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

#include <operator.hpp>

Inheritance diagram for mfem::TimeDependentOperator:

Collaboration diagram for mfem::TimeDependentOperator:

Public Types
enum	Type { EXPLICIT , IMPLICIT , HOMOGENEOUS }

enum	EvalMode { NORMAL , ADDITIVE_TERM_1 , ADDITIVE_TERM_2 }
	Evaluation mode. See SetEvalMode() for details. More...

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

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

virtual real_t	GetTime () const
	Read the currently set time.

virtual void	SetTime (const real_t t_)
	Set the current time.

bool	isExplicit () const
	True if type is EXPLICIT.

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

bool	isHomogeneous () const
	True if type is HOMOGENEOUS.

EvalMode	GetEvalMode () const
	Return the current evaluation mode. See SetEvalMode() for details.

virtual void	SetEvalMode (const EvalMode new_eval_mode)
	Set the evaluation mode of the time-dependent operator.

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.

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.

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.

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

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

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

virtual int	SUNImplicitSetup (const Vector &x, const Vector &fx, int jok, int *jcur, real_t gamma)
	Setup the ODE linear system \( A(x,t) = (I - gamma J) \) or \( A = (M - gamma J) \), where \( J(x,t) = \frac{df}{dt(x,t)} \).

virtual int	SUNImplicitSolve (const Vector &b, Vector &x, real_t tol)
	Solve the ODE linear system \( A x = b \) as setup by the method SUNImplicitSetup().

virtual int	SUNMassSetup ()
	Setup the mass matrix in the ODE system \( M y' = f(y,t) \) .

virtual int	SUNMassSolve (const Vector &b, Vector &x, real_t tol)
	Solve the mass matrix linear system \( M x = b \) as setup by the method SUNMassSetup().

virtual int	SUNMassMult (const Vector &x, Vector &v)
	Compute the mass matrix-vector product \( v = M x \) .

virtual	~TimeDependentOperator ()

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.

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

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

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

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

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

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

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

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.

virtual void	AddMult (const Vector &x, Vector &y, const real_t a=1.0) const
	Operator application: `y+=A(x)` (default) or `y+=a*A(x)`.

virtual void	AddMultTranspose (const Vector &x, Vector &y, const real_t a=1.0) const
	Operator transpose application: `y+=A^t(x)` (default) or `y+=a*A^t(x)`.

virtual void	ArrayMult (const Array< const Vector * > &X, Array< Vector * > &Y) const
	Operator application on a matrix: `Y=A(X)`.

virtual void	ArrayMultTranspose (const Array< const Vector * > &X, Array< Vector * > &Y) const
	Action of the transpose operator on a matrix: `Y=A^t(X)`.

virtual void	ArrayAddMult (const Array< const Vector * > &X, Array< Vector * > &Y, const real_t a=1.0) const
	Operator application on a matrix: `Y+=A(X)` (default) or `Y+=a*A(X)`.

virtual void	ArrayAddMultTranspose (const Array< const Vector * > &X, Array< Vector * > &Y, const real_t a=1.0) const
	Operator transpose application on a matrix: `Y+=A^t(X)` (default) or `Y+=a*A^t(X)`.

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.

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.

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

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

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

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

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

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.

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.

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().

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

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).

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

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

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

virtual	~Operator ()
	Virtual destructor.

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

Protected Attributes
real_t	t
	Current time.

Type	type
	Describes the form of the TimeDependentOperator.

EvalMode	eval_mode
	Current evaluation mode.

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

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

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

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

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".

Detailed Description

Base abstract class for first order 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 316 of file operator.hpp.

Member Enumeration Documentation

◆ EvalMode

enum mfem::TimeDependentOperator::EvalMode

Evaluation mode. See SetEvalMode() for details.

Enumerator
NORMAL	Normal evaluation.
ADDITIVE_TERM_1	Assuming additive split, f(x,t) = f1(x,t) + f2(x,t), evaluate the first term, f1.
ADDITIVE_TERM_2	Assuming additive split, f(x,t) = f1(x,t) + f2(x,t), evaluate the second term, f2.

Definition at line 327 of file operator.hpp.

◆ Type

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 319 of file operator.hpp.

Constructor & Destructor Documentation

◆ TimeDependentOperator() [1/2]

mfem::TimeDependentOperator::TimeDependentOperator	(	int	n = 0,
		real_t	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 347 of file operator.hpp.

◆ TimeDependentOperator() [2/2]

mfem::TimeDependentOperator::TimeDependentOperator	(	int	h,
		int	w,
		real_t	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 353 of file operator.hpp.

◆ ~TimeDependentOperator()

virtual mfem::TimeDependentOperator::~TimeDependentOperator ( )

inlinevirtual

Definition at line 499 of file operator.hpp.

Member Function Documentation

◆ ExplicitMult()

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

virtual

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 282 of file operator.cpp.

◆ GetEvalMode()

EvalMode mfem::TimeDependentOperator::GetEvalMode ( ) const

inline

Return the current evaluation mode. See SetEvalMode() for details.

Definition at line 370 of file operator.hpp.

◆ GetExplicitGradient()

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

virtual

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 312 of file operator.cpp.

◆ GetImplicitGradient()

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

virtual

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 304 of file operator.cpp.

◆ GetTime()

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

inlinevirtual

Read the currently set time.

Definition at line 357 of file operator.hpp.

◆ ImplicitMult()

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

virtual

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 287 of file operator.cpp.

◆ ImplicitSolve()

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

virtual

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, mfem::electromagnetics::MaxwellSolver, and mfem::SecondOrderTimeDependentOperator.

Definition at line 298 of file operator.cpp.

◆ isExplicit()

bool mfem::TimeDependentOperator::isExplicit ( ) const

inline

True if type is EXPLICIT.

Definition at line 363 of file operator.hpp.

◆ isHomogeneous()

bool mfem::TimeDependentOperator::isHomogeneous ( ) const

inline

True if type is HOMOGENEOUS.

Definition at line 367 of file operator.hpp.

◆ isImplicit()

bool mfem::TimeDependentOperator::isImplicit ( ) const

inline

True if type is IMPLICIT or HOMOGENEOUS.

Definition at line 365 of file operator.hpp.

◆ Mult()

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

virtual

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.

Implements mfem::Operator.

Reimplemented in mfem::AdvectionOper, mfem::DGHyperbolicConservationLaws, mfem::electromagnetics::MagneticDiffusionEOperator, mfem::electromagnetics::MaxwellSolver, mfem::ParAdvectorCGOper, mfem::SecondOrderTimeDependentOperator, and mfem::SerialAdvectorCGOper.

Definition at line 293 of file operator.cpp.

◆ SetEvalMode()

virtual void mfem::TimeDependentOperator::SetEvalMode ( const EvalMode new_eval_mode )

inlinevirtual

Set the evaluation mode of the time-dependent operator.

The evaluation mode is a switch that allows time-stepping methods to request evaluation of separate components/terms of the time-dependent operator. For example, IMEX methods typically assume additive split of the operator: f(x,t) = f1(x,t) + f2(x,t) and they rely on the ability to evaluate the two terms separately.

Generally, setting the evaluation mode should affect the behavior of all evaluation-related methods in the class, such as Mult(), ImplicitSolve(), etc. However, the exact list of methods that need to support a specific mode will depend on the used time-stepping method.

Definition at line 383 of file operator.hpp.

◆ SetTime()

virtual void mfem::TimeDependentOperator::SetTime ( const real_t t_ )

inlinevirtual

Set the current time.

Reimplemented in mfem::electromagnetics::MagneticDiffusionEOperator.

Definition at line 360 of file operator.hpp.

◆ SUNImplicitSetup()

int mfem::TimeDependentOperator::SUNImplicitSetup	(	const Vector &	x,
		const Vector &	fx,
		int	jok,
		int *	jcur,
		real_t	gamma )

virtual

Setup the ODE linear system \( A(x,t) = (I - gamma J) \) or \( A = (M - gamma J) \), where \( J(x,t) = \frac{df}{dt(x,t)} \).

