#include <iterative_linear_solver.h>

Inheritance diagram for oomph::GMRES< MATRIX >:

Public Member Functions
	GMRES ()
	Constructor. More...

virtual	~GMRES ()
	Destructor (cleanup storage) More...

	GMRES (const GMRES &)
	Broken copy constructor. More...

void	operator= (const GMRES &)
	Broken assignment operator. More...

void	disable_resolve ()
	Overload disable resolve so that it cleans up memory too. More...

void	solve (Problem *const &problem_pt, DoubleVector &result)
	Solver: Takes pointer to problem and returns the results vector which contains the solution of the linear system defined by the problem's fully assembled Jacobian and residual vector. More...

void	solve (DoubleMatrixBase *const &matrix_pt, const DoubleVector &rhs, DoubleVector &solution)
	Linear-algebra-type solver: Takes pointer to a matrix and rhs vector and returns the solution of the linear system. More...

void	solve (DoubleMatrixBase *const &matrix_pt, const Vector< double > &rhs, Vector< double > &result)
	Linear-algebra-type solver: Takes pointer to a matrix and rhs vector and returns the solution of the linear system Call the broken base-class version. If you want this, please implement it. More...

void	resolve (const DoubleVector &rhs, DoubleVector &result)
	Re-solve the system defined by the last assembled Jacobian and the rhs vector specified here. Solution is returned in the vector result. More...

unsigned	iterations () const
	Number of iterations taken. More...

bool	iteration_restart () const
	access function indicating whether restarted GMRES is used More...

void	enable_iteration_restart (const unsigned &restart)
	switches on iteration restarting and takes as an argument the number of iterations after which the construction of the orthogonalisation basis vectors should be restarted More...

void	disable_iteration_restart ()
	switches off iteration restart More...

void	set_preconditioner_LHS ()
	Set left preconditioning (the default) More...

void	set_preconditioner_RHS ()
	Enable right preconditioning. More...

Public Member Functions inherited from oomph::IterativeLinearSolver
	IterativeLinearSolver ()
	Constructor: Set (default) trivial preconditioner and set defaults for tolerance and max. number of iterations. More...

	IterativeLinearSolver (const IterativeLinearSolver &)
	Broken copy constructor. More...

void	operator= (const IterativeLinearSolver &)
	Broken assignment operator. More...

virtual	~IterativeLinearSolver ()
	Destructor (empty) More...

Preconditioner *&	preconditioner_pt ()
	Access function to preconditioner. More...

Preconditioner *const &	preconditioner_pt () const
	Access function to preconditioner (const version) More...

double &	tolerance ()
	Access to convergence tolerance. More...

unsigned &	max_iter ()
	Access to max. number of iterations. More...

void	enable_doc_convergence_history ()
	Enable documentation of the convergence history. More...

void	disable_doc_convergence_history ()
	Disable documentation of the convergence history. More...

void	open_convergence_history_file_stream (const std::string &file_name, const std::string &zone_title="")
	Write convergence history into file with specified filename (automatically switches on doc). Optional second argument is a string that can be used (as a zone title) to identify what case we're running (e.g. what combination of linear solver and preconditioner or parameter values are used). More...

void	close_convergence_history_file_stream ()
	Close convergence history output stream. More...

double	jacobian_setup_time () const
	returns the time taken to assemble the jacobian matrix and residual vector More...

double	linear_solver_solution_time () const
	return the time taken to solve the linear system More...

virtual double	preconditioner_setup_time () const
	returns the the time taken to setup the preconditioner More...

void	enable_setup_preconditioner_before_solve ()
	Setup the preconditioner before the solve. More...

void	disable_setup_preconditioner_before_solve ()
	Don't set up the preconditioner before the solve. More...

void	enable_error_after_max_iter ()
	Throw an error if we don't converge within max_iter. More...

void	disable_error_after_max_iter ()
	Don't throw an error if we don't converge within max_iter (default). More...

void	enable_iterative_solver_as_preconditioner ()

void	disable_iterative_solver_as_preconditioner ()

Public Member Functions inherited from oomph::LinearSolver
	LinearSolver ()
	Empty constructor, initialise the member data. More...

	LinearSolver (const LinearSolver &dummy)
	Broken copy constructor. More...

void	operator= (const LinearSolver &)
	Broken assignment operator. More...

virtual	~LinearSolver ()
	Empty virtual destructor. More...

void	enable_doc_time ()
	Enable documentation of solve times. More...

void	disable_doc_time ()
	Disable documentation of solve times. More...

bool	is_doc_time_enabled () const
	Is documentation of solve times enabled? More...

bool	is_resolve_enabled () const
	Boolean flag indicating if resolves are enabled. More...

virtual void	enable_resolve ()
	Enable resolve (i.e. store matrix and/or LU decomposition, say) Virtual so it can be overloaded to perform additional tasks. More...

virtual void	enable_computation_of_gradient ()
	function to enable the computation of the gradient required for the globally convergent Newton method More...

void	disable_computation_of_gradient ()
	function to disable the computation of the gradient required for the globally convergent Newton method More...

void	reset_gradient ()
	function to reset the size of the gradient before each Newton solve More...

void	get_gradient (DoubleVector &gradient)
	function to access the gradient, provided it has been computed More...

Public Member Functions inherited from oomph::DistributableLinearAlgebraObject
	DistributableLinearAlgebraObject ()
	Default constructor - create a distribution. More...

	DistributableLinearAlgebraObject (const DistributableLinearAlgebraObject &matrix)
	Broken copy constructor. More...

void	operator= (const DistributableLinearAlgebraObject &)
	Broken assignment operator. More...

virtual	~DistributableLinearAlgebraObject ()
	Destructor. More...

LinearAlgebraDistribution *	distribution_pt () const
	access to the LinearAlgebraDistribution More...

unsigned	nrow () const
	access function to the number of global rows. More...

unsigned	nrow_local () const
	access function for the num of local rows on this processor. More...

unsigned	nrow_local (const unsigned &p) const
	access function for the num of local rows on this processor. More...

unsigned	first_row () const
	access function for the first row on this processor More...

unsigned	first_row (const unsigned &p) const
	access function for the first row on this processor More...

bool	distributed () const
	distribution is serial or distributed More...

bool	distribution_built () const

void	build_distribution (const LinearAlgebraDistribution *const dist_pt)
	setup the distribution of this distributable linear algebra object More...

void	build_distribution (const LinearAlgebraDistribution &dist)
	setup the distribution of this distributable linear algebra object More...

Private Member Functions
void	solve_helper (DoubleMatrixBase *const &matrix_pt, const DoubleVector &rhs, DoubleVector &solution)
	General interface to solve function. More...

void	clean_up_memory ()
	Cleanup data that's stored for resolve (if any has been stored) More...

void	update (const unsigned &k, const Vector< Vector< double > > &H, const Vector< double > &s, const Vector< DoubleVector > &v, DoubleVector &x)
	Helper function to update the result vector using the result, x=x_0+V_m*y. More...

void	generate_plane_rotation (double &dx, double &dy, double &cs, double &sn)
	Helper function: Generate a plane rotation. This is done by finding the values of $\cos(\theta)$ (i.e. cs) and () (i.e. sn) such that: $\begin{bmatrix} \cos\theta & \sin\theta \newline -\sin\theta & \cos\theta \end{bmatrix} \begin{bmatrix} dx \newline dy \end{bmatrix} = \begin{bmatrix} r \newline 0 \end{bmatrix},$ where $r=\sqrt{pow(dx,2)+pow(dy,2)}$ . The values of a and b are given by: $\cos\theta&=\dfrac{dx}{\sqrt{pow(dx,2)+pow(dy,2)}},$ and $\sin\theta&=\dfrac{dy}{\sqrt{pow(dx,2)+pow(dy,2)}}.$ Taken from: Saad Y."Iterative methods for sparse linear systems", p.192. More...

void	apply_plane_rotation (double &dx, double &dy, double &cs, double &sn)
	Helper function: Apply plane rotation. This is done using the update: $\begin{bmatrix} dx \newline dy \end{bmatrix} \leftarrow \begin{bmatrix} \cos\theta & \sin\theta \newline -\sin\theta & \cos\theta \end{bmatrix} \begin{bmatrix} dx \newline dy \end{bmatrix}.$ . More...

