MFEM  v4.0
Finite element discretization library
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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:
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Collaboration diagram for mfem::ComplexOperator:
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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 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...
 
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

OperatorOp_Real_
 
OperatorOp_Imag_
 
bool ownReal_
 
bool ownImag_
 
Convention convention_
 
Vector x_r_
 
Vector x_i_
 
Vector y_r_
 
Vector y_i_
 
Vectoru_
 
Vectorv_
 
- 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

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: