Solver for the discontinuous Galerkin mass matrix. More...

#include <dgmassinv.hpp>

Inheritance diagram for mfem::DGMassInverse:

Collaboration diagram for mfem::DGMassInverse:

Public Member Functions
	DGMassInverse (FiniteElementSpace &fes_, int btype=BasisType::GaussLegendre)
	Construct the DG inverse mass operator for fes_.

	DGMassInverse (FiniteElementSpace &fes_, Coefficient &coeff, int btype=BasisType::GaussLegendre)
	Construct the DG inverse mass operator for fes_ with Coefficient coeff.

	DGMassInverse (FiniteElementSpace &fes_, Coefficient &coeff, const IntegrationRule &ir, int btype=BasisType::GaussLegendre)
	Construct the DG inverse mass operator for fes_ with Coefficient coeff and IntegrationRule ir.

	DGMassInverse (FiniteElementSpace &fes_, const IntegrationRule &ir, int btype=BasisType::GaussLegendre)
	Construct the DG inverse mass operator for fes_ with IntegrationRule ir.

void	Mult (const Vector &b, Vector &u) const
	Solve the system M b = u.

void	MultTranspose (const Vector &b, Vector &u) const
	Same as Mult() since the mass matrix is symmetric.

void	SetOperator (const Operator &op)
	Not implemented. Aborts.

void	SetRelTol (const real_t rel_tol_)
	Set the relative tolerance.

void	SetAbsTol (const real_t abs_tol_)
	Set the absolute tolerance.

void	SetMaxIter (const real_t max_iter_)
	Set the maximum number of iterations.

void	Update ()
	Recompute operator and preconditioner (when coefficient or mesh changes).

	~DGMassInverse ()

template<int DIM, int D1D = 0, int Q1D = 0>
void	DGMassCGIteration (const Vector &b_, Vector &u_) const
	Solve the system M b = u. Not part of the public interface.

Public Member Functions inherited from mfem::Solver
	Solver (int s=0, bool iter_mode=false)
	Initialize a square Solver with size s.

	Solver (int h, int w, bool iter_mode=false)
	Initialize a Solver with height h and width w.

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	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 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.

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 Operator *	GetProlongation () const
	Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. `NULL` means identity.

virtual const Operator *	GetRestriction () const
	Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. `NULL` means identity.

virtual const Operator *	GetOutputProlongation () const
	Prolongation operator from linear algebra (linear system) vectors, to output vectors for the operator. `NULL` means identity.

virtual const Operator *	GetOutputRestrictionTranspose () const
	Transpose of GetOutputRestriction, directly available in this form to facilitate matrix-free RAP-type operators.

virtual const Operator *	GