#include <ex18.hpp>

Inheritance diagram for FE_Evolution:

Collaboration diagram for FE_Evolution:

Public Member Functions
	FE_Evolution (FiniteElementSpace &_vfes, Operator &_A, SparseMatrix &_Aflux)

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	~FE_Evolution ()

	FE_Evolution (BilinearForm &_M, BilinearForm &_K, const Vector &_b)

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	~FE_Evolution ()

	FE_Evolution (ParBilinearForm &_M, ParBilinearForm &_K, const Vector &_b)

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	~FE_Evolution ()

	FE_Evolution (HypreParMatrix &_M, HypreParMatrix &_K, const Vector &_b, bool M_in_lhs)

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

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

virtual	~FE_Evolution ()

	FE_Evolution (SparseMatrix &_M, SparseMatrix &_K, const Vector &_b, BilinearForm &_bf, Vector &M_rs)

void	SetTimeStep (double _dt)

void	SetK (SparseMatrix &_K)

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	~FE_Evolution ()

	FE_Evolution (HypreParMatrix &_M, HypreParMatrix &_K, const Vector &_b, ParBilinearForm &_pbf, Vector &M_rs)

void	SetTimeStep (double _dt)

void	SetK (HypreParMatrix &_K)

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	~FE_Evolution ()

	FE_Evolution (SparseMatrix &_M, SparseMatrix &_K, const Vector &_b)

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	~FE_Evolution ()

	FE_Evolution (HypreParMatrix &_M, HypreParMatrix &_K, const Vector &_b)

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	~FE_Evolution ()

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

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

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

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

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

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

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

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

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. 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 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 *	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=0, int m=0) const
	Prints operator with input size n and output size m in Matlab format. More...

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

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

Additional Inherited Members
Public Types inherited from mfem::TimeDependentOperator
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	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 }
	Enumeration defining IDs for some classes derived from Operator. 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, taking in input/output Prolongation matrices. More...

Protected Attributes inherited from mfem::TimeDependentOperator
double	t
	Current time. More...

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

EvalMode	eval_mode
	Current evaluation mode. 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

A time-dependent operator for the right-hand side of the ODE. The DG weak form of du/dt = -v.grad(u) is M du/dt = K u + b, where M and K are the mass and advection matrices, and b describes the flow on the boundary. This can be written as a general ODE, du/dt = M^{-1} (K u + b), and this class is used to evaluate the right-hand side.

A time-dependent operator for the ODE as F(u,du/dt,t) = G(u,t) The DG weak form of du/dt = -v.grad(u) is M du/dt = K u + b, where M and K are the mass and advection matrices, and b describes the flow on the boundary. This can be also written as a general ODE with the right-hand side only as du/dt = M^{-1} (K u + b). This class is used to evaluate the right-hand side and the left-hand side.

Definition at line 20 of file ex18.hpp.

Constructor & Destructor Documentation

FE_Evolution::FE_Evolution	(	FiniteElementSpace &	_vfes,
		Operator &	_A,
		SparseMatrix &	_Aflux
	)

Definition at line 104 of file ex18.hpp.

FE_Evolution::~FE_Evolution ( )

inlinevirtual

Definition at line 43 of file ex18.hpp.

FE_Evolution::FE_Evolution	(	BilinearForm &	_M,
		BilinearForm &	_K,
		const Vector &	_b
	)

Definition at line 428 of file ex9.cpp.

virtual FE_Evolution::~FE_Evolution ( )

virtual

FE_Evolution::FE_Evolution	(	ParBilinearForm &	_M,
		ParBilinearForm &	_K,
		const Vector &	_b
	)

Definition at line 508 of file ex9p.cpp.

virtual FE_Evolution::~FE_Evolution ( )

virtual

FE_Evolution::FE_Evolution	(	HypreParMatrix &	_M,
		HypreParMatrix &	_K,
		const Vector &	_b,
		bool	M_in_lhs
	)

Definition at line 492 of file ex9p.cpp.

virtual FE_Evolution::~FE_Evolution ( )

inlinevirtual

Definition at line 89 of file ex9p.cpp.

FE_Evolution::FE_Evolution	(	SparseMatrix &	_M,
		SparseMatrix &	_K,
		const Vector &	_b,
		BilinearForm &	_bf,
		Vector &	M_rs
	)

Definition at line 473 of file ex9.cpp.

virtual FE_Evolution::~FE_Evolution ( )

inlinevirtual

Definition at line 207 of file ex9.cpp.

FE_Evolution::FE_Evolution	(	HypreParMatrix &	_M,
		HypreParMatrix &	_K,
		const Vector &	_b,
		ParBilinearForm &	_pbf,
		Vector &	M_rs
	)

Definition at line 575 of file ex9p.cpp.

virtual FE_Evolution::~FE_Evolution ( )

inlinevirtual

Definition at line 232 of file ex9p.cpp.

FE_Evolution::FE_Evolution	(	SparseMatrix &	_M,
		SparseMatrix &	_K,
		const Vector &	_b
	)

Definition at line 352 of file ex9.cpp.

virtual FE_Evolution::~FE_Evolution ( )

inlinevirtual

Definition at line 77 of file ex9.cpp.

FE_Evolution::FE_Evolution	(	HypreParMatrix &	_M,
		HypreParMatrix &	_K,
		const Vector &	_b
	)

Definition at line 421 of file ex9p.cpp.

virtual FE_Evolution::~FE_Evolution ( )

inlinevirtual

Definition at line 76 of file ex9p.cpp.

Member Function Documentation

void FE_Evolution::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.

Reimplemented from mfem::TimeDependentOperator.

Definition at line 515 of file ex9p.cpp.

Operator & FE_Evolution::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.

Reimplemented from mfem::TimeDependentOperator.

Definition at line 555 of file ex9p.cpp.

Operator & FE_Evolution::GetImplicitGradient	(	const Vector &	x,
		const Vector &	k,
		double	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.

Reimplemented from mfem::TimeDependentOperator.

Definition at line 570 of file ex9p.cpp.

void FE_Evolution::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.

Reimplemented from mfem::TimeDependentOperator.

Definition at line 533 of file ex9p.cpp.

void FE_Evolution::ImplicitSolve	(	const double	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 from mfem::TimeDependentOperator.

Definition at line 461 of file ex9.cpp.

virtual void FE_Evolution::ImplicitSolve	(	const double	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 from mfem::TimeDependentOperator.

void FE_Evolution::Mult	(	const Vector &	x,
		Vector &	y
	)		const

virtual