MFEM
v3.4
Finite element discretization library
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Abstract operator. More...
#include <operator.hpp>
Inherited by mfem::BlockNonlinearForm, mfem::BlockOperator, mfem::ComplexOperator, mfem::ConformingProlongationOperator, mfem::ConstrainedOperator, mfem::FiniteElementSpace::RefinementOperator, mfem::HypreParMatrix, mfem::IdentityOperator, mfem::Matrix, mfem::miniapps::IrrotationalProjector, mfem::NonlinearForm, mfem::PetscParMatrix, mfem::ProductOperator, mfem::RAPOperator, mfem::Solver, mfem::STRUMPACKRowLocMatrix, mfem::SuperLURowLocMatrix, mfem::TBilinearForm< meshType, solFESpace, IR, IntegratorType, solVecLayout_t, complex_t, real_t >, mfem::TimeDependentOperator, mfem::TransposeOperator, mfem::TripleProductOperator, ReducedSystemOperator, ReducedSystemOperator, ReducedSystemOperator, ReducedSystemOperator, ReducedSystemOperator, RubberOperator, and RubberOperator.
Public Types | |
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 | |
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 | Mult (const Vector &x, Vector &y) const =0 |
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 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 Attributes | |
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... | |
Abstract operator.
Definition at line 21 of file operator.hpp.
enum mfem::Operator::Type |
Enumeration defining IDs for some classes derived from Operator.
This enumeration is primarily used with class OperatorHandle.
Enumerator | |
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ANY_TYPE |
ID for the base class Operator, i.e. any type. |
MFEM_SPARSEMAT |
ID for class SparseMatrix. |
Hypre_ParCSR |
ID for class HypreParMatrix. |
PETSC_MATAIJ |
ID for class PetscParMatrix, MATAIJ format. |
PETSC_MATIS |
ID for class PetscParMatrix, MATIS format. |
PETSC_MATSHELL |
ID for class PetscParMatrix, MATSHELL format. |
PETSC_MATNEST |
ID for class PetscParMatrix, MATNEST format. |
PETSC_MATHYPRE |
ID for class PetscParMatrix, MATHYPRE format. |
PETSC_MATGENERIC |
ID for class PetscParMatrix, unspecified format. |
Definition at line 124 of file operator.hpp.
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inlineexplicit |
Construct a square Operator with given size s (default 0).
Definition at line 29 of file operator.hpp.
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inline |
Construct an Operator with the given height (output size) and width (input size).
Definition at line 33 of file operator.hpp.
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inlinevirtual |
Virtual destructor.
Definition at line 120 of file operator.hpp.
void mfem::Operator::FormLinearSystem | ( | const Array< int > & | ess_tdof_list, |
Vector & | x, | ||
Vector & | b, | ||
Operator *& | A, | ||
Vector & | X, | ||
Vector & | B, | ||
int | copy_interior = 0 |
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) |
Form a constrained linear system using a matrix-free approach.
Assuming square operator, form the operator linear system A(X)=B
, corresponding to it and the right-hand side b, by applying any necessary transformations such as: parallel assembly, conforming constraints for non-conforming AMR and eliminating boundary conditions.
The constraints are specified through the prolongation P from GetProlongation(), and restriction R from GetRestriction() methods, which are e.g. available through the (parallel) finite element space of any (parallel) bilinear form operator. We assume that the operator is square, using the same input and output space, so we have: A(X)=[P^t (*this) P](X)
, B=P^t(b)
, and x=P(X)
.
The vector x must contain the essential boundary condition values. These are eliminated through the ConstrainedOperator class and the vector X is initialized by setting its essential entries to the boundary conditions and all other entries to zero (copy_interior == 0) or copied from x (copy_interior != 0).
After solving the system A(X)=B
, the (finite element) solution x can be recovered by calling Operator::RecoverFEMSolution() with the same vectors X, b, and x.
Definition at line 21 of file operator.cpp.
Evaluate the gradient operator at the point x. The default behavior in class Operator is to generate an error.
Reimplemented in mfem::BlockNonlinearForm, mfem::NonlinearForm, mfem::ParBlockNonlinearForm, and mfem::ParNonlinearForm.
Definition at line 57 of file operator.hpp.
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inlinevirtual |
Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. NULL
means identity.
Reimplemented in mfem::BilinearForm, mfem::NonlinearForm, mfem::ParBilinearForm, and mfem::TBilinearForm< meshType, solFESpace, IR, IntegratorType, solVecLayout_t, complex_t, real_t >.
Definition at line 65 of file operator.hpp.
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inlinevirtual |
Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. NULL
means identity.
Reimplemented in mfem::BilinearForm, mfem::NonlinearForm, mfem::ParBilinearForm, and mfem::TBilinearForm< meshType, solFESpace, IR, IntegratorType, solVecLayout_t, complex_t, real_t >.
