The SPBCGS (Scaled, Preconditioned, Bi-Conjugate Gradient,
Stabilized [V1992]) implementation of the SUNLinearSolver
module
provided with SUNDIALS, SUNLinSol_SPBCGS, is an iterative linear
solver that is designed to be compatible with any N_Vector
implementation (serial, threaded, parallel, and user-supplied) that
supports a minimal subset of operations (N_VClone()
,
N_VDotProd()
, N_VScale()
,
N_VLinearSum()
, N_VProd()
, N_VDiv()
, and
N_VDestroy()
). Unlike the SPGMR and SPFGMR algorithms,
SPBCGS requires a fixed amount of memory that does not increase with
the number of allowed iterations.
The header file to be included when using this module
is sunlinsol/sunlinsol_spbcgs.h
. The SUNLinSol_SPBCGS module
is accessible from all SUNDIALS solvers without
linking to the libsundials_sunlinsolspbcgs
module library.
The module SUNLinSol_SPBCGS provides the following user-callable routines:
SUNLinSol_SPBCGS
(N_Vector y, int pretype, int maxl)¶This constructor function creates and allocates memory for a SPBCGS
SUNLinearSolver
. Its arguments are an N_Vector
, the desired
type of preconditioning, and the number of linear iterations to allow.
This routine will perform consistency checks to ensure that it is
called with a consistent N_Vector
implementation (i.e. that it
supplies the requisite vector operations). If y
is
incompatible, then this routine will return NULL
.
A maxl
argument that is \(\le0\) will result in the default
value (5).
Allowable inputs for pretype
are PREC_NONE
(0),
PREC_LEFT
(1), PREC_RIGHT
(2) and PREC_BOTH
(3);
any other integer input will result in the default (no
preconditioning). We note that some SUNDIALS solvers are designed
to only work with left preconditioning (IDA and IDAS) and others
with only right preconditioning (KINSOL). While it is possible to
configure a SUNLinSol_SPBCGS object to use any of the
preconditioning options with these solvers, this use mode is not
supported and may result in inferior performance.
SUNLinSol_SPBCGSSetPrecType
(SUNLinearSolver S, int pretype)¶This function updates the type of preconditioning to use. Supported
values are PREC_NONE
(0), PREC_LEFT
(1),
PREC_RIGHT
(2), and PREC_BOTH
(3).
This routine will return with one of the error codes
SUNLS_ILL_INPUT
(illegal pretype
), SUNLS_MEM_NULL
(S
is NULL
), or SUNLS_SUCCESS
.
SUNLinSol_SPBCGSSetMaxl
(SUNLinearSolver S, int maxl)¶This function updates the number of linear solver iterations to allow.
A maxl
argument that is \(\le0\) will result in the default
value (5).
This routine will return with one of the error codes
SUNLS_MEM_NULL
(S
is NULL
) or SUNLS_SUCCESS
.
SUNLinSolSetInfoFile_SPBCGS
(SUNLinearSolver LS, FILE* info_file)¶The function SUNLinSolSetInfoFile_SPBCGS()
sets the
output file where all informative (non-error) messages should be directed.
stdout
by default);NULL
input will disable outputNULL
Notes:
This function is intended for users that wish to monitor the linear
solver progress. By default, the file pointer is set to stdout
.
SUNDIALS must be built with the CMake option ``SUNDIALS_BUILD_WITH_MONITORING``, to utilize this function. See section Configuration options (Unix/Linux) for more information.
SUNLinSolSetPrintLevel_SPBCGS
(SUNLinearSolver LS, int print_level)¶The function SUNLinSolSetPrintLevel_SPBCGS()
specifies the
level of verbosity of the output.
LS – a SUNLinSol object
print_level – flag indicating level of verbosity; must be one of:
- 0, no information is printed (default)
- 1, for each linear iteration the residual norm is printed
NULL
Notes: This function is intended for users that wish to monitor the linear solver progress. By default, the print level is 0.
SUNDIALS must be built with the CMake option ``SUNDIALS_BUILD_WITH_MONITORING``, to utilize this function. See section Configuration options (Unix/Linux) for more information.
For backwards compatibility, we also provide the wrapper functions, each with identical input and output arguments to the routines that they wrap:
SUNSPBCGS
(N_Vector y, int pretype, int maxl)¶Wrapper function for SUNLinSol_SPBCGS()
SUNSPBCGSSetPrecType
(SUNLinearSolver S, int pretype)¶Wrapper function for SUNLinSol_SPBCGSSetPrecType()
SUNSPBCGSSetMaxl
(SUNLinearSolver S, int maxl)¶Wrapper function for SUNLinSol_SPBCGSSetMaxl()
For solvers that include a Fortran interface module, the
SUNLinSol_SPBCGS module also includes the Fortran-callable
function FSUNSPBCGSInit()
to initialize this
SUNLinSol_SPBCGS module for a given SUNDIALS solver.
FSUNSPBCGSInit
(CODE, PRETYPE, MAXL, IER)¶Initializes a SPBCGS SUNLinearSolver
structure for
use in a SUNDIALS package.
This routine must be called after the N_Vector
object has
been initialized.
int
, input) – flag denoting the SUNDIALS solver
this matrix will be used for: CVODE=1, IDA=2, KINSOL=3, ARKode=4.int
, input) – flag denoting type of
preconditioning to use: none=0, left=1, right=2, both=3.int
, input) – number of SPBCGS iterations to allow.int
, output) – return flag (0 success, -1 for failure).Additionally, when using ARKode with a non-identity mass matrix, the
Fortran-callable function FSUNMassSPBCGSInit()
initializes
this SUNLinSol_SPBCGS module for solving mass matrix linear systems.
FSUNMassSPBCGSInit
(PRETYPE, MAXL, IER)¶Initializes a SPBCGS SUNLinearSolver
structure for use in
solving mass matrix systems in ARKode.
This routine must be called after the N_Vector
object has
been initialized.
int
, input) – flag denoting type of
preconditioning to use: none=0, left=1, right=2, both=3.int
, input) – number of SPBCGS iterations to allow.int
, output) – return flag (0 success, -1 for failure).The SUNLinSol_SPBCGSSetPrecType()
and SUNLinSol_SPBCGSSetMaxl()
routines also support Fortran interfaces for the system and mass
matrix solvers:
FSUNSPBCGSSetPrecType
(CODE, PRETYPE, IER)¶Fortran interface to SUNLinSol_SPBCGSSetPrecType()
for system
linear solvers.
This routine must be called after FSUNSPBCGSInit()
has
been called.
Arguments: all should have type int
, and have meanings
identical to those listed above.
FSUNMassSPBCGSSetPrecType
(PRETYPE, IER)¶Fortran interface to SUNLinSol_SPBCGSSetPrecType()
for mass matrix
linear solvers in ARKode.
This routine must be called after FSUNMassSPBCGSInit()
has
been called.
Arguments: all should have type int
, and have meanings
identical to those listed above.
FSUNSPBCGSSetMaxl
(CODE, MAXL, IER)¶Fortran interface to SUNLinSol_SPBCGSSetMaxl()
for system
linear solvers.
This routine must be called after FSUNSPBCGSInit()
has
been called.
Arguments: all should have type int
, and have meanings
identical to those listed above.
FSUNMassSPBCGSSetMaxl
(MAXL, IER)¶Fortran interface to SUNLinSol_SPBCGSSetMaxl()
for mass matrix
linear solvers in ARKode.
This routine must be called after FSUNMassSPBCGSInit()
has
been called.
Arguments: all should have type int
, and have meanings
identical to those listed above.
The SUNLinSol_SPBCGS module defines the content field of a
SUNLinearSolver
to be the following structure:
struct _SUNLinearSolverContent_SPBCGS {
int maxl;
int pretype;
int numiters;
realtype resnorm;
int last_flag;
ATimesFn ATimes;
void* ATData;
PSetupFn Psetup;
PSolveFn Psolve;
void* PData;
N_Vector s1;
N_Vector s2;
N_Vector r;
N_Vector r_star;
N_Vector p;
N_Vector q;
N_Vector u;
N_Vector Ap;
N_Vector vtemp;
int print_level;
FILE* info_file;
};
These entries of the content field contain the following information:
maxl
- number of SPBCGS iterations to allow (default is 5),pretype
- flag for type of preconditioning to employ
(default is none),numiters
- number of iterations from the most-recent solve,resnorm
- final linear residual norm from the most-recent
solve,last_flag
- last error return flag from an internal
function,ATimes
- function pointer to perform \(Av\) product,ATData
- pointer to structure for ATimes
,Psetup
- function pointer to preconditioner setup routine,Psolve
- function pointer to preconditioner solve routine,PData
- pointer to structure for Psetup
and Psolve
,s1, s2
- vector pointers for supplied scaling matrices
(default is NULL
),r
- a N_Vector
which holds the current scaled,
preconditioned linear system residual,r_star
- a N_Vector
which holds the initial scaled,
preconditioned linear system residual,p, q, u, Ap, vtemp
- N_Vector
used for workspace by the
SPBCGS algorithm.print_level
- controls the amount of information to be printed to the info fileinfo_file
- the file where all informative (non-error) messages will be directedThis solver is constructed to perform the following operations:
N_Vector
solver data is allocated, with
vectors cloned from a template N_Vector
that is input, and
default solver parameters are set.ATimes
,
PSetup
, and Psolve
function pointers and s1
and s2
scaling vectors.NULL
PSetup
function is
called. Typically, this is provided by the SUNDIALS solver itself,
that translates between the generic PSetup
function and the
solver-specific routine (solver-supplied or user-supplied).The SUNLinSol_SPBCGS module defines implementations of all “iterative” linear solver operations listed in the section The SUNLinearSolver API:
SUNLinSolGetType_SPBCGS
SUNLinSolInitialize_SPBCGS
SUNLinSolSetATimes_SPBCGS
SUNLinSolSetPreconditioner_SPBCGS
SUNLinSolSetScalingVectors_SPBCGS
SUNLinSolSetup_SPBCGS
SUNLinSolSolve_SPBCGS
SUNLinSolNumIters_SPBCGS
SUNLinSolResNorm_SPBCGS
SUNLinSolResid_SPBCGS
SUNLinSolLastFlag_SPBCGS
SUNLinSolSpace_SPBCGS
SUNLinSolFree_SPBCGS