi solver is chosen as ’KRM_KPREC’: ILU(5 applies here.

’KRM_GLOBAL’ +class="td11">

’KRM_GLOBAL’

character(len=*) +class="td11">

character(len=*)

’TRUE’, +class="td11">

’TRUE’, ’FALSE’

’FALSE’ +class="td11">

’FALSE’

Choose between a global Krylov solver, all +class="td11">

Choose between a global Krylov solver, all unknowns on a single node, or a distributed one. The default choice is the distributed solver. @@ -1440,28 +1478,28 @@ class="td11">

Choose between a global Kryl

’KRM_EPS’

real(kind_parameter)

Real

’KRM_EPS’

real(kind_parameter)

Real < 1

10

10-6

The stopping tolerance.

’KRM_IRST’ +class="td11">

’KRM_IRST’

integer +class="td11">

integer

Integer -

Integer +

≥ 1

30 +class="td11">

30

An integer specifying the restart parameter. +class="td11">

An integer specifying the restart parameter. This is employed for the BiCGSTABL or RGMRES @@ -1470,16 +1508,16 @@ class="cmtt-10x-x-109">RGMRES

’KRM_ISTOPC’ +class="td11">

’KRM_ISTOPC’

integer +class="td11">

integer

Integers +class="td11">

Integers 1,2,3

2 +class="td11">

2

If

If 1 then the method uses the normwise backward error in the infinity norm; if 2, the @@ -1493,33 +1531,33 @@ href="userhtmlli5.html#XPSBLASGUIDE">21] guide

’KRM_ITMAX’ +class="td11">

’KRM_ITMAX’

integer +class="td11">

integer

Integer -

Integer +

≥ 1

40 +class="td11">

40

The maximum number of iterations to +class="td11">

The maximum number of iterations to perform.

’KRM_ITRACE’ +class="td11">

’KRM_ITRACE’

integer +class="td11">

integer

Integer -

Integer +

≥ 0

-1 +class="td11">

-1

If

If > 0 print out an informational message about convergence every ’KRM_ITRACE’ iterations. If = 0 print a @@ -1528,17 +1566,17 @@ class="cmmi-10x-x-109">> 0 print out

’KRM_FILLIN’ +class="td11">

’KRM_FILLIN’

integer +class="td11">

integer

Integer -

Integer +

≥ 0

0 +class="td11">

0

Fill-in level

Fill-in level p of the ILU factorizations and first fill-in for the approximate inverses.

what

what

dtype

val

val

deault

cots

’SMOOTHER_TYPE’ +class="td11">

’SMOOTHER_TYPE’

character(len=*) +class="td11">

character(len=*)

’JACOBI’ -

’GS’ -

’BGS’ -

’BJAC’ -

’AS’ -

’L1-JACOBI’ -

’L1-BJAC’ -

’L1-FBGS’ -

’POLY’ +class="td11">

’JACOBI’ +

’GS’ +

’BGS’ +

’BJAC’ +

’AS’ +

’L1-JACOBI’ +

’L1-BJAC’ +

’L1-FBGS’ +

’POLY’

’FBGS’ +class="td11">

’FBGS’

Type of smoother used in the multilevel preconditioner: point-Jacobi, hybrid @@ -1656,30 +1694,34 @@ class="cmr-10">[15] -

and Remark 3 (p. 21). +

It is ignored by one-level preconditioners.

’SUB_SOLVE’ +class="td11">

’SUB_SOLVE’

character(len=*) +class="td11">

character(len=*)

’JACOBI’ +class="td11">

’JACOBI’ ’GS’ -

’BGS’ -

’ILU’ -

’ILUT’ -

’MILU’ -

’MUMPS’ -

’SLU’ -

’UMF’ -

’INVT’ -

’INVK’ -

’AINV’ +

’BGS’ +

’ILU’ +

’ILUT’ +

’MILU’ +

’MUMPS’ +

’SLU’ +

’UMF’ +

’INVT’ +

’INVK’ +

’AINV’

GS and BGS multilevel class="cmr-10">preconditioners, respectively -

ILU for block-Jacobi one-level preconditioners

The local solver to be used with the smoother or one-level preconditioner (see @@ -1759,22 +1801,22 @@ class="cmr-10">Note for details on hybrid Gauss-Seidel.

