#include <inmost_solver.h>

Collaboration diagram for INMOST::Solver:

Classes
class	OrderInfo
	Base class for low level operations with objects of Solver class. More...

Public Types
enum	Type { INNER_ILU2, INNER_DDPQILUC, INNER_MPTILUC, INNER_MPTILU2, Trilinos_Aztec, Trilinos_Belos, Trilinos_ML, Trilinos_Ifpack, PETSc, ANI, FCBIILU2, K3BIILU2 }
	Type of the Solver can be currently used in this version of INMOST. More...

Public Member Functions
INMOST_DATA_REAL_TYPE	GetConditionNumberL ()

INMOST_DATA_REAL_TYPE	GetConditionNumberU ()

void	SetParameterEnum (std::string name, INMOST_DATA_ENUM_TYPE value)

void	SetParameterReal (std::string name, INMOST_DATA_REAL_TYPE value)

std::string	GetName ()
	Get the used defined name of the Solver. More...

Type	GetPackage () const
	Get the package Type. More...

void	SetMatrix (Sparse::Matrix &A, bool OldPreconditioner=false)

bool	Solve (Sparse::Vector &RHS, Sparse::Vector &SOL)

INMOST_DATA_ENUM_TYPE	Iterations ()

INMOST_DATA_REAL_TYPE	Residual ()

std::string	GetReason ()

INMOST_DATA_REAL_TYPE	Condest (INMOST_DATA_REAL_TYPE tol, INMOST_DATA_ENUM_TYPE maxits=100)

	Solver (Type pack, std::string _name="", INMOST_MPI_Comm comm=INMOST_MPI_COMM_WORLD)

	~Solver ()

void	Clear ()
	Clear all internal data of the current solver including matrix, preconditioner etc. More...

Static Public Member Functions
static std::string	TypeName (Type t)

static void	Initialize (int argc, char *argv, const char database="")

static void	Finalize ()

static bool	isInitialized ()

static bool	isFinalized ()

Detailed Description

Main class to set and solve linear system. Solver class is used to set the coefficient Matrix, the right-hand side Vector and the initial guess Vector, construct the preconditioner and Solve the linear system.

Formally, Solver class is independent of INMOST::Mesh class.

See Also: Sparse::Matrix; Sparse::Vector; Sparse::Solve

Definition at line 38 of file inmost_solver.h.

Member Enumeration Documentation

enum INMOST::Solver::Type

Type of the Solver can be currently used in this version of INMOST.

Enumerator
INNER_ILU2	inner Solver based on BiCGStab(L) solver with second order ILU factorization as preconditioner.
INNER_DDPQILUC	inner Solver based on BiCGStab(L) solver with second order Crout-ILU with inversed-based condition estimation and unsymmetric reordering for diagonal dominance as preconditioner.
INNER_MPTILUC	inner Solver based on BiCGStab(L) solver with second order Crout-ILU with inversed-based condition estimation and maximum product transversal reordering as preconditioner.
INNER_MPTILU2	inner Solver based on BiCGStab(L) solver with second order ILU and maximum product transversal reordering as preconditioner.
Trilinos_Aztec	external Solver AztecOO from Trilinos package.
Trilinos_Belos	external Solver Belos from Trilinos package, currently without preconditioner.
Trilinos_ML	external Solver AztecOO with ML preconditioner.
Trilinos_Ifpack	external Solver AztecOO with Ifpack preconditioner.
PETSc	external Solver PETSc, See Also http://www.mcs.anl.gov/petsc/
ANI	external Solver from ANI3D based on ILU2 (sequential Fortran version), See Also http://ani3d.sourceforge.net/
FCBIILU2	external FCBIILU2 Solver (BIILU2 parallel F2C version).
K3BIILU2	inner K3BIILU2 Solver (BIILU2 parallel version).

Definition at line 44 of file inmost_solver.h.

Constructor & Destructor Documentation

INMOST::Solver::Solver	(	Type	pack,
		std::string	_name = `""`,
		INMOST_MPI_Comm	comm = `INMOST_MPI_COMM_WORLD`
	)

Main constructor of the solver. Solver name provided here is used to extract options from database file for PETSc and Trilinos packages.

