#include <operator.hpp>

Inheritance diagram for mfem::TimeDependentAdjointOperator:

Collaboration diagram for mfem::TimeDependentAdjointOperator:

Public Member Functions
	TimeDependentAdjointOperator (int dim, int adjdim, real_t t=0., Type type=EXPLICIT)
	The TimedependentAdjointOperator extends the TimeDependentOperator class to use features in SUNDIALS CVODESSolver for computing quadratures and solving adjoint problems.

virtual	~TimeDependentAdjointOperator ()
	Destructor.

virtual void	QuadratureIntegration (const Vector &y, Vector &qdot) const
	Provide the operator integration of a quadrature equation.

virtual void	AdjointRateMult (const Vector &y, Vector &yB, Vector &yBdot) const =0
	Perform the action of the operator: yBdot = k = f(y,@2 yB, t), where.

virtual void	QuadratureSensitivityMult (const Vector &y, const Vector &yB, Vector &qBdot) const
	Provides the sensitivity of the quadrature w.r.t to primal and adjoint solutions.

virtual int	SUNImplicitSetupB (const real_t t, const Vector &x, const Vector &xB, const Vector &fxB, int jokB, int *jcurB, real_t gammaB)
	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	SUNImplicitSolveB (Vector &x, const Vector &b, real_t tol)
	Solve the ODE linear system \( A(x,xB,t) xB = b \) as setup by the method SUNImplicitSetup().

int	GetAdjointHeight ()
	Returns the size of the adjoint problem state space.

Public Member Functions inherited from mfem::TimeDependentOperator
	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
int	adjoint_height

Protected Attributes inherited from mfem::TimeDependentOperator
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
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	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...

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

TimeDependentAdjointOperator is a TimeDependentOperator with Adjoint rate equations to be used with CVODESSolver.

Definition at line 505 of file operator.hpp.

Constructor & Destructor Documentation

◆ TimeDependentAdjointOperator()

mfem::TimeDependentAdjointOperator::TimeDependentAdjointOperator	(	int	dim,
		int	adjdim,
		real_t	t = 0.,
		Type	type = EXPLICIT )

inline

The TimedependentAdjointOperator extends the TimeDependentOperator class to use features in SUNDIALS CVODESSolver for computing quadratures and solving adjoint problems.

To solve adjoint problems one needs to implement the AdjointRateMult method to tell CVODES what the adjoint rate equation is.

QuadratureIntegration (optional) can be used to compute values over the forward problem

QuadratureSensitivityMult (optional) can be used to find the sensitivity of the quadrature using the adjoint solution in part.

SUNImplicitSetupB (optional) can be used to setup custom solvers for the newton solve for the adjoint problem.

SUNImplicitSolveB (optional) actually uses the solvers from SUNImplicitSetupB to solve the adjoint problem.

See SUNDIALS user manuals for specifics.

Parameters

[in]	dim	Dimension of the forward operator
[in]	adjdim	Dimension of the adjoint operator. Typically it is the same size as dim. However, SUNDIALS allows users to specify the size if one wants to perform custom operations.
[in]	t	Starting time to set
[in]	type	The TimeDependentOperator type

Definition at line 538 of file operator.hpp.

◆ ~TimeDependentAdjointOperator()

virtual mfem::TimeDependentAdjointOperator::~TimeDependentAdjointOperator ( )

inlinevirtual

Destructor.

Definition at line 545 of file operator.hpp.

Member Function Documentation

◆ AdjointRateMult()

virtual void mfem::TimeDependentAdjointOperator::AdjointRateMult	(	const Vector &	y,
		Vector &	yB,
		Vector &	yBdot ) const

pure virtual

Perform the action of the operator: yBdot = k = f(y,@2 yB, t), where.

Parameters

[in]	y	The primal solution at time t
[in]	yB	The adjoint solution at time t
[out]	yBdot	the rate at time t

◆ GetAdjointHeight()

int mfem::TimeDependentAdjointOperator::GetAdjointHeight ( )

inline

Returns the size of the adjoint problem state space.

Definition at line 621 of file operator.hpp.

◆ QuadratureIntegration()

virtual void mfem::TimeDependentAdjointOperator::QuadratureIntegration	(	const Vector &	y,
		Vector &	qdot ) const

inlinevirtual

Provide the operator integration of a quadrature equation.

Parameters

[in]	y	The current value at time t
[out]	qdot	The current quadrature rate value at t

Definition at line 553 of file operator.hpp.

◆ QuadratureSensitivityMult()

virtual void mfem::TimeDependentAdjointOperator::QuadratureSensitivityMult	(	const Vector &	y,
		const Vector &	yB,
		Vector &	qBdot ) const

inlinevirtual

Provides the sensitivity of the quadrature w.r.t to primal and adjoint solutions.

Parameters

[in]	y	the value of the primal solution at time t
[in]	yB	the value of the adjoint solution at time t
[out]	qBdot	the value of the sensitivity of the quadrature rate at time t

Definition at line 574 of file operator.hpp.

◆ SUNImplicitSetupB()

virtual int mfem::TimeDependentAdjointOperator::SUNImplicitSetupB	(	const real_t	t,
		const Vector &	x,
		const Vector &	xB,
		const Vector &	fxB,
		int	jokB,
		int *	jcurB,
		real_t	gammaB )

inlinevirtual

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]	t	The current time
[in]	x	The state at which \(A(x,xB,t)\) should be evaluated.
[in]	xB	The state at which \(A(x,xB,t)\) should be evaluated.
[in]	fxB	The current value of the ODE rhs function, \(f(x,t)\).
[in]	jokB	Flag indicating if the Jacobian should be updated.
[out]	jcurB	Flag to signal if the Jacobian was updated.
[in]	gammaB	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 593 of file operator.hpp.

◆ SUNImplicitSolveB()

virtual int mfem::TimeDependentAdjointOperator::SUNImplicitSolveB	(	Vector &	x,
		const Vector &	b,
		real_t	tol )

inlinevirtual

Solve the ODE linear system \( A(x,xB,t) xB = b \) 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 613 of file operator.hpp.

Member Data Documentation

◆ adjoint_height

int mfem::TimeDependentAdjointOperator::adjoint_height

protected

Definition at line 624 of file operator.hpp.

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

linalg/operator.hpp

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ TimeDependentAdjointOperator()

◆ ~TimeDependentAdjointOperator()

Member Function Documentation

◆ AdjointRateMult()

◆ GetAdjointHeight()

◆ QuadratureIntegration()

◆ QuadratureSensitivityMult()

◆ SUNImplicitSetupB()

◆ SUNImplicitSolveB()

Member Data Documentation

◆ adjoint_height