Definition at line 68 of file operator.hpp.
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inline |
Return the type ID of the Operator class.
This method is intentionally non-virtual, so that it returns the ID of the specific pointer or reference type used when calling this method. If not overridden by derived classes, they will automatically use the type ID of the base Operator class, ANY_TYPE.
Definition at line 142 of file operator.hpp.
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inline |
Get the height (size of output) of the Operator. Synonym with NumRows().
Definition at line 36 of file operator.hpp.
Operator application: y=A(x)
.
Implemented in mfem::HypreSolver, mfem::PetscNonlinearSolver, mfem::HypreSmoother, mfem::DenseMatrixInverse, mfem::PetscPreconditioner, mfem::PetscLinearSolver, mfem::ConstrainedOperator, mfem::MixedBilinearForm, mfem::KLUSolver, mfem::HypreParMatrix, mfem::KinSolver, mfem::TripleProductOperator, mfem::UMFPackSolver, mfem::ConformingProlongationOperator, mfem::RAPOperator, mfem::ProductOperator, mfem::SLBQPOptimizer, mfem::TransposeOperator, mfem::IdentityOperator, mfem::NewtonSolver, mfem::BlockLowerTriangularPreconditioner, mfem::BlockNonlinearForm, mfem::MINRESSolver, mfem::PetscParMatrix, mfem::TimeDependentOperator, mfem::BiCGSTABSolver, mfem::electromagnetics::MagneticDiffusionEOperator, mfem::SparseMatrix, mfem::miniapps::DivergenceFreeProjector, mfem::FGMRESSolver, mfem::BilinearForm, mfem::BlockDiagonalPreconditioner, mfem::GMRESSolver, mfem::FiniteElementSpace::RefinementOperator, mfem::miniapps::IrrotationalProjector, mfem::CGSolver, mfem::NonlinearForm, mfem::BlockMatrix, mfem::DenseMatrix, mfem::TBilinearForm< meshType, solFESpace, IR, IntegratorType, solVecLayout_t, complex_t, real_t >, mfem::ParBlockNonlinearForm, mfem::AbstractSparseMatrix, mfem::SuperLUSolver, mfem::SLISolver, mfem::BlockOperator, mfem::ComplexOperator, FE_Evolution, mfem::STRUMPACKSolver, FE_Evolution, FE_Evolution, mfem::DSmoother, FE_Evolution, FE_Evolution, mfem::SuperLURowLocMatrix, mfem::electromagnetics::MaxwellSolver, mfem::ParNonlinearForm, mfem::GSSmoother, mfem::STRUMPACKRowLocMatrix, and FE_Evolution.
Action of the transpose operator: y=A^t(x)
. The default behavior in class Operator is to generate an error.
Reimplemented in mfem::MixedBilinearForm, mfem::KLUSolver, mfem::HypreParMatrix, mfem::TripleProductOperator, mfem::UMFPackSolver, mfem::ConformingProlongationOperator, mfem::RAPOperator, mfem::ProductOperator, mfem::TransposeOperator, mfem::BlockLowerTriangularPreconditioner, mfem::PetscParMatrix, mfem::SparseMatrix, mfem::BilinearForm, mfem::BlockDiagonalPreconditioner, mfem::BlockMatrix, mfem::DenseMatrix, mfem::AbstractSparseMatrix, mfem::BlockOperator, and mfem::ComplexOperator.
Definition at line 52 of file operator.hpp.
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inline |
Get the number of columns (size of input) of the Operator. Synonym with Width().
Definition at line 45 of file operator.hpp.
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inline |
Get the number of rows (size of output) of the Operator. Synonym with Height().
Definition at line 39 of file operator.hpp.
void mfem::Operator::PrintMatlab | ( | std::ostream & | out, |
int | n = 0 , |
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int | m = 0 |
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) | const |
Prints operator with input size n and output size m in Matlab format.
Definition at line 72 of file operator.cpp.
Reconstruct a solution vector x (e.g. a GridFunction) from the solution X of a constrained linear system obtained from Operator::FormLinearSystem().
Call this method after solving a linear system constructed using Operator::FormLinearSystem() to recover the solution as an input vector, x, for this Operator (presumably a finite element grid function). This method has identical signature to the analogous method for bilinear forms, though currently b is not used in the implementation.
Reimplemented in mfem::BilinearForm, and mfem::ParBilinearForm.
Definition at line 57 of file operator.cpp.
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inline |
Get the width (size of input) of the Operator. Synonym with NumCols().
Definition at line 42 of file operator.hpp.
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protected |
Dimension of the output / number of rows in the matrix.
Definition at line 24 of file operator.hpp.
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protected |
Dimension of the input / number of columns in the matrix.
Definition at line 25 of file operator.hpp.