Interface to the KINSOL library – nonlinear solver methods. More...

#include <sundials.hpp>

Inheritance diagram for mfem::KINSolver:

Collaboration diagram for mfem::KINSolver:

Public Member Functions
	KINSolver (int strategy, bool oper_grad=true)
	Construct a serial wrapper to SUNDIALS' KINSOL nonlinear solver. More...

	KINSolver (MPI_Comm comm, int strategy, bool oper_grad=true)
	Construct a parallel wrapper to SUNDIALS' KINSOL nonlinear solver. More...

virtual	~KINSolver ()
	Destroy the associated KINSOL memory. More...

virtual void	SetOperator (const Operator &op)
	Set the nonlinear Operator of the system and initialize KINSOL. More...

virtual void	SetSolver (Solver &solver)
	Set the linear solver for inverting the Jacobian. More...

virtual void	SetPreconditioner (Solver &solver)
	Equivalent to SetSolver(solver). More...

void	SetScaledStepTol (double sstol)
	Set KINSOL's scaled step tolerance. More...

void	SetMaxSetupCalls (int max_calls)
	Set maximum number of nonlinear iterations without a Jacobian update. More...

void	SetMAA (int maa)
	Set the number of acceleration vectors to use with KIN_FP or KIN_PICARD. More...

void	SetJFNK (bool use_jfnk)
	Set the Jacobian Free Newton Krylov flag. The default is false. More...

void	SetLSMaxIter (int m)
	Set the maximum number of linear solver iterations. More...

void	SetLSMaxRestarts (int m)
	Set the maximum number of linear solver restarts. More...

virtual void	SetPrintLevel (int print_lvl)
	Set the print level for the KINSetPrintLevel function. More...

virtual void	SetPrintLevel (PrintLevel)
	This method is not supported and will throw an error. More...

virtual void	Mult (const Vector &b, Vector &x) const
	Solve the nonlinear system \( F(x) = 0 \). More...

void	Mult (Vector &x, const Vector &x_scale, const Vector &fx_scale) const
	Solve the nonlinear system \( F(x) = 0 \). More...

Public Member Functions inherited from mfem::NewtonSolver
	NewtonSolver ()

	NewtonSolver (MPI_Comm comm_)

virtual double	ComputeScalingFactor (const Vector &x, const Vector &b) const
	This method can be overloaded in derived classes to implement line search algorithms. More...

virtual void	ProcessNewState (const Vector &x) const
	This method can be overloaded in derived classes to perform computations that need knowledge of the newest Newton state. More...

void	SetAdaptiveLinRtol (const int type=2, const double rtol0=0.5, const double rtol_max=0.9, const double alpha=0.5 *(1.0+sqrt(5.0)), const double gamma=1.0)
	Enable adaptive linear solver relative tolerance algorithm. More...

Public Member Functions inherited from mfem::IterativeSolver
	IterativeSolver ()

	IterativeSolver (MPI_Comm comm_)

void	SetMonitor (IterativeSolverMonitor &m)
	Set the iterative solver monitor. More...

MPI_Comm	GetComm () const
	Return the associated MPI communicator, or MPI_COMM_NULL if no communicator is set. More...

void	SetRelTol (double rtol)

void	SetAbsTol (double atol)

void	SetMaxIter (int max_it)

int	GetNumIterations () const

bool	GetConverged () const

double	GetFinalNorm () const

Public Member Functions inherited from mfem::Solver
	Solver (int s=0, bool iter_mode=false)
	Initialize a square Solver with size s. More...

	Solver (int h, int w, bool iter_mode=false)
	Initialize a Solver with height h and width w. More...

Public Member Functions inherited from mfem::Operator
void	InitTVectors (const Operator Po, const Operator Ri, const Operator *Pi, Vector &x, Vector &b, Vector &X, Vector &B) const
	Initializes memory for true vectors of linear system. More...

	Operator (int s=0)
	Construct a square Operator with given size s (default 0). More...