Parameters

pack	The package Type to be used for solution.
_name	The user specified name of the current solver.
comm	Communicator for parallel data exchanges, MPI_COMM_WORLD by default.

See Also: Solver::Initialize; Solver::SetMatrix; Solver::Solve; Solver::Finalize

INMOST::Solver::~Solver ( )

Member Function Documentation

void INMOST::Solver::Clear ( )

Clear all internal data of the current solver including matrix, preconditioner etc.

INMOST_DATA_REAL_TYPE INMOST::Solver::Condest	(	INMOST_DATA_REAL_TYPE	tol,
		INMOST_DATA_ENUM_TYPE	maxits = `100`
	)

Computes the smallest and the largest eigenvalue with the power method. Requires SetMatrix to be called to compute the preconditioner. Currently works for internal methods only, since it uses internal matrix-vector multiplication. Largest eigenvalue: vprev = 0; v = rand(); while( |v|-|vprev| > tol ) {vprev = v; v = A*v; v /= |v|;} lambda_max = |v|; Smallest eigenvalue: vprev = 0; v = rand(); while( |v|-|vprev| > tol ){vprev = v; solve(A*v = v); v /= |v|;} lambda_min = 1.0/|v|; See answer by Blair Perot in: https://www.researchgate.net/post/What_is_the_best_way_to_estimate_the_condition_number_of_a_sparse_matrix.

Parameters

tol	Tolerance used for power series.
maxits	Maximum number of iterations allowed.

Returns: Condition number or 1.0e100 if not converged.

static void INMOST::Solver::Finalize ( )

static

Finalize the stage of parallel solution. If MPI was initialized in Solver::Initialize, then it will be finalized. By this reason, do not use any MPI function after call to this function.

See Also: Solver::Initialize; Solver::isFinalized

INMOST_DATA_REAL_TYPE INMOST::Solver::GetConditionNumberL ( )

Retrive approximate condition number produced by INNER_MPTILUC. The number is cond(L^-1).

INMOST_DATA_REAL_TYPE INMOST::Solver::GetConditionNumberU ( )

Retrive approximate condition number produced by INNER_MPTILUC. The number is cond(U^-1).

std::string INMOST::Solver::GetName ( )

inline

Get the used defined name of the Solver.

Definition at line 255 of file inmost_solver.h.

Type INMOST::Solver::GetPackage ( ) const

inline

Get the package Type.

Definition at line 258 of file inmost_solver.h.

std::string INMOST::Solver::GetReason ( )

Get the reason of convergence or divergence of the last solution.

See Also: Sparse::Solve

static void INMOST::Solver::Initialize	(	int *	argc,
		char ***	argv,
		const char *	database = `""`
	)

static

Initialize the stage of parallel solution. If MPI is not initialized yet, then it will be initialized.

database file is used to pass parameters to PETSc and Trilinos packages. if database file for is provided any changes through SetParameterEnum, SetParameterReal would not be effective for PETSc and Trilinos packages. Currently this database file provides directions for package-specific files. In future it is supposed to set up parameters for internal solvers.

Parameters

argc	The number of arguments transmitted to the function main.
argv	The pointer to arguments transmitted to the function main.
database	Usually the name of the file with the Solver parameters.

The shortest call to this function with the default solver parameters is the following: Initialize(NULL,NULL,"");

See Also: Solver::Finalize; Solver::isInitialized

Example of contents of the database file:

PETSc: petsc_options.txt
Trilinos_Ifpack: trilinos_ifpack_options.xml
Trilinos_ML: trilinos_ml_options.xml
Trilinos_Aztec: trilinos_aztec_options.xml
Trilinos_Belos: trilinos_belos_options.xml

static bool INMOST::Solver::isFinalized ( )

inlinestatic

Definition at line 349 of file inmost_solver.h.

static bool INMOST::Solver::isInitialized ( )

inlinestatic

Definition at line 348 of file inmost_solver.h.

INMOST_DATA_ENUM_TYPE INMOST::Solver::Iterations ( )

Return the number of iterations performed by the last solution.

See Also: Sparse::Solve

INMOST_DATA_REAL_TYPE INMOST::Solver::Residual ( )

Return the final residual achieved by the last solution.