’SMOOTHER_SWEEPS’ +class="td11">

’SMOOTHER_SWEEPS’

integer +class="td11">

integer

Any integer -

number ≥ 0

1

Number of sweeps of the smoother or one-level preconditioner. In the multilevel @@ -1793,13 +1835,13 @@ class="cmr-10">respectively. Is ignored if the smoother is

’POLY_DEGREE’ +class="td11">

’POLY_DEGREE’

integer +class="td11">

integer

Any integer -

number ≥  ≤ 30

1

Degree of the polynomial accelerator, is equal to the number of matrix-vector @@ -1839,7 +1881,7 @@ preconditioner. -

@@ -1847,7 +1889,7 @@ preconditioner.
-

+

what

what

dtype

val

val

deault

cots

’SUB_OVR’ +class="td11">

’SUB_OVR’

integer +class="td11">

integer

Any integer -

number ≥ 0

1

Number of overlap layers, for Additive Schwarz only.

’SUB_RESTR’ +class="td11">

’SUB_RESTR’

character(len=*) +class="td11">

character(len=*)

’HALO’ -

’NONE’ +class="td11">

’HALO’ +

’NONE’

’HALO’ +class="td11">

’HALO’

Type of restriction operator, for Additive Schwarz only: for taking into account the overlap, ’NONE’ for neglecting it. -

Note that HALO must be chosen for the @@ -1943,16 +1985,16 @@ class="cmr-10">its RAS variant.

’SUB_PROL’ +class="td11">

’SUB_PROL’

character(len=*) +class="td11">

character(len=*)

’SUM’ -

’NONE’ +class="td11">

’SUM’ +

’NONE’

’NONE’ +class="td11">

’NONE’

Type of prolongation operator, for Additive Schwarz only: ’SUM’ contributions from the overlap, for neglecting them. -

Note that ’SUM’ must be chosen for the for its RAS variant.

’SUB_FILLIN’ +class="td11">

’SUB_FILLIN’

integer +class="td11">

integer

Any integer -

number ≥ 0

0

Fill-in level p of the incomplete LU @@ -1998,11 +2040,11 @@ class="cmr-10">factorizations.

’SUB_ILUTHRS’ +class="td11">

’SUB_ILUTHRS’

real(kind_parameter) +class="td11">

real(kind_parameter)

Any real number ≥ 0

0

Drop tolerance t in the ILU(factorization.

’MUMPS_LOC_GLOB’ +class="td11">

’MUMPS_LOC_GLOB’

character(len=*) +class="td11">

character(len=*)

’LOCAL_SOLVER’ -

’GLOBAL_SOLVER’ +class="td11">

’LOCAL_SOLVER’ +

’GLOBAL_SOLVER’

’GLOBAL_SOLVER’ +class="td11">

’GLOBAL_SOLVER’

Whether MUMPS should be used as a distributed solver, or as a serial solver acting @@ -2046,19 +2088,19 @@ class="cmr-10">process.

’MUMPS_IPAR_ENTRY’ +class="td11">

’MUMPS_IPAR_ENTRY’

integer +class="td11">

integer

Any integer number

0

Set an entry in the MUMPS integer control array, as chosen via the idx argument.

’MUMPS_RPAR_ENTRY’ +class="td11">

’MUMPS_RPAR_ENTRY’

real +class="td11">

real

Any real number

0

Set an entry in the MUMPS real control array, as chosen via the idx Parameters defining the smoother or the details of the one-level -

@@ -2112,7 +2154,7 @@ class="content">Parameters defining the smoother or the details of the one-level
-

+

what

what

dtype

val

val

deault

cots

’POLY_VARIANT’ +class="td11">

’POLY_VARIANT’

character(len=*) +class="td11">

character(len=*)

’CHEB_4’ -

’CHEB_4_OPT’ -

’CHEB_1_OPT’ +class="td11">

’CHEB_4’ +

’CHEB_4_OPT’ +

’CHEB_1_OPT’

’CHEB_4’ +class="td11">

’CHEB_4’

Select the type of polynomial accelerator. @@ -2217,15 +2259,15 @@ class="cmr-10">-kind.

