The SUNLinSol_SPBCGS Module

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.

SUNLinSol_SPBCGS Usage

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:

SUNLinearSolver 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.

int 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.

int 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.

int SUNLinSolSetInfoFile_SPBCGS(SUNLinearSolver LS, FILE* info_file)

The function SUNLinSolSetInfoFile_SPBCGS() sets the output file where all informative (non-error) messages should be directed.

Arguments:
  • LS – a SUNLinSol object
  • info_file – pointer to output file (stdout by default);
    a NULL input will disable output
Return value:
  • SUNLS_SUCCESS if successful
  • SUNLS_MEM_NULL if the SUNLinearSolver memory was NULL
  • SUNLS_ILL_INPUT if SUNDIALS was not built with monitoring enabled

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.

int SUNLinSolSetPrintLevel_SPBCGS(SUNLinearSolver LS, int print_level)

The function SUNLinSolSetPrintLevel_SPBCGS() specifies the level of verbosity of the output.

Arguments:
  • 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
Return value:
  • SUNLS_SUCCESS if successful
  • SUNLS_MEM_NULL if the SUNLinearSolver memory was NULL
  • SUNLS_ILL_INPUT if SUNDIALS was not built with monitoring enabled, or if the print level value was invalid

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:

SUNLinearSolver SUNSPBCGS(N_Vector y, int pretype, int maxl)

Wrapper function for SUNLinSol_SPBCGS()

int SUNSPBCGSSetPrecType(SUNLinearSolver S, int pretype)

Wrapper function for SUNLinSol_SPBCGSSetPrecType()

int 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.

subroutine 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.

Arguments:
  • CODE (int, input) – flag denoting the SUNDIALS solver this matrix will be used for: CVODE=1, IDA=2, KINSOL=3, ARKode=4.
  • PRETYPE (int, input) – flag denoting type of preconditioning to use: none=0, left=1, right=2, both=3.
  • MAXL (int, input) – number of SPBCGS iterations to allow.
  • IER (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.

subroutine 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.

Arguments:
  • PRETYPE (int, input) – flag denoting type of preconditioning to use: none=0, left=1, right=2, both=3.
  • MAXL (int, input) – number of SPBCGS iterations to allow.
  • IER (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:

subroutine 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.

subroutine 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.

subroutine 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.

subroutine 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.

SUNLinSol_SPBCGS Description

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 file
  • info_file - the file where all informative (non-error) messages will be directed

This solver is constructed to perform the following operations:

  • During construction all N_Vector solver data is allocated, with vectors cloned from a template N_Vector that is input, and default solver parameters are set.
  • User-facing “set” routines may be called to modify default solver parameters.
  • Additional “set” routines are called by the SUNDIALS solver that interfaces with SUNLinSol_SPBCGS to supply the ATimes, PSetup, and Psolve function pointers and s1 and s2 scaling vectors.
  • In the “initialize” call, the solver parameters are checked for validity.
  • In the “setup” call, any non-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).
  • In the “solve” call the SPBCGS iteration is performed. This will include scaling and preconditioning if those options have been 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