Parameters

[in]	x	The state at which \(A(x,t)\) should be evaluated.
[in]	fx	The current value of the ODE rhs function, \(f(x,t)\).
[in]	jok	Flag indicating if the Jacobian should be updated.
[out]	jcur	Flag to signal if the Jacobian was updated.
[in]	gamma	The scaled time step value.

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

Presently, this method is used by SUNDIALS ODE solvers, for more details, see the SUNDIALS User Guides.

Definition at line 319 of file operator.cpp.

◆ SUNImplicitSolve()

int mfem::TimeDependentOperator::SUNImplicitSolve	(	const Vector &	b,
		Vector &	x,
		real_t	tol )

virtual

Solve the ODE linear system \( A x = b \) as setup by the method SUNImplicitSetup().

Parameters

[in]	b	The linear system right-hand side.
[in,out]	x	On input, the initial guess. On output, the solution.
[in]	tol	Linear solve tolerance.

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

Presently, this method is used by SUNDIALS ODE solvers, for more details, see the SUNDIALS User Guides.

Definition at line 327 of file operator.cpp.

◆ SUNMassMult()

int mfem::TimeDependentOperator::SUNMassMult	(	const Vector &	x,
		Vector &	v )

virtual

Compute the mass matrix-vector product \( v = M x \) .

Parameters

[in]	x	The vector to multiply.
[out]	v	The result of the matrix-vector product.

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

Presently, this method is used by SUNDIALS ARKStep integrator, for more details, see the ARKode User Guide.

Definition at line 345 of file operator.cpp.

◆ SUNMassSetup()

int mfem::TimeDependentOperator::SUNMassSetup ( )

virtual

Setup the mass matrix in the ODE system \( M y' = f(y,t) \) .

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

Presently, this method is used by SUNDIALS ARKStep integrator, for more details, see the ARKode User Guide.

Definition at line 333 of file operator.cpp.

◆ SUNMassSolve()

int mfem::TimeDependentOperator::SUNMassSolve	(	const Vector &	b,
		Vector &	x,
		real_t	tol )

virtual

Solve the mass matrix linear system \( M x = b \) as setup by the method SUNMassSetup().

Parameters

[in]	b	The linear system right-hand side.
[in,out]	x	On input, the initial guess. On output, the solution.
[in]	tol	Linear solve tolerance.

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

Presently, this method is used by SUNDIALS ARKStep integrator, for more details, see the ARKode User Guide.

Definition at line 339 of file operator.cpp.

Member Data Documentation

◆ eval_mode

EvalMode mfem::TimeDependentOperator::eval_mode

protected

Current evaluation mode.

Definition at line 342 of file operator.hpp.

◆ t

real_t mfem::TimeDependentOperator::t

protected

Current time.

Definition at line 340 of file operator.hpp.

◆ type

Type mfem::TimeDependentOperator::type

protected

Describes the form of the TimeDependentOperator.

Definition at line 341 of file operator.hpp.

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

linalg/operator.hpp
linalg/operator.cpp

Public Types

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Enumeration Documentation

◆ EvalMode

◆ Type

Constructor & Destructor Documentation

◆ TimeDependentOperator() [1/2]

◆ TimeDependentOperator() [2/2]

◆ ~TimeDependentOperator()

Member Function Documentation

◆ ExplicitMult()

◆ GetEvalMode()

◆ GetExplicitGradient()

◆ GetImplicitGradient()

◆ GetTime()

◆ ImplicitMult()

◆ ImplicitSolve()

◆ isExplicit()

◆ isHomogeneous()

◆ isImplicit()

◆ Mult()

◆ SetEvalMode()

◆ SetTime()

◆ SUNImplicitSetup()

◆ SUNImplicitSolve()

◆ SUNMassMult()

◆ SUNMassSetup()

◆ SUNMassSolve()

Member Data Documentation

◆ eval_mode

◆ t

◆ type