MFEM  v4.4.0 Finite element discretization library
mfem::TimeDependentOperator Class Reference

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

#include <operator.hpp>

Inheritance diagram for mfem::TimeDependentOperator:
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Collaboration diagram for mfem::TimeDependentOperator:
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## Public Types

enum  Type { EXPLICIT, IMPLICIT, HOMOGENEOUS }

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
}
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...

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 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 OperatorGetImplicitGradient (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 OperatorGetExplicitGradient (const Vector &x) const
Return an Operator representing dG/dx at the given point x and the currently set time. 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 OperatorGetGradient (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 OperatorGetProlongation () const
Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. NULL means identity. More...

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

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

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

virtual const OperatorGetOutputRestriction () 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...

## Protected Attributes

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...

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...

OperatorSetupRAP (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...

## 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 285 of file operator.hpp.

## Member Enumeration Documentation

Evaluation mode. See SetEvalMode() for details.

Enumerator
NORMAL

Normal evaluation.

Assuming additive split, f(x,t) = f1(x,t) + f2(x,t), evaluate the first term, f1.

Assuming additive split, f(x,t) = f1(x,t) + f2(x,t), evaluate the second term, f2.

Definition at line 296 of file operator.hpp.

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 288 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 316 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 322 of file operator.hpp.

 virtual mfem::TimeDependentOperator::~TimeDependentOperator ( )
inlinevirtual

Definition at line 468 of file operator.hpp.

## Member Function Documentation

 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.

Reimplemented in FE_Evolution.

Definition at line 219 of file operator.cpp.

 EvalMode mfem::TimeDependentOperator::GetEvalMode ( ) const
inline

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

Definition at line 339 of file operator.hpp.

 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.

Reimplemented in FE_Evolution.

Definition at line 249 of file operator.cpp.

 Operator & mfem::TimeDependentOperator::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 in FE_Evolution.

Definition at line 241 of file operator.cpp.

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

Definition at line 326 of file operator.hpp.

 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.

Reimplemented in FE_Evolution.

Definition at line 224 of file operator.cpp.

 void mfem::TimeDependentOperator::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.

Definition at line 235 of file operator.cpp.

 bool mfem::TimeDependentOperator::isExplicit ( ) const
inline

True if type is EXPLICIT.

Definition at line 332 of file operator.hpp.

 bool mfem::TimeDependentOperator::isHomogeneous ( ) const
inline

True if type is HOMOGENEOUS.

Definition at line 336 of file operator.hpp.

 bool mfem::TimeDependentOperator::isImplicit ( ) const
inline

True if type is IMPLICIT or HOMOGENEOUS.

Definition at line 334 of file operator.hpp.

 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.

Definition at line 230 of file operator.cpp.

 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 352 of file operator.hpp.

 virtual void mfem::TimeDependentOperator::SetTime ( const double t_ )
inlinevirtual

Set the current time.

Reimplemented in mfem::electromagnetics::MagneticDiffusionEOperator.

Definition at line 329 of file operator.hpp.

 int mfem::TimeDependentOperator::SUNImplicitSetup ( const Vector & x, const Vector & fx, int jok, int * jcur, double 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 256 of file operator.cpp.

 int mfem::TimeDependentOperator::SUNImplicitSolve ( const Vector & b, Vector & x, double 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 264 of file operator.cpp.

 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 282 of file operator.cpp.

 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 270 of file operator.cpp.

 int mfem::TimeDependentOperator::SUNMassSolve ( const Vector & b, Vector & x, double 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 276 of file operator.cpp.

## Member Data Documentation

 EvalMode mfem::TimeDependentOperator::eval_mode
protected

Current evaluation mode.

Definition at line 311 of file operator.hpp.

 double mfem::TimeDependentOperator::t
protected

Current time.

Definition at line 309 of file operator.hpp.

 Type mfem::TimeDependentOperator::type
protected

Describes the form of the TimeDependentOperator.

Definition at line 310 of file operator.hpp.

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