	Operator (int h, int w)
	Construct an Operator with the given height (output size) and width (input size). More...

int	Height () const
	Get the height (size of output) of the Operator. Synonym with NumRows(). More...

int	NumRows () const
	Get the number of rows (size of output) of the Operator. Synonym with Height(). More...

int	Width () const
	Get the width (size of input) of the Operator. Synonym with NumCols(). More...

int	NumCols () const
	Get the number of columns (size of input) of the Operator. Synonym with Width(). More...

virtual MemoryClass	GetMemoryClass () const
	Return the MemoryClass preferred by the Operator. More...

virtual void	MultTranspose (const Vector &x, Vector &y) const
	Action of the transpose operator: `y=A^t(x)`. The default behavior in class Operator is to generate an error. More...

virtual Operator &	GetGradient (const Vector &x) const
	Evaluate the gradient operator at the point x. The default behavior in class Operator is to generate an error. More...

virtual void	AssembleDiagonal (Vector &diag) const
	Computes the diagonal entries into diag. Typically, this operation only makes sense for linear Operators. In some cases, only an approximation of the diagonal is computed. More...

virtual const Operator *	GetProlongation () const
	Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. `NULL` means identity. More...

virtual const Operator *	GetRestriction () const
	Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. `NULL` means identity. More...

virtual const Operator *	GetOutputProlongation () const
	Prolongation operator from linear algebra (linear system) vectors, to output vectors for the operator. `NULL` means identity. More...

virtual const Operator *	GetOutputRestrictionTranspose () const
	Transpose of GetOutputRestriction, directly available in this form to facilitate matrix-free RAP-type operators. More...

virtual const Operator *	GetOutputRestriction () const
	Restriction operator from output vectors for the operator to linear algebra (linear system) vectors. `NULL` means identity. More...

void	FormLinearSystem (const Array< int > &ess_tdof_list, Vector &x, Vector &b, Operator *&A, Vector &X, Vector &B, int copy_interior=0)
	Form a constrained linear system using a matrix-free approach. More...

void	FormRectangularLinearSystem (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, Vector &x, Vector &b, Operator *&A, Vector &X, Vector &B)
	Form a column-constrained linear system using a matrix-free approach. More...

virtual void	RecoverFEMSolution (const Vector &X, const Vector &b, Vector &x)
	Reconstruct a solution vector x (e.g. a GridFunction) from the solution X of a constrained linear system obtained from Operator::FormLinearSystem() or Operator::FormRectangularLinearSystem(). More...

void	FormSystemOperator (const Array< int > &ess_tdof_list, Operator *&A)
	Return in A a parallel (on truedofs) version of this square operator. More...

void	FormRectangularSystemOperator (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, Operator *&A)
	Return in A a parallel (on truedofs) version of this rectangular operator (including constraints). More...

void	FormDiscreteOperator (Operator *&A)
	Return in A a parallel (on truedofs) version of this rectangular operator. More...

void	PrintMatlab (std::ostream &out, int n, int m=0) const
	Prints operator with input size n and output size m in Matlab format. More...

virtual void	PrintMatlab (std::ostream &out) const
	Prints operator in Matlab format. More...

virtual	~Operator ()
	Virtual destructor. More...

Type	GetType () const
	Return the type ID of the Operator class. More...

Public Member Functions inherited from mfem::SundialsSolver
void *	GetMem () const
	Access the SUNDIALS memory structure. More...

int	GetFlag () const
	Returns the last flag returned by a call to a SUNDIALS function. More...

Protected Member Functions
void	SetJFNKSolver (Solver &solver)

Protected Member Functions inherited from mfem::NewtonSolver
void	AdaptiveLinRtolPreSolve (const Vector &x, const int it, const double fnorm) const
	Method for the adaptive linear solver rtol invoked before the linear solve. More...

void	AdaptiveLinRtolPostSolve (const Vector &x, const Vector &b, const int it, const double fnorm) const
	Method for the adaptive linear solver rtol invoked after the linear solve. More...