See Also: Sparse::Solve

void INMOST::Solver::SetMatrix	(	Sparse::Matrix &	A,
		bool	OldPreconditioner = `false`
	)

Set the matrix and construct the preconditioner.

Parameters

A	Matrix A in linear problem Ax = b
OldPreconditioner	If this parameter is set to true, then the previous preconditioner will be used, otherwise the new preconditioner will be constructed.

Preconditioner will be constructed on call to this function

for INNER_*, PETSc and ANI packages
for Trilinos preconditioner will be constructed each time Sparse::Solve is called

Any changes to preconditioner parameters should happen before that point. If you increase gmres_substep after this point, inner methods most likely will fail

void INMOST::Solver::SetParameterEnum	(	std::string	name,
		INMOST_DATA_ENUM_TYPE	value
	)

Set the solver parameter of the integer type. You can find defaults for parameters in the top of the file inmost_solver.h.

Parameters:

"maximum_iterations" - total number of iterations
"schwartz_overlap" - number of overlapping levels for additive schwartz method, works for: INNER_ILU2, INNER_MLILUC Trilinos_Aztec, Trilinos_Belos, Trilinos_ML, Trilinos_Ifpack PETSc
"gmres_substeps" - number of gmres steps performed after each bicgstab step, works for: INNER_ILU2, INNER_MLILUC
"reorder_nonzeros" - place sparser rows at the beggining of matrix during reordering, works for: INNER_MLILUC
"rescale_iterations" - number of iterations for two-side matrix rescaling, works for: INNER_ILU2, INNER_MLILUC
"condition_estimation" - exploit condition estimation of inversed factors to adapt drop and reuse tolerances, works for: INNER_MLILUC
"adapt_ddpq_tolerance" - adapt ddpq tolerance depending from the complexity of calculation of Schur complement, works for: INNER_MLILUC

void INMOST::Solver::SetParameterReal	(	std::string	name,
		INMOST_DATA_REAL_TYPE	value
	)

Set the solver parameter of the real type. You can find defaults for parameters in the top of the file inmost_solver.h.

Parameters:

"absolute_tolerance" - iterative method will stop on i-th iteration if ||A x(i)-b|| < absolute_tolerance
"relative_tolerance" - iterative method will stop on i-th iteration if ||A x(i)-b||/||A x(0) - b||
"divergence_tolerance" - iterative method will fail if ||A x(i) - b|| > divergence_tolerance
"drop_tolerance" - tolerance for dropping values during incomplete factorization, works for: INNER_ILU2, INNER_MLILUC Trilinos_Aztec, Trilinos_Ifpack PETSc
"reuse_tolerance" - tolerance for reusing values during incomplete factorization, these values are used only during calculation of L and U factors and/or Schur complement and discarded once factorization is done, value should be less then "drop_tolerance", typical value is drop_tolerance^2, works for: INNER_ILU2, INNER_MLILUC
"ddpq_tolerance" - by this tolerance most diagonnaly-dominant elements will be selected to form the next level of factorization, the closer the tolerance is to one the smaller will be the level. Actual rule is: A(i,j)/(sum(A(i,:))+sum(A(:,j))-A(i,j)) > ddpq_tolerance * A(imax,jmax)/(sum(A(imax,:))+sum(A(:,jmax))-A(imax,jmax)) where on imax, jmax maximum is reached. works for: INNER_MLILUC
"fill_level" - level of fill for ILU-type preconditioners, works for: INNER_ILU2 (if LFILL is defined in solver_ilu2.hpp) Trilinos, Trilinos_Ifpack

bool INMOST::Solver::Solve	(	Sparse::Vector &	RHS,
		Sparse::Vector &	SOL
	)

Solver the linear system: A*x = b. Prior to this call you should call SetMatrix

Parameters

RHS	The right-hand side Vector b.
SOL	The initial guess to the solution on input and the solution Vector x on return.

It is assumed that the coefficient matrix A have been set and the preconditioner have been already constructed.

See Also: Sparse::SetMatrix

static std::string INMOST::Solver::TypeName ( Type t )

static

The documentation for this class was generated from the following file:

INMOST.lib/Source/Headers/inmost_solver.h

Classes

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation