MFEM v4.7.0
Finite element discretization library
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Public Member Functions | Protected Attributes | List of all members
mfem::ConstrainedOperator Class Reference

Square Operator for imposing essential boundary conditions using only the action, Mult(), of a given unconstrained Operator. More...

#include <operator.hpp>

Inheritance diagram for mfem::ConstrainedOperator:
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Collaboration diagram for mfem::ConstrainedOperator:
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Public Member Functions

 ConstrainedOperator (Operator *A, const Array< int > &list, bool own_A=false, DiagonalPolicy diag_policy=DIAG_ONE)
 Constructor from a general Operator and a list of essential indices/dofs.
 
MemoryClass GetMemoryClass () const override
 Returns the type of memory in which the solution and temporaries are stored.
 
void SetDiagonalPolicy (const DiagonalPolicy diag_policy_)
 Set the diagonal policy for the constrained operator.
 
void AssembleDiagonal (Vector &diag) const override
 Diagonal of A, modified according to the used DiagonalPolicy.
 
void EliminateRHS (const Vector &x, Vector &b) const
 Eliminate "essential boundary condition" values specified in x from the given right-hand side b.
 
void Mult (const Vector &x, Vector &y) const override
 Constrained operator action.
 
void AddMult (const Vector &x, Vector &y, const real_t a=1.0) const override
 Operator application: y+=A(x) (default) or y+=a*A(x).
 
void MultTranspose (const Vector &x, Vector &y) const override
 Action of the transpose operator: y=A^t(x). The default behavior in class Operator is to generate an error.
 
void ConstrainedMult (const Vector &x, Vector &y, const bool transpose) const
 Implementation of Mult or MultTranspose. TODO - Generalize to allow constraining rows and columns differently.
 
 ~ConstrainedOperator () override
 Destructor: destroys the unconstrained Operator, if owned.
 
- 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.
 
 Operator (int s=0)
 Construct a square Operator with given size s (default 0).
 
 Operator (int h, int w)
 Construct an Operator with the given height (output size) and width (input size).
 
int Height () const
 Get the height (size of output) of the Operator. Synonym with NumRows().
 
int NumRows () const
 Get the number of rows (size of output) of the Operator. Synonym with Height().
 
int Width () const
 Get the width (size of input) of the Operator. Synonym with NumCols().
 
int NumCols () const
 Get the number of columns (size of input) of the Operator. Synonym with Width().
 
virtual MemoryClass GetMemoryClass () const
 Return the MemoryClass preferred by the Operator.
 
virtual void Mult (const Vector &x, Vector &y) const =0
 Operator application: y=A(x).
 
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.
 
virtual void AddMult (const Vector &x, Vector &y, const real_t a=1.0) const
 Operator application: y+=A(x) (default) or y+=a*A(x).
 
virtual void AddMultTranspose (const Vector &x, Vector &y, const real_t a=1.0) const
 Operator transpose application: y+=A^t(x) (default) or y+=a*A^t(x).
 
virtual void ArrayMult (const Array< const Vector * > &X, Array< Vector * > &Y) const
 Operator application on a matrix: Y=A(X).
 
virtual void ArrayMultTranspose (const Array< const Vector * > &X, Array< Vector * > &Y) const
 Action of the transpose operator on a matrix: Y=A^t(X).
 
virtual void ArrayAddMult (const Array< const Vector * > &X, Array< Vector * > &Y, const real_t a=1.0) const
 Operator application on a matrix: Y+=A(X) (default) or Y+=a*A(X).
 
virtual void ArrayAddMultTranspose (const Array< const Vector * > &X, Array< Vector * > &Y, const real_t a=1.0) const
 Operator transpose application on a matrix: Y+=A^t(X) (default) or Y+=a*A^t(X).
 
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.
 
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.
 
virtual const OperatorGetProlongation () const
 Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. NULL means identity.
 
virtual const OperatorGetRestriction () const
 Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. NULL means identity.
 
virtual const OperatorGetOutputProlongation () const
 Prolongation operator from linear algebra (linear system) vectors, to output vectors for the operator. NULL means identity.
 
virtual const OperatorGetOutputRestrictionTranspose () const
 Transpose of GetOutputRestriction, directly available in this form to facilitate matrix-free RAP-type operators.
 
virtual const OperatorGetOutputRestriction () const
 Restriction operator from output vectors for the operator to linear algebra (linear system) vectors. NULL means identity.
 
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.
 
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.
 
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().
 
void FormSystemOperator (const Array< int > &ess_tdof_list, Operator *&A)
 Return in A a parallel (on truedofs) version of this square operator.
 
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).
 
void FormDiscreteOperator (Operator *&A)
 Return in A a parallel (on truedofs) version of this rectangular operator.
 
void PrintMatlab (std::ostream &out, int n, int m=0) const
 Prints operator with input size n and output size m in Matlab format.
 
virtual void PrintMatlab (std::ostream &out) const
 Prints operator in Matlab format.
 
virtual ~Operator ()
 Virtual destructor.
 
Type GetType () const
 Return the type ID of the Operator class.
 

Protected Attributes

Array< int > constraint_list
 List of constrained indices/dofs.
 
OperatorA
 The unconstrained Operator.
 
bool own_A
 Ownership flag for A.
 
Vector z
 
Vector w
 Auxiliary vectors.
 
MemoryClass mem_class
 
DiagonalPolicy diag_policy
 Diagonal policy for constrained dofs.
 
- Protected Attributes inherited from mfem::Operator
int height
 Dimension of the output / number of rows in the matrix.
 
int width
 Dimension of the input / number of columns in the matrix.
 

Additional Inherited Members

- 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()
 
void FormRectangularConstrainedSystemOperator (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, RectangularConstrainedOperator *&Aout)
 see FormRectangularSystemOperator()
 
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".
 

Detailed Description

Square Operator for imposing essential boundary conditions using only the action, Mult(), of a given unconstrained Operator.

Square operator constrained by fixing certain entries in the solution to given "essential boundary condition" values. This class is used by the general, matrix-free system formulation of Operator::FormLinearSystem.

Do not confuse with ConstrainedSolver, which despite the name has very different functionality.

Definition at line 894 of file operator.hpp.

Constructor & Destructor Documentation

◆ ConstrainedOperator()

mfem::ConstrainedOperator::ConstrainedOperator ( Operator A,
const Array< int > &  list,
bool  own_A = false,
DiagonalPolicy  diag_policy = DIAG_ONE 
)

Constructor from a general Operator and a list of essential indices/dofs.

Specify the unconstrained operator *A and a list of indices to constrain, i.e. each entry list[i] represents an essential dof. If the ownership flag own_A is true, the operator *A will be destroyed when this object is destroyed. The diag_policy determines how the operator sets entries corresponding to essential dofs.

Definition at line 511 of file operator.cpp.

◆ ~ConstrainedOperator()

mfem::ConstrainedOperator::~ConstrainedOperator ( )
inlineoverride

Destructor: destroys the unconstrained Operator, if owned.

Definition at line 959 of file operator.hpp.

Member Function Documentation

◆ AddMult()

void mfem::ConstrainedOperator::AddMult ( const Vector x,
Vector y,
const real_t  a = 1.0 
) const
overridevirtual

Operator application: y+=A(x) (default) or y+=a*A(x).

Reimplemented from mfem::Operator.

Definition at line 660 of file operator.cpp.

◆ AssembleDiagonal()

void mfem::ConstrainedOperator::AssembleDiagonal ( Vector diag) const
overridevirtual

Diagonal of A, modified according to the used DiagonalPolicy.

Reimplemented from mfem::Operator.

Definition at line 528 of file operator.cpp.

◆ ConstrainedMult()

void mfem::ConstrainedOperator::ConstrainedMult ( const Vector x,
Vector y,
const bool  transpose 
) const

Implementation of Mult or MultTranspose. TODO - Generalize to allow constraining rows and columns differently.

Definition at line 586 of file operator.cpp.

◆ EliminateRHS()

void mfem::ConstrainedOperator::EliminateRHS ( const Vector x,
Vector b 
) const

Eliminate "essential boundary condition" values specified in x from the given right-hand side b.

Performs the following steps:

z = A((0,x_b));  b_i -= z_i;  b_b = x_b;

where the "_b" subscripts denote the essential (boundary) indices/dofs of the vectors, and "_i" – the rest of the entries.

Note
This method is consistent with DiagonalPolicy::DIAG_ONE.

Definition at line 559 of file operator.cpp.

◆ GetMemoryClass()

MemoryClass mfem::ConstrainedOperator::GetMemoryClass ( ) const
inlineoverridevirtual

Returns the type of memory in which the solution and temporaries are stored.

Reimplemented from mfem::Operator.

Definition at line 917 of file operator.hpp.

◆ Mult()

void mfem::ConstrainedOperator::Mult ( const Vector x,
Vector y 
) const
overridevirtual

Constrained operator action.

Performs the following steps:

z = A((x_i,0));  y_i = z_i;  y_b = x_b;

where the "_b" subscripts denote the essential (boundary) indices/dofs of the vectors, and "_i" – the rest of the entries.

Implements mfem::Operator.

Definition at line 648 of file operator.cpp.

◆ MultTranspose()

void mfem::ConstrainedOperator::MultTranspose ( const Vector x,
Vector y 
) const
overridevirtual

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 654 of file operator.cpp.

◆ SetDiagonalPolicy()

void mfem::ConstrainedOperator::SetDiagonalPolicy ( const DiagonalPolicy  diag_policy_)
inline

Set the diagonal policy for the constrained operator.

Definition at line 920 of file operator.hpp.

Member Data Documentation

◆ A

Operator* mfem::ConstrainedOperator::A
protected

The unconstrained Operator.

Definition at line 898 of file operator.hpp.

◆ constraint_list

Array<int> mfem::ConstrainedOperator::constraint_list
protected

List of constrained indices/dofs.

Definition at line 897 of file operator.hpp.

◆ diag_policy

DiagonalPolicy mfem::ConstrainedOperator::diag_policy
protected

Diagonal policy for constrained dofs.

Definition at line 902 of file operator.hpp.

◆ mem_class

MemoryClass mfem::ConstrainedOperator::mem_class
protected

Definition at line 901 of file operator.hpp.

◆ own_A

bool mfem::ConstrainedOperator::own_A
protected

Ownership flag for A.

Definition at line 899 of file operator.hpp.

◆ w

Vector mfem::ConstrainedOperator::w
protected

Auxiliary vectors.

Definition at line 900 of file operator.hpp.

◆ z

Vector mfem::ConstrainedOperator::z
mutableprotected

Definition at line 900 of file operator.hpp.


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