Protected Member Functions inherited from mfem::IterativeSolver
double	Dot (const Vector &x, const Vector &y) const

double	Norm (const Vector &x) const

void	Monitor (int it, double norm, const Vector &r, const Vector &x, bool final=false) const

PrintLevel	FromLegacyPrintLevel (int)
	Convert a legacy print level integer to a PrintLevel object. More...

Protected Member Functions inherited from mfem::Operator
void	FormConstrainedSystemOperator (const Array< int > &ess_tdof_list, ConstrainedOperator *&Aout)
	see FormSystemOperator() More...

void	FormRectangularConstrainedSystemOperator (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, RectangularConstrainedOperator *&Aout)
	see FormRectangularSystemOperator() More...

Operator *	SetupRAP (const Operator Pi, const Operator Po)
	Returns RAP Operator of this, using input/output Prolongation matrices Pi corresponds to "P", Po corresponds to "Rt". More...

Protected Member Functions inherited from mfem::SundialsSolver
bool	Parallel () const

bool	Parallel () const

	SundialsSolver ()
	Protected constructor: objects of this type should be constructed only as part of a derived class. More...

void	AllocateEmptyNVector (N_Vector &y)

void	AllocateEmptyNVector (N_Vector &y, MPI_Comm comm)

Static Protected Member Functions
static int	Mult (const N_Vector u, N_Vector fu, void *user_data)
	Wrapper to compute the nonlinear residual \( F(u) = 0 \). More...

static int	GradientMult (N_Vector v, N_Vector Jv, N_Vector u, booleantype new_u, void user_data)
	Wrapper to compute the Jacobian-vector product \( J(u) v = Jv \). More...

static int	LinSysSetup (N_Vector u, N_Vector fu, SUNMatrix J, void *user_data, N_Vector tmp1, N_Vector tmp2)
	Setup the linear system \( J u = b \). More...

static int	LinSysSolve (SUNLinearSolver LS, SUNMatrix J, N_Vector u, N_Vector b, realtype tol)
	Solve the linear system \( J u = b \). More...

static int	PrecSetup (N_Vector uu, N_Vector uscale, N_Vector fval, N_Vector fscale, void *user_data)
	Setup the preconditioner. More...

static int	PrecSolve (N_Vector uu, N_Vector uscale, N_Vector fval, N_Vector fscale, N_Vector vv, void *user_data)
	Solve the preconditioner equation \( Pz = v \). More...

Static Protected Member Functions inherited from mfem::IterativeSolver
static int	GuessLegacyPrintLevel (PrintLevel)
	Use some heuristics to guess a legacy print level corresponding to the given PrintLevel. More...

Protected Attributes
int	global_strategy
	KINSOL solution strategy. More...

bool	use_oper_grad
	use the Jv prod function More...

SundialsNVector *	y_scale

SundialsNVector *	f_scale
	scaling vectors More...

const Operator *	jacobian
	stores oper->GetGradient() More...

int	maa
	number of acceleration vectors More...

bool	jfnk = false
	enable JFNK More...

Vector	wrk
	Work vector needed for the JFNK PC. More...

int	maxli = 5
	Maximum linear iterations. More...

int	maxlrs = 0
	Maximum linear solver restarts. More...

Protected Attributes inherited from mfem::NewtonSolver
Vector	r

Vector	c

Operator *	grad

int	lin_rtol_type = 0

double	lin_rtol0

double	lin_rtol_max

double	fnorm_last = 0.0

double	lnorm_last = 0.0

double	eta_last = 0.0

double	gamma

double	alpha

Protected Attributes inherited from mfem::IterativeSolver
const Operator *	oper

Solver *	prec

IterativeSolverMonitor *	monitor = nullptr

int	max_iter
	Limit for the number of iterations the solver is allowed to do. More...

double	rel_tol
	Relative tolerance. More...

double	abs_tol
	Absolute tolerance. More...

int	final_iter

bool	converged

double	final_norm

int	print_level = -1
	(DEPRECATED) Legacy print level definition, which is left for compatibility with custom iterative solvers. More...

