MFEM  v4.1.0 Finite element discretization library
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, Complex_Operator, MFEM_ComplexSparseMat, Complex_Hypre_ParCSR
}
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 ()

bool hasRealPart () const
Check for existence of real or imaginary part of the operator. More...

bool hasImagPart () const

virtual Operatorreal ()
Real or imaginary part accessor methods. More...

virtual Operatorimag ()

virtual const Operatorreal () const

virtual const Operatorimag () const

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...

virtual Type GetType () const

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 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...

virtual const OperatorGetOutputProlongation () const
Prolongation operator from linear algebra (linear system) vectors, to output vectors for the operator. NULL means identity. 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=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 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, taking in input/output Prolongation matrices. More...

## 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.

If we let (y_r + i y_i) = (Op_r + i Op_i)(x_r + i x_i) then Matrix-vector products are 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 / In other words, Matrix-vector products with Convention::BLOCK_SYMMETRIC compute the complex conjugate of Op*x.

Either convention can be used with a given complex operator, however, each of them may be best suited for different 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 also 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 64 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 67 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 39 of file complex_operator.cpp.

 mfem::ComplexOperator::~ComplexOperator ( )
virtual

Definition at line 57 of file complex_operator.cpp.

## Member Function Documentation

 virtual Type mfem::ComplexOperator::GetType ( ) const
inlinevirtual

Reimplemented in mfem::ComplexHypreParMatrix, and mfem::ComplexSparseMatrix.

Definition at line 110 of file complex_operator.hpp.

 bool mfem::ComplexOperator::hasImagPart ( ) const
inline

Definition at line 94 of file complex_operator.hpp.

 bool mfem::ComplexOperator::hasRealPart ( ) const
inline

Check for existence of real or imaginary part of the operator.

These methods do not check that the operators are non-zero but only that the operators have been set.

Definition at line 93 of file complex_operator.hpp.

 Operator & mfem::ComplexOperator::imag ( )
virtual

Reimplemented in mfem::ComplexHypreParMatrix, and mfem::ComplexSparseMatrix.

Definition at line 71 of file complex_operator.cpp.

 const Operator & mfem::ComplexOperator::imag ( ) const
virtual

Reimplemented in mfem::ComplexHypreParMatrix, and mfem::ComplexSparseMatrix.

Definition at line 83 of file complex_operator.cpp.

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

Operator application: y=A(x).

Implements mfem::Operator.

Definition at line 89 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 101 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 129 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 141 of file complex_operator.cpp.

 Operator & mfem::ComplexOperator::real ( )
virtual

Real or imaginary part accessor methods.

The following accessor methods should only be called if the requested part of the opertor is known to exist. This can be checked with hasRealPart() or hasImagPart().

Reimplemented in mfem::ComplexHypreParMatrix, and mfem::ComplexSparseMatrix.

Definition at line 65 of file complex_operator.cpp.

 const Operator & mfem::ComplexOperator::real ( ) const
virtual

Reimplemented in mfem::ComplexHypreParMatrix, and mfem::ComplexSparseMatrix.

Definition at line 77 of file complex_operator.cpp.

## Member Data Documentation

 Convention mfem::ComplexOperator::convention_
protected

Definition at line 127 of file complex_operator.hpp.

 Operator* mfem::ComplexOperator::Op_Imag_
protected

Definition at line 122 of file complex_operator.hpp.

 Operator* mfem::ComplexOperator::Op_Real_
protected

Definition at line 121 of file complex_operator.hpp.

 bool mfem::ComplexOperator::ownImag_
protected

Definition at line 125 of file complex_operator.hpp.

 bool mfem::ComplexOperator::ownReal_
protected

Definition at line 124 of file complex_operator.hpp.

 Vector* mfem::ComplexOperator::u_
mutableprotected

Definition at line 130 of file complex_operator.hpp.

 Vector * mfem::ComplexOperator::v_
mutableprotected

Definition at line 130 of file complex_operator.hpp.

 Vector mfem::ComplexOperator::x_i_
mutableprotected

Definition at line 129 of file complex_operator.hpp.

 Vector mfem::ComplexOperator::x_r_
mutableprotected

Definition at line 129 of file complex_operator.hpp.

 Vector mfem::ComplexOperator::y_i_
mutableprotected

Definition at line 129 of file complex_operator.hpp.

 Vector mfem::ComplexOperator::y_r_
mutableprotected

Definition at line 129 of file complex_operator.hpp.

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