Private Attributes
unsigned	Iterations
	Number of iterations taken. More...

unsigned	Restart
	The number of iterations before the iteration proceedure is restarted if iteration restart is used. More...

bool	Iteration_restart
	boolean indicating if iteration restarting is used More...

MATRIX *	Matrix_pt
	Pointer to matrix. More...

bool	Resolving
	Boolean flag to indicate if the solve is done in re-solve mode, bypassing setup of matrix and preconditioner. More...

bool	Matrix_can_be_deleted
	Boolean flag to indicate if the matrix pointed to be Matrix_pt can be deleted. More...

bool	Preconditioner_LHS
	boolean indicating use of left hand preconditioning (if true) or right hand preconditioning (if false) More...

Additional Inherited Members
Protected Member Functions inherited from oomph::DistributableLinearAlgebraObject
void	clear_distribution ()
	clear the distribution of this distributable linear algebra object More...

Protected Attributes inherited from oomph::IterativeLinearSolver
bool	Doc_convergence_history
	Flag indicating if the convergence history is to be documented. More...

std::ofstream	Output_file_stream
	Output file stream for convergence history. More...

double	Tolerance
	Convergence tolerance. More...

unsigned	Max_iter
	Maximum number of iterations. More...

Preconditioner *	Preconditioner_pt
	Pointer to the preconditioner. More...

double	Jacobian_setup_time
	Jacobian setup time. More...

double	Solution_time
	linear solver solution time More...

double	Preconditioner_setup_time
	Preconditioner setup time. More...

bool	Setup_preconditioner_before_solve
	indicates whether the preconditioner should be setup before solve. Default = true; More...

bool	Throw_error_after_max_iter
	Should we throw an error instead of just returning when we hit the max iterations? More...

bool	Use_iterative_solver_as_preconditioner
	Use the iterative solver as preconditioner. More...

bool	First_time_solve_when_used_as_preconditioner

Protected Attributes inherited from oomph::LinearSolver
bool	Enable_resolve
	Boolean that indicates whether the matrix (or its factors, in the case of direct solver) should be stored so that the resolve function can be used. More...

bool	Doc_time
	Boolean flag that indicates whether the time taken. More...

bool	Compute_gradient
	flag that indicates whether the gradient required for the globally convergent Newton method should be computed or not More...

bool	Gradient_has_been_computed
	flag that indicates whether the gradient was computed or not More...

DoubleVector	Gradient_for_glob_conv_newton_solve
	DoubleVector storing the gradient for the globally convergent Newton method. More...

Static Protected Attributes inherited from oomph::IterativeLinearSolver
static IdentityPreconditioner	Default_preconditioner
	Default preconditioner: The base class for preconditioners is a fully functional (if trivial!) preconditioner. More...

Detailed Description

template<typename MATRIX>
class oomph::GMRES< MATRIX >

The GMRES method.

Definition at line 1246 of file iterative_linear_solver.h.

Constructor & Destructor Documentation

◆ GMRES() [1/2]

template<typename MATRIX >

oomph::GMRES< MATRIX >::GMRES ( )

inline

Constructor.

Definition at line 1252 of file iterative_linear_solver.h.

◆ ~GMRES()

template<typename MATRIX >

virtual oomph::GMRES< MATRIX >::~GMRES ( )

inlinevirtual

Destructor (cleanup storage)

Definition at line 1262 of file iterative_linear_solver.h.

References oomph::LinearSolver::clean_up_memory().

◆ GMRES() [2/2]

template<typename MATRIX >

oomph::GMRES< MATRIX >::GMRES ( const GMRES< MATRIX > & )

inline

Broken copy constructor.

Definition at line 1268 of file iterative_linear_solver.h.

References oomph::BrokenCopy::broken_copy().

Member Function Documentation

◆ apply_plane_rotation()

template<typename MATRIX >

void oomph::GMRES< MATRIX >::apply_plane_rotation	(	double &	dx,
		double &	dy,
		double &	cs,
		double &	sn
	)

inlineprivate

Helper function: Apply plane rotation. This is done using the update:

$\begin{bmatrix} dx \newline dy \end{bmatrix} \leftarrow \begin{bmatrix} \cos\theta & \sin\theta \newline -\sin\theta & \cos\theta \end{bmatrix} \begin{bmatrix} dx \newline dy \end{bmatrix}.$

.

Definition at line 1533 of file iterative_linear_solver.h.

◆ clean_up_memory()

template<typename MATRIX >

void oomph::GMRES< MATRIX >::clean_up_memory ( )

inlineprivatevirtual

Cleanup data that's stored for resolve (if any has been stored)

Reimplemented from oomph::LinearSolver.

Definition at line 1371 of file iterative_linear_solver.h.

◆ disable_iteration_restart()

template<typename MATRIX >

void oomph::GMRES< MATRIX >::disable_iteration_restart ( )

inline

switches off iteration restart

Definition at line 1352 of file iterative_linear_solver.h.

◆ disable_resolve()

template<typename MATRIX >

void oomph::GMRES< MATRIX >::disable_resolve ( )

inlinevirtual

Overload disable resolve so that it cleans up memory too.

Reimplemented from oomph::LinearSolver.

Definition at line 1280 of file iterative_linear_solver.h.

References oomph::LinearSolver::clean_up_memory(), oomph::LinearSolver::disable_resolve(), and oomph::LinearSolver::solve().

◆ enable_iteration_restart()

template<typename MATRIX >

void oomph::GMRES< MATRIX >::enable_iteration_restart ( const unsigned & restart )

inline

switches on iteration restarting and takes as an argument the number of iterations after which the construction of the orthogonalisation basis vectors should be restarted

Definition at line 1345 of file iterative_linear_solver.h.

◆ generate_plane_rotation()

template<typename MATRIX >

void oomph::GMRES< MATRIX >::generate_plane_rotation	(	double &	dx,
		double &	dy,
		double &	cs,
		double &	sn
	)

inlineprivate

Helper function: Generate a plane rotation. This is done by finding the values of $\cos(\theta)$ (i.e. cs) and () (i.e. sn) such that:

$\begin{bmatrix} \cos\theta & \sin\theta \newline -\sin\theta & \cos\theta \end{bmatrix} \begin{bmatrix} dx \newline dy \end{bmatrix} = \begin{bmatrix} r \newline 0 \end{bmatrix},$

where $r=\sqrt{pow(dx,2)+pow(dy,2)}$ . The values of a and b are given by:

$\cos\theta&=\dfrac{dx}{\sqrt{pow(dx,2)+pow(dy,2)}},$

and

$\sin\theta&=\dfrac{dy}{\sqrt{pow(dx,2)+pow(dy,2)}}.$

Taken from: Saad Y."Iterative methods for sparse linear systems", p.192.

Definition at line 1475 of file iterative_linear_solver.h.

◆ iteration_restart()

template<typename MATRIX >

bool oomph::GMRES< MATRIX >::iteration_restart ( ) const

inline

access function indicating whether restarted GMRES is used

Definition at line 1337 of file iterative_linear_solver.h.

◆ iterations()

template<typename MATRIX >

unsigned oomph::GMRES< MATRIX >::iterations ( ) const

inlinevirtual

Number of iterations taken.

Implements oomph::IterativeLinearSolver.

Definition at line 1331 of file iterative_linear_solver.h.

◆ operator=()

template<typename MATRIX >

void oomph::GMRES< MATRIX >::operator= ( const GMRES< MATRIX > & )

inline

Broken assignment operator.

Definition at line 1274 of file iterative_linear_solver.h.

References oomph::BrokenCopy::broken_assign().

◆ resolve()

template<typename MATRIX >

void oomph::GMRES< MATRIX >::resolve	(	const DoubleVector &	rhs,
		DoubleVector &	result
	)

virtual

Re-solve the system defined by the last assembled Jacobian and the rhs vector specified here. Solution is returned in the vector result.

Reimplemented from oomph::LinearSolver.

Definition at line 2162 of file iterative_linear_solver.cc.

References oomph::LinearSolver::solve().

◆ set_preconditioner_LHS()

template<typename MATRIX >

void oomph::GMRES< MATRIX >::set_preconditioner_LHS ( )

inline

Set left preconditioning (the default)

Definition at line 1358 of file iterative_linear_solver.h.

◆ set_preconditioner_RHS()

template<typename MATRIX >

void oomph::GMRES< MATRIX >::set_preconditioner_RHS ( )

inline

Enable right preconditioning.

Definition at line 1361 of file iterative_linear_solver.h.

◆ solve() [1/3]

template<typename MATRIX >

void oomph::GMRES< MATRIX >::solve	(	Problem *const &	problem_pt,
		DoubleVector &	result
	)

virtual

Solver: Takes pointer to problem and returns the results vector which contains the solution of the linear system defined by the problem's fully assembled Jacobian and residual vector.

Implements oomph::LinearSolver.

Definition at line 2191 of file iterative_linear_solver.cc.

References oomph::DoubleVector::build(), oomph::DistributableLinearAlgebraObject::build_distribution(), oomph::DoubleVector::built(), oomph::LinearSolver::clean_up_memory(), oomph::Problem::communicator_pt(), oomph::DistributableLinearAlgebraObject::distribution_pt(), oomph::LinearSolver::Doc_time, oomph::LinearSolver::Enable_resolve, oomph::Problem::get_jacobian(), oomph::IterativeLinearSolver::Jacobian_setup_time, oomph::Problem::ndof(), oomph::oomph_info, oomph::DoubleVector::redistribute(), and oomph::TimingHelpers::timer().

◆ solve() [2/3]

template<typename MATRIX >

void oomph::GMRES< MATRIX >::solve	(	DoubleMatrixBase *const &	matrix_pt,
		const DoubleVector &	rhs,
		DoubleVector &	solution
	)

inlinevirtual

Linear-algebra-type solver: Takes pointer to a matrix and rhs vector and returns the solution of the linear system.

Reimplemented from oomph::LinearSolver.

Definition at line 1293 of file iterative_linear_solver.h.

References oomph::DistributableLinearAlgebraObject::build_distribution(), oomph::DistributableLinearAlgebraObject::distribution_pt(), and oomph::LinearSolver::Enable_resolve.

◆ solve() [3/3]

template<typename MATRIX >

void oomph::GMRES< MATRIX >::solve	(	DoubleMatrixBase *const &	matrix_pt,
		const Vector< double > &	rhs,
		Vector< double > &	result
	)

inlinevirtual

Linear-algebra-type solver: Takes pointer to a matrix and rhs vector and returns the solution of the linear system Call the broken base-class version. If you want this, please implement it.

Reimplemented from oomph::LinearSolver.

Definition at line 1319 of file iterative_linear_solver.h.

References oomph::LinearSolver::resolve(), and oomph::LinearSolver::solve().

◆ solve_helper()

template<typename MATRIX >

void oomph::GMRES< MATRIX >::solve_helper	(	DoubleMatrixBase *const &	matrix_pt,
		const DoubleVector &	rhs,
		DoubleVector &	solution
	)

private

General interface to solve function.

Linear-algebra-type solver: Takes pointer to a matrix and rhs vector and returns the solution of the linear system. based on the algorithm presented in Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, Barrett, Berry et al, SIAM, 2006 and the implementation in the IML++ library : http://math.nist.gov/iml++/

Definition at line 2272 of file iterative_linear_solver.cc.

◆ update()

template<typename MATRIX >

void oomph::GMRES< MATRIX >::update	(	const unsigned &	k,
		const Vector< Vector< double > > &	H,
		const Vector< double > &	s,
		const Vector< DoubleVector > &	v,
		DoubleVector &	x
	)

inlineprivate

Helper function to update the result vector using the result, x=x_0+V_m*y.

Definition at line 1381 of file iterative_linear_solver.h.

References oomph::DistributableLinearAlgebraObject::distribution_pt(), i, oomph::DistributableLinearAlgebraObject::nrow(), oomph::IterativeLinearSolver::preconditioner_pt(), oomph::Preconditioner::preconditioner_solve(), and oomph::DoubleVector::values_pt().

Member Data Documentation

◆ Iteration_restart

template<typename MATRIX >

bool oomph::GMRES< MATRIX >::Iteration_restart

private

boolean indicating if iteration restarting is used

Definition at line 1553 of file iterative_linear_solver.h.

◆ Iterations

template<typename MATRIX >

unsigned oomph::GMRES< MATRIX >::Iterations

private

Number of iterations taken.

Definition at line 1546 of file iterative_linear_solver.h.

◆ Matrix_can_be_deleted

template<typename MATRIX >

bool oomph::GMRES< MATRIX >::Matrix_can_be_deleted

private

Boolean flag to indicate if the matrix pointed to be Matrix_pt can be deleted.

Definition at line 1564 of file iterative_linear_solver.h.

◆ Matrix_pt

template<typename MATRIX >

MATRIX* oomph::GMRES< MATRIX >::Matrix_pt

private

Pointer to matrix.

Definition at line 1556 of file iterative_linear_solver.h.

◆ Preconditioner_LHS

template<typename MATRIX >

bool oomph::GMRES< MATRIX >::Preconditioner_LHS

private

boolean indicating use of left hand preconditioning (if true) or right hand preconditioning (if false)

Definition at line 1568 of file iterative_linear_solver.h.

◆ Resolving

template<typename MATRIX >

bool oomph::GMRES< MATRIX >::Resolving

private

Boolean flag to indicate if the solve is done in re-solve mode, bypassing setup of matrix and preconditioner.

Definition at line 1560 of file iterative_linear_solver.h.

◆ Restart

template<typename MATRIX >

unsigned oomph::GMRES< MATRIX >::Restart

private

The number of iterations before the iteration proceedure is restarted if iteration restart is used.

Definition at line 1550 of file iterative_linear_solver.h.

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

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<typename MATRIX> class oomph::GMRES< MATRIX >

Constructor & Destructor Documentation

◆ GMRES() [1/2]

◆ ~GMRES()

◆ GMRES() [2/2]

Member Function Documentation

◆ apply_plane_rotation()

◆ clean_up_memory()

◆ disable_iteration_restart()

◆ disable_resolve()

◆ enable_iteration_restart()

◆ generate_plane_rotation()

◆ iteration_restart()

◆ iterations()

◆ operator=()

◆ resolve()

◆ set_preconditioner_LHS()

◆ set_preconditioner_RHS()

◆ solve() [1/3]

◆ solve() [2/3]

◆ solve() [3/3]

◆ solve_helper()

◆ update()

Member Data Documentation

◆ Iteration_restart

◆ Iterations

◆ Matrix_can_be_deleted

◆ Matrix_pt

◆ Preconditioner_LHS

◆ Resolving

◆ Restart

template<typename MATRIX>
class oomph::GMRES< MATRIX >