PrintLevel	print_options
	Output behavior for the iterative solver. More...

Protected Attributes inherited from mfem::Operator
int	height
	Dimension of the output / number of rows in the matrix. More...

int	width
	Dimension of the input / number of columns in the matrix. More...

Protected Attributes inherited from mfem::SundialsSolver
void *	sundials_mem
	SUNDIALS mem structure. More...

int	flag
	Last flag returned from a call to SUNDIALS. More...

bool	reinit
	Flag to signal memory reinitialization is need. More...

long	saved_global_size
	Global vector length on last initialization. More...

SundialsNVector *	Y
	State vector. More...

SUNMatrix	A

SUNMatrix	M
	Mass matrix M. More...

SUNLinearSolver	LSA
	Linear solver for A. More...

SUNLinearSolver	LSM
	Linear solver for M. More...

SUNNonlinearSolver	NLS
	Nonlinear solver. More...

Additional Inherited Members
Public Types inherited from mfem::Operator
enum	DiagonalPolicy { DIAG_ZERO, DIAG_ONE, DIAG_KEEP }
	Defines operator diagonal policy upon elimination of rows and/or columns. More...

enum	Type { ANY_TYPE, MFEM_SPARSEMAT, Hypre_ParCSR, PETSC_MATAIJ, PETSC_MATIS, PETSC_MATSHELL, PETSC_MATNEST, PETSC_MATHYPRE, PETSC_MATGENERIC, Complex_Operator, MFEM_ComplexSparseMat, Complex_Hypre_ParCSR, Complex_DenseMat, MFEM_Block_Matrix, MFEM_Block_Operator }
	Enumeration defining IDs for some classes derived from Operator. More...

Public Attributes inherited from mfem::Solver
bool	iterative_mode
	If true, use the second argument of Mult() as an initial guess. More...

Static Protected Attributes inherited from mfem::SundialsSolver
static constexpr double	default_rel_tol = 1e-4
	Default scalar relative tolerance. More...

static constexpr double	default_abs_tol = 1e-9
	Default scalar absolute tolerance. More...

Detailed Description

Interface to the KINSOL library – nonlinear solver methods.

Definition at line 835 of file sundials.hpp.

Constructor & Destructor Documentation

mfem::KINSolver::KINSolver	(	int	strategy,
		bool	oper_grad = `true`
	)

Construct a serial wrapper to SUNDIALS' KINSOL nonlinear solver.

Parameters

[in]	strategy	Specifies the nonlinear solver strategy: KIN_NONE / KIN_LINESEARCH / KIN_PICARD / KIN_FP.
[in]	oper_grad	Specifies whether the solver should use its Operator's GetGradient() method to compute the Jacobian of the system.

Definition at line 1914 of file sundials.cpp.

mfem::KINSolver::KINSolver	(	MPI_Comm	comm,
		int	strategy,
		bool	oper_grad = `true`
	)

Construct a parallel wrapper to SUNDIALS' KINSOL nonlinear solver.

Parameters

[in]	comm	The MPI communicator used to partition the system.
[in]	strategy	Specifies the nonlinear solver strategy: KIN_NONE / KIN_LINESEARCH / KIN_PICARD / KIN_FP.
[in]	oper_grad	Specifies whether the solver should use its Operator's GetGradient() method to compute the Jacobian of the system.

Definition at line 1928 of file sundials.cpp.

mfem::KINSolver::~KINSolver ( )

virtual

Destroy the associated KINSOL memory.

Definition at line 2266 of file sundials.cpp.

Member Function Documentation

int mfem::KINSolver::GradientMult	(	N_Vector	v,
		N_Vector	Jv,
		N_Vector	u,
		booleantype *	new_u,
		void *	user_data
	)

staticprotected

Wrapper to compute the Jacobian-vector product \( J(u) v = Jv \).

