MFEM  v3.3.2 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 (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 ()

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 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 (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...

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 ~TimeDependentOperator () Public Member Functions inherited from mfem::Operator
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 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 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...

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...

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(). 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... Public Types inherited from mfem::TimeDependentOperator
enum  Type { EXPLICIT, IMPLICIT, HOMOGENEOUS } Public Types inherited from mfem::Operator
enum  Type {
MFEM_SPARSEMAT, Hypre_ParCSR, PETSC_MATAIJ, PETSC_MATIS,
PETSC_MATSHELL, PETSC_MATNEST, PETSC_MATHYPRE, PETSC_MATGENERIC
}
Enumeration defining IDs for some classes derived from Operator. More... Protected Attributes inherited from mfem::TimeDependentOperator
double t
Current time. More...

Type type
Describes the form of the TimeDependentOperator. 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.

 virtual FE_Evolution::~FE_Evolution ( )
inlinevirtual

Definition at line 43 of file ex18.hpp.

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

Definition at line 316 of file ex9.cpp.

 virtual FE_Evolution::~FE_Evolution ( )
inlinevirtual

Definition at line 75 of file ex9.cpp.

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

Definition at line 385 of file ex9p.cpp.

 virtual FE_Evolution::~FE_Evolution ( )
inlinevirtual

Definition at line 74 of file ex9p.cpp.

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

Definition at line 492 of file petsc/ex9p.cpp.

 virtual FE_Evolution::~FE_Evolution ( )
inlinevirtual

Definition at line 89 of file petsc/ex9p.cpp.

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

Definition at line 77 of file sundials/ex9.cpp.

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

Definition at line 76 of file sundials/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 petsc/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 petsc/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 petsc/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 petsc/ex9p.cpp.

 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 130 of file ex18.hpp.

 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.

 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.

 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.

 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.

 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.

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