Base abstract class for time dependent operators. More...

#include <operator.hpp>

Inherited by ConductionOperator, ConductionOperator, FE_Evolution, FE_Evolution, FE_Evolution, FE_Evolution, FE_Evolution, HyperelasticOperator, HyperelasticOperator, HyperelasticOperator, HyperelasticOperator, HyperelasticOperator, and mfem::electromagnetics::MagneticDiffusionEOperator.

Collaboration diagram for mfem::TimeDependentOperator:

[legend]

Public Types
enum	Type { EXPLICIT, IMPLICIT, HOMOGENEOUS }

Public Types inherited from mfem::Operator
enum	Type { MFEM_SPARSEMAT, HYPRE_PARCSR, PETSC_MATAIJ, PETSC_MATIS, PETSC_MATSHELL, PETSC_MATNEST }
	Enumeration defining IDs for some classes derived from Operator. More...

Public Member Functions
	TimeDependentOperator (int n=0, double t_=0.0, Type type_=EXPLICIT)
	Construct a "square" TimeDependentOperator y = f(x,t), where x and y have the same dimension n. More...

	TimeDependentOperator (int h, int w, double t_=0.0, Type type_=EXPLICIT)
	Construct a TimeDependentOperator y = f(x,t), where x and y have dimensions w and h, respectively. More...

virtual double	GetTime () const
	Read the currently set time. More...

virtual void	SetTime (const double _t)
	Set the current time. More...

bool	isExplicit () const
	True if type is EXPLICIT. More...

bool	isImplicit () const
	True if type is IMPLICIT or HOMOGENEOUS. More...

bool	isHomogeneous () const
	True if type is HOMOGENEOUS. More...

virtual void	ExplicitMult (const Vector &x, Vector &y) const
	Perform the action of the explicit part of the operator, G: y = G(x, t) where t is the current time. More...

virtual void	ImplicitMult (const Vector &x, const Vector &k, Vector &y) const
	Perform the action of the implicit part of the operator, F: y = F(x, k, t) where t is the current time. More...

virtual void	Mult (const Vector &x, Vector &y) const
	Perform the action of the operator: y = k = f(x, t), where k solves the algebraic equation F(x, k, t) = G(x, t) and t is the current time. More...

virtual void	ImplicitSolve (const double dt, const Vector &x, Vector &k)
	Solve the equation: k = f(x + dt k, t), for the unknown k at the current time t. More...

virtual Operator &	GetImplicitGradient (const Vector &x, const Vector &k, double shift) const
	Return an Operator representing (dF/dk shift + dF/dx) at the given x, k, and the currently set time. More...

virtual Operator &	GetExplicitGradient (const Vector &x) const
	Return an Operator representing dG/dx at the given point x and the currently set time. More...

virtual	~TimeDependentOperator ()

Public Member Functions inherited from mfem::Operator
	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 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 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...

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...

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(). More...

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

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

Protected Attributes
double	t
	Current time. More...

Type	type
	Describes the form of the TimeDependentOperator. 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...

Detailed Description

Base abstract class for time dependent operators.

Operator of the form: (x,t) -> f(x,t), where k = f(x,t) generally solves the algebraic equation F(x,k,t) = G(x,t). The functions F and G represent the implicit and explicit parts of the operator, respectively. For explicit operators, F(x,k,t) = k, so f(x,t) = G(x,t).

Definition at line 140 of file operator.hpp.

Member Enumeration Documentation

enum mfem::TimeDependentOperator::Type

Enumerator
EXPLICIT	This type assumes F(x,k,t) = k, i.e. k = f(x,t) = G(x,t).
IMPLICIT	This is the most general type, no assumptions on F and G.
HOMOGENEOUS	This type assumes that G(x,t) = 0.

Definition at line 143 of file operator.hpp.

Constructor & Destructor Documentation

mfem::TimeDependentOperator::TimeDependentOperator	(	int	n = `0`,
		double	t_ = `0.0`,
		Type	type_ = `EXPLICIT`
	)

inlineexplicit

Construct a "square" TimeDependentOperator y = f(x,t), where x and y have the same dimension n.

Definition at line 157 of file operator.hpp.

mfem::TimeDependentOperator::TimeDependentOperator	(	int	h,
		int	w,
		double	t_ = `0.0`,
		Type	type_ = `EXPLICIT`
	)

inline

Construct a TimeDependentOperator y = f(x,t), where x and y have dimensions w and h, respectively.

Definition at line 163 of file operator.hpp.

virtual mfem::TimeDependentOperator::~TimeDependentOperator ( )

inlinevirtual

Definition at line 253 of file operator.hpp.

Member Function Documentation

virtual void mfem::TimeDependentOperator::ExplicitMult	(	const Vector &	x,
		Vector &	y
	)		const

inlinevirtual

Perform the action of the explicit part of the operator, G: y = G(x, t) where t is the current time.

Presently, this method is used by some PETSc ODE solvers, for more details, see the PETSc Manual.

Definition at line 184 of file operator.hpp.

virtual Operator& mfem::TimeDependentOperator::GetExplicitGradient ( const Vector & x ) const

inlinevirtual

Return an Operator representing dG/dx at the given point x and the currently set time.

Presently, this method is used by some PETSc ODE solvers, for more details, see the PETSc Manual.

Definition at line 246 of file operator.hpp.

virtual Operator& mfem::TimeDependentOperator::GetImplicitGradient	(	const Vector &	x,
		const Vector &	k,
		double	shift
	)		const

inlinevirtual

Return an Operator representing (dF/dk shift + dF/dx) at the given x, k, and the currently set time.

Presently, this method is used by some PETSc ODE solvers, for more details, see the PETSc Manual.

Definition at line 233 of file operator.hpp.

virtual double mfem::TimeDependentOperator::GetTime ( ) const

inlinevirtual

Read the currently set time.

Definition at line 167 of file operator.hpp.

virtual void mfem::TimeDependentOperator::ImplicitMult	(	const Vector &	x,
		const Vector &	k,
		Vector &	y
	)		const

inlinevirtual

Perform the action of the implicit part of the operator, F: y = F(x, k, t) where t is the current time.

Presently, this method is used by some PETSc ODE solvers, for more details, see the PETSc Manual.

Definition at line 194 of file operator.hpp.

virtual void mfem::TimeDependentOperator::ImplicitSolve	(	const double	dt,
		const Vector &	x,
		Vector &	k
	)

inlinevirtual

Solve the equation: k = f(x + dt k, t), for the unknown k at the current time t.

For general F and G, the equation for k becomes: F(x + dt k, k, t) = G(x + dt k, t).

The input vector x corresponds to time index (or cycle) n, while the currently set time, t, and the result vector k correspond to time index n+1. The time step dt corresponds to the time interval between cycles n and n+1.

This method allows for the abstract implementation of some time integration methods, including diagonal implicit Runge-Kutta (DIRK) methods and the backward Euler method in particular.

If not re-implemented, this method simply generates an error.

Reimplemented in mfem::electromagnetics::MagneticDiffusionEOperator.

Definition at line 223 of file operator.hpp.

bool mfem::TimeDependentOperator::isExplicit ( ) const

inline

True if type is EXPLICIT.

Definition at line 173 of file operator.hpp.

bool mfem::TimeDependentOperator::isHomogeneous ( ) const

inline

True if type is HOMOGENEOUS.

Definition at line 177 of file operator.hpp.

bool mfem::TimeDependentOperator::isImplicit ( ) const