Definition at line 1823 of file sundials.cpp.

int mfem::KINSolver::LinSysSetup	(	N_Vector	u,
		N_Vector	fu,
		SUNMatrix	J,
		void *	user_data,
		N_Vector	tmp1,
		N_Vector	tmp2
	)

staticprotected

Setup the linear system \( J u = b \).

Definition at line 1846 of file sundials.cpp.

int mfem::KINSolver::LinSysSolve	(	SUNLinearSolver	LS,
		SUNMatrix	J,
		N_Vector	u,
		N_Vector	b,
		realtype	tol
	)

staticprotected

Solve the linear system \( J u = b \).

Definition at line 1863 of file sundials.cpp.

int mfem::KINSolver::Mult	(	const N_Vector	u,
		N_Vector	fu,
		void *	user_data
	)

staticprotected

Wrapper to compute the nonlinear residual \( F(u) = 0 \).

Definition at line 1809 of file sundials.cpp.

void mfem::KINSolver::Mult	(	const Vector &	b,
		Vector &	x
	)		const

virtual

Solve the nonlinear system \( F(x) = 0 \).

This method computes the x_scale and fx_scale vectors and calls the other Mult(Vector&, Vector&, Vector&) const method. The x_scale vector is a vector of ones and values of fx_scale are determined by comparing the chosen relative and functional norm (i.e. absolute) tolerances.

Parameters

[in]	b	Not used, KINSOL always assumes zero RHS
[in,out]	x	On input, initial guess, if iterative_mode = true, otherwise the initial guess is zero; on output, the solution

Reimplemented from mfem::NewtonSolver.

Definition at line 2153 of file sundials.cpp.

void mfem::KINSolver::Mult	(	Vector &	x,
		const Vector &	x_scale,
		const Vector &	fx_scale
	)		const

Solve the nonlinear system \( F(x) = 0 \).

Calls KINSol() to solve the nonlinear system. Before calling KINSol(), this functions uses the data members inherited from class IterativeSolver to set corresponding KINSOL options.

Parameters

[in,out]	x	On input, initial guess, if iterative_mode = true, otherwise the initial guess is zero; on output, the solution
[in]	x_scale	Elements of a diagonal scaling matrix D, s.t. D*x has all elements roughly the same when x is close to a solution
[in]	fx_scale	Elements of a diagonal scaling matrix E, s.t. D*F(x) has all elements roughly the same when x is not too close to a solution

Definition at line 2205 of file sundials.cpp.

int mfem::KINSolver::PrecSetup	(	N_Vector	uu,
		N_Vector	uscale,
		N_Vector	fval,
		N_Vector	fscale,
		void *	user_data
	)

staticprotected

Setup the preconditioner.

Definition at line 1876 of file sundials.cpp.

int mfem::KINSolver::PrecSolve	(	N_Vector	uu,
		N_Vector	uscale,
		N_Vector	fval,
		N_Vector	fscale,
		N_Vector	vv,
		void *	user_data
	)

staticprotected

Solve the preconditioner equation \( Pz = v \).

Definition at line 1894 of file sundials.cpp.

void mfem::KINSolver::SetJFNK ( bool use_jfnk )

inline

Set the Jacobian Free Newton Krylov flag. The default is false.

This flag indicates to use JFNK as the linear solver for KINSOL. This means that the Solver object set in SetSolver() or SetPreconditioner() is used as a preconditioner for an FGMRES algorithm provided by SpFGMR from SUNDIALS. Furthermore, all Jacobian-vector products in the outer Krylov method are approximated by a difference quotient and the relative tolerance for the outer Krylov method is adaptive. See the KINSOL User Manual for details.

Definition at line 948 of file sundials.hpp.

void mfem::KINSolver::SetJFNKSolver ( Solver & solver )

protected

Definition at line 2092 of file sundials.cpp.

void mfem::KINSolver::SetLSMaxIter ( int m )

inline

Set the maximum number of linear solver iterations.

Note: Only valid in combination with JFNK

Definition at line 952 of file sundials.hpp.

void mfem::KINSolver::SetLSMaxRestarts ( int m )

inline

Set the maximum number of linear solver restarts.

Note: Only valid in combination with JFNK

Definition at line 956 of file sundials.hpp.

void mfem::KINSolver::SetMAA ( int maa )

Set the number of acceleration vectors to use with KIN_FP or KIN_PICARD.

The default is 0. @ note This method must be called before SetOperator() to set the maximum size of the acceleration space. The value of maa can be altered after SetOperator() is called but it can't be higher than initial maximum.

Definition at line 2135 of file sundials.cpp.

void mfem::KINSolver::SetMaxSetupCalls ( int max_calls )

Set maximum number of nonlinear iterations without a Jacobian update.

The default is 10.

Note: This method must be called after SetOperator().

Definition at line 2129 of file sundials.cpp.

void mfem::KINSolver::SetOperator ( const Operator & op )

virtual

Set the nonlinear Operator of the system and initialize KINSOL.

Note: If this method is called a second time with a different problem size, then non-default KINSOL-specific options will be lost and will need to be set again.

Reimplemented from mfem::NewtonSolver.

Definition at line 1943 of file sundials.cpp.

virtual void mfem::KINSolver::SetPreconditioner ( Solver & solver )

inlinevirtual

Equivalent to SetSolver(solver).

Reimplemented from mfem::IterativeSolver.

Definition at line 919 of file sundials.hpp.

virtual void mfem::KINSolver::SetPrintLevel ( int print_lvl )

inlinevirtual

Set the print level for the KINSetPrintLevel function.

Reimplemented from mfem::IterativeSolver.

Definition at line 959 of file sundials.hpp.

void mfem::KINSolver::SetPrintLevel ( PrintLevel )

virtual

This method is not supported and will throw an error.

Reimplemented from mfem::IterativeSolver.

Definition at line 2147 of file sundials.cpp.

void mfem::KINSolver::SetScaledStepTol ( double sstol )

Set KINSOL's scaled step tolerance.

The default tolerance is \( U^\frac{2}{3} \) , where U = machine unit round-off.

Note: This method must be called after SetOperator().

Definition at line 2123 of file sundials.cpp.

void mfem::KINSolver::SetSolver ( Solver & solver )

virtual

Set the linear solver for inverting the Jacobian.

Note: This function assumes that Operator::GetGradient(const Vector &) is implemented by the Operator specified by SetOperator(const Operator &).

This method must be called after SetOperator().

Reimplemented from mfem::NewtonSolver.

Definition at line 2051 of file sundials.cpp.

Member Data Documentation

SundialsNVector * mfem::KINSolver::f_scale

mutableprotected

scaling vectors

Definition at line 840 of file sundials.hpp.

int mfem::KINSolver::global_strategy

protected

KINSOL solution strategy.

Definition at line 838 of file sundials.hpp.

const Operator* mfem::KINSolver::jacobian

protected

stores oper->GetGradient()

Definition at line 841 of file sundials.hpp.

bool mfem::KINSolver::jfnk = false

protected

enable JFNK

Definition at line 843 of file sundials.hpp.

int mfem::KINSolver::maa

protected

number of acceleration vectors

Definition at line 842 of file sundials.hpp.

int mfem::KINSolver::maxli = 5

protected

Maximum linear iterations.

Definition at line 845 of file sundials.hpp.

int mfem::KINSolver::maxlrs = 0

protected

Maximum linear solver restarts.

Definition at line 846 of file sundials.hpp.

bool mfem::KINSolver::use_oper_grad

protected

use the Jv prod function

Definition at line 839 of file sundials.hpp.

Vector mfem::KINSolver::wrk

protected

Work vector needed for the JFNK PC.

Definition at line 844 of file sundials.hpp.

SundialsNVector* mfem::KINSolver::y_scale

mutableprotected

Definition at line 840 of file sundials.hpp.

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

linalg/sundials.hpp
linalg/sundials.cpp

Public Member Functions

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation