mfem::ComplexOperator Class Reference

Mimic the action of a complex operator using two real operators. More...

#include <complex_operator.hpp>

Inheritance diagram for mfem::ComplexOperator:

Collaboration diagram for mfem::ComplexOperator:

Public Types
enum	Convention { HERMITIAN, BLOCK_SYMMETRIC }
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 }
	Enumeration defining IDs for some classes derived from Operator. More...

Public Member Functions
	ComplexOperator (Operator *Op_Real, Operator *Op_Imag, bool ownReal, bool ownImag, Convention convention=HERMITIAN)
	Constructs complex operator object. More...
virtual	~ComplexOperator ()
virtual void	Mult (const Vector &x, Vector &y) const
	Operator application: y=A(x). 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...
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 MemoryClass	GetMemoryClass () const
	Return the MemoryClass preferred by the Operator. 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...
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...
Type	GetType () const
	Return the type ID of the Operator class. More...

Protected Member Functions
void	Mult (const Vector &x_r, const Vector &x_i, Vector &y_r, Vector &y_i) const
void	MultTranspose (const Vector &x_r, const Vector &x_i, Vector &y_r, Vector &y_i) const

Protected Attributes
Operator *	Op_Real_
Operator *	Op_Imag_
bool	ownReal_
bool	ownImag_
Convention	convention_
Vector	x_r_
Vector	x_i_
Vector	y_r_
Vector	y_i_
Vector *	u_
Vector *	v_
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

Mimic the action of a complex operator using two real operators.

This operator requires vectors that are twice the length of its internally stored real operators, Op_Real and Op_Imag. It is assumed that these vectors store the real part of the vector first followed by its imaginary part.

ComplexOperator allows one to choose a convention upon construction, which facilitates symmetry.

Matrix-vector products are then computed as:

1. When Convention::HERMITIAN is used (default) / y_r \ / Op_r -Op_i \ / x_r \ | | = | | | | \ y_i / \ Op_i Op_r / \ x_i /
2. When Convention::BLOCK_SYMMETRIC is used / y_r \ / Op_r -Op_i \ / x_r \ | | = | | | | -y_i / -Op_i -Op_r / \ x_i /

Either convention can be used with a given complex operator, however, each of them is best suited for certain classes of problems. For example:

1. Convention::HERMITIAN, is well suited for Hermitian operators, i.e. operators where the real part is symmetric and the imaginary part of the operator is anti-symmetric, hence the name. In such cases the resulting 2 x 2 operator will be symmetric.
2. Convention::BLOCK_SYMMETRIC, is well suited for operators where both the real and imaginary parts are symmetric. In this case the resulting 2 x 2 operator will again be symmetric. Such operators are common when studying damped oscillations, for example.

Note: this class cannot be used to represent a general nonlinear complex operator.

Definition at line 59 of file complex_operator.hpp.

Member Enumeration Documentation

enum mfem::ComplexOperator::Convention

Enumerator
HERMITIAN	Native convention for Hermitian operators.
BLOCK_SYMMETRIC	Alternate convention for damping operators.

Definition at line 62 of file complex_operator.hpp.

Constructor & Destructor Documentation

mfem::ComplexOperator::ComplexOperator	(	Operator *	Op_Real,
		Operator *	Op_Imag,
		bool	ownReal,
		bool	ownImag,
		Convention	convention = HERMITIAN
	)

Constructs complex operator object.

Note that either Op_Real or Op_Imag can be NULL, thus eliminating their action (see documentation of the class for more details).

In case ownership of the passed operator is transferred to this class through ownReal and ownImag, the operators will be explicitly destroyed at the end of the life of this object.

Definition at line 17 of file complex_operator.cpp.

mfem::ComplexOperator::~ComplexOperator ( )

virtual

Definition at line 34 of file complex_operator.cpp.

Member Function Documentation

void mfem::ComplexOperator::Mult ( const Vector &  x, Vector &  y  ) const

virtual

Operator application: y=A(x).

Implements mfem::Operator.

Definition at line 42 of file complex_operator.cpp.

void mfem::ComplexOperator::Mult ( const Vector &  x_r, const Vector &  x_i, Vector &  y_r, Vector &  y_i  ) const

protected

Definition at line 54 of file complex_operator.cpp.

void mfem::ComplexOperator::MultTranspose ( const Vector &  x, Vector &  y  ) const

virtual

Action of the transpose operator: y=A^t(x). The default behavior in class Operator is to generate an error.

Reimplemented from mfem::Operator.

Definition at line 82 of file complex_operator.cpp.

void mfem::ComplexOperator::MultTranspose ( const Vector &  x_r, const Vector &  x_i, Vector &  y_r, Vector &  y_i  ) const

protected

Definition at line 94 of file complex_operator.cpp.

Member Data Documentation

Convention mfem::ComplexOperator::convention_

protected

Definition at line 103 of file complex_operator.hpp.

Operator* mfem::ComplexOperator::Op_Imag_

protected

Definition at line 98 of file complex_operator.hpp.

Operator* mfem::ComplexOperator::Op_Real_

protected

Definition at line 97 of file complex_operator.hpp.

bool mfem::ComplexOperator::ownImag_

protected

Definition at line 101 of file complex_operator.hpp.

bool mfem::ComplexOperator::ownReal_

protected

Definition at line 100 of file complex_operator.hpp.

Vector* mfem::ComplexOperator::u_

mutableprotected

Definition at line 106 of file complex_operator.hpp.

Vector * mfem::ComplexOperator::v_

mutableprotected

Definition at line 106 of file complex_operator.hpp.

Vector mfem::ComplexOperator::x_i_

mutableprotected

Definition at line 105 of file complex_operator.hpp.

Vector mfem::ComplexOperator::x_r_

mutableprotected

Definition at line 105 of file complex_operator.hpp.

Vector mfem::ComplexOperator::y_i_

mutableprotected

Definition at line 105 of file complex_operator.hpp.

Vector mfem::ComplexOperator::y_r_

mutableprotected

Definition at line 105 of file complex_operator.hpp.

---

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

• linalg/complex_operator.hpp
• linalg/complex_operator.cpp