MFEM  v4.5.2 Finite element discretization library
FE_Evolution Class Reference

#include <ex18.hpp>

Inheritance diagram for FE_Evolution:
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Collaboration diagram for FE_Evolution:
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## 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_, PrecType prec_type)

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 (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 (ParBilinearForm &M_, ParBilinearForm &K_, const Vector &b_, bool implicit)

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

virtual OperatorGetImplicitGradient (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 (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 ()

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

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

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

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

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

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

Public Types inherited from mfem::TimeDependentOperator
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,
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() 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...

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.

## ◆ FE_Evolution() [1/8]

 FE_Evolution::FE_Evolution ( FiniteElementSpace & vfes_, Operator & A_, SparseMatrix & Aflux_ )

Definition at line 81 of file ex18.hpp.

## ◆ ~FE_Evolution() [1/8]

 FE_Evolution::~FE_Evolution ( )
inlinevirtual

Definition at line 43 of file ex18.hpp.

## ◆ FE_Evolution() [2/8]

 FE_Evolution::FE_Evolution ( BilinearForm & M_, BilinearForm & K_, const Vector & b_ )

Definition at line 452 of file ex9.cpp.

## ◆ ~FE_Evolution() [2/8]

 virtual FE_Evolution::~FE_Evolution ( )
virtual

## ◆ FE_Evolution() [3/8]

 FE_Evolution::FE_Evolution ( ParBilinearForm & M_, ParBilinearForm & K_, const Vector & b_, PrecType prec_type )

Definition at line 656 of file ex9p.cpp.

## ◆ ~FE_Evolution() [3/8]

 virtual FE_Evolution::~FE_Evolution ( )
virtual

## ◆ FE_Evolution() [4/8]

 FE_Evolution::FE_Evolution ( SparseMatrix & M_, SparseMatrix & K_, const Vector & b_, BilinearForm & bf_, Vector & M_rs )

Definition at line 477 of file ex9.cpp.

## ◆ ~FE_Evolution() [4/8]

 virtual FE_Evolution::~FE_Evolution ( )
inlinevirtual

Definition at line 211 of file ex9.cpp.

## ◆ FE_Evolution() [5/8]

 FE_Evolution::FE_Evolution ( HypreParMatrix & M_, HypreParMatrix & K_, const Vector & b_, ParBilinearForm & pbf_, Vector & M_rs )

Definition at line 576 of file ex9p.cpp.

## ◆ ~FE_Evolution() [5/8]

 virtual FE_Evolution::~FE_Evolution ( )
inlinevirtual

Definition at line 236 of file ex9p.cpp.

## ◆ FE_Evolution() [6/8]

 FE_Evolution::FE_Evolution ( ParBilinearForm & M_, ParBilinearForm & K_, const Vector & b_, bool implicit )

Definition at line 521 of file ex9p.cpp.

## ◆ ~FE_Evolution() [6/8]

 virtual FE_Evolution::~FE_Evolution ( )
inlinevirtual

Definition at line 91 of file ex9p.cpp.

## ◆ FE_Evolution() [7/8]

 FE_Evolution::FE_Evolution ( BilinearForm & M_, BilinearForm & K_, const Vector & b_ )

## ◆ ~FE_Evolution() [7/8]

 virtual FE_Evolution::~FE_Evolution ( )
virtual

## ◆ FE_Evolution() [8/8]

 FE_Evolution::FE_Evolution ( ParBilinearForm & M_, ParBilinearForm & K_, const Vector & b_ )

Definition at line 592 of file ex9p.cpp.

## ◆ ~FE_Evolution() [8/8]

 virtual FE_Evolution::~FE_Evolution ( )
virtual

## ◆ ExplicitMult()

 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 566 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 606 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 623 of file ex9p.cpp.

## ◆ ImplicitMult()

 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 584 of file ex9p.cpp.

## ◆ ImplicitSolve() [1/4]

 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.

## ◆ ImplicitSolve() [2/4]

 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 484 of file ex9.cpp.

## ◆ ImplicitSolve() [3/4]

 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.

## ◆ ImplicitSolve() [4/4]

 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.

## ◆ Mult() [1/8]

 void FE_Evolution::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.

Reimplemented from mfem::TimeDependentOperator.

Definition at line 107 of file ex18.hpp.

## ◆ Mult() [2/8]

 virtual void FE_Evolution::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.

Reimplemented from mfem::TimeDependentOperator.

## ◆ Mult() [3/8]

 virtual void FE_Evolution::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.

Reimplemented from mfem::TimeDependentOperator.

## ◆ Mult() [4/8]

 virtual void FE_Evolution::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.

Reimplemented from mfem::TimeDependentOperator.

## ◆ Mult() [5/8]

 virtual void FE_Evolution::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.

Reimplemented from mfem::TimeDependentOperator.

## ◆ Mult() [6/8]

 virtual void FE_Evolution::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.

Reimplemented from mfem::TimeDependentOperator.

## ◆ Mult() [7/8]

 virtual void FE_Evolution::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.

Reimplemented from mfem::TimeDependentOperator.

## ◆ Mult() [8/8]

 virtual void FE_Evolution::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.

Reimplemented from mfem::TimeDependentOperator.

## ◆ SetK() [1/2]

 void FE_Evolution::SetK ( SparseMatrix & K_ )
inline

Definition at line 208 of file ex9.cpp.

## ◆ SetK() [2/2]

 void FE_Evolution::SetK ( HypreParMatrix & K_ )
inline

Definition at line 233 of file ex9p.cpp.

## ◆ SetTimeStep() [1/2]

 void FE_Evolution::SetTimeStep ( double dt_ )
inline

Definition at line 207 of file ex9.cpp.

## ◆ SetTimeStep() [2/2]

 void FE_Evolution::SetTimeStep ( double dt_ )
inline

Definition at line 232 of file ex9p.cpp.

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