’POLY_RHO_ESTIMATE’ +class="td11">

’POLY_RHO_ESTIMATE’

character(len=*) +class="td11">

character(len=*)

’POLY_RHO_EST_POWER’ +class="td11">

’POLY_RHO_EST_POWER’

’POLY_RHO_EST_POWER’ +class="td11">

’POLY_RHO_EST_POWER’

Algorithm for estimating the spectral @@ -2249,21 +2291,21 @@ class="cmr-10">two following options.

’POLY_RHO_ESTIMATE_ITERATIONS’ +class="td11">

’POLY_RHO_ESTIMATE_ITERATIONS’

integer +class="td11">

integer

Any integer -

number ≥ 1

20

Number of iterations for the spectral radius @@ -2273,23 +2315,23 @@ class="cmr-10">estimate.

’POLY_RHO_BA’ +class="td11">

’POLY_RHO_BA’

real(kind_parameter) +class="td11">

real(kind_parameter)

Any real -

number ∈ (0,1]

1

Sets an estimate of the spectral radius of @@ -2319,7 +2361,7 @@ class="content">Parameters defining the smoother or the details of the one-level -

[next] [up]

-

diff --git a/docs/src/userinterface.tex b/docs/src/userinterface.tex index 339b6b5c..f2b3df1a 100644 --- a/docs/src/userinterface.tex +++ b/docs/src/userinterface.tex @@ -147,7 +147,7 @@ default values, is given in Tables~\ref{tab:p_cycle}-\ref{tab:p_smoother_1}.\\ \textbf{Remark 2.} A smoother is usually obtained by combining two objects: a smoother (\fortinline|'SMOOTHER_TYPE'|) and a local solver (\fortinline|'SUB_SOLVE'|), -as specified in Tables~\ref{tab:p_smoother}-\ref{tab:p_smoother_1}. +as specified in Tables~\ref{tab:p_smoother}-\ref{tab:p_smoother_2}. For example, the block-Jacobi smoother using ILU(0) on the blocks is obtained by combining the block-Jacobi smoother object with the ILU(0) solver object. Similarly, @@ -176,7 +176,16 @@ Similar considerations apply to the point-Jacobi, Gauss-Seidel and block-Jacobi coarsest-level solvers, and shortcuts are available in this case too (see Table~\ref{tab:p_coarse_1}). \\ -\textbf{Remark 3.} Many of the coarsest-level solvers apply to a +\textbf{Remark 3.} The polynomial-accelerated smoother described in Tables~\ref{tab:p_smoother} +and~\ref{tab:p_smoother_2} redefines a sweep or iteration as corresponding to the degree of +the polynomial used. Consequently, the \fortinline|'SMOOTHER_SWEEPS'| option is overridden by +the \fortinline|'POLY_DEGREE'| option. This smoother is paired with a base smoother +object, whose iterations are accelerated using the specified polynomial smoothing technique. +By default, the $\ell_1$-Jacobi smoother serves as the base smoother, offering theoretical +guarantees on the resulting convergence factor~\cite{DDFMT2024,LOTTES}. Alternative combinations +are experimental and lack established guarantees.\\ + +\textbf{Remark 4.} Many of the coarsest-level solvers apply to a specific coarsest-matrix layout; therefore, setting the solver after the layout may change the layout to either distributed or replicated. @@ -425,7 +434,7 @@ the parameter \texttt{ilev}.} \\ distributed, \texttt{MUMPS} can be used with either a replicated or a distributed matrix. When any of the previous solvers is specified, the matrix layout is set to a default - value which allows the use of the solver (see Remark 3, p.~24). + value which allows the use of the solver (see Remark 4, p.~21). Note also that UMFPACK and SuperLU\_Dist are available only in double precision. \\\hline% \ifpdf @@ -578,7 +587,7 @@ level (continued).\label{tab:p_coarse_1}} & Type of smoother used in the multilevel preconditioner: point-Jacobi, hybrid (forward) Gauss-Seidel, hybrid backward Gauss-Seidel, block-Jacobi, $\ell_1$-Jacobi, $\ell_1$--hybrid (forward) Gauss-Seidel, $\ell_1$-point-Jacobi and - Additive Schwarz, polynomial accelerators; see~\cite{DDFMT2024} \par + Additive Schwarz, polynomial accelerators; see~\cite{DDFMT2024} and Remark~3 (p.~21).\par It is ignored by one-level preconditioners. \\ \hline \fortinline|'SUB_SOLVE'| & \fortinline|character(len=*)| & \fortinline|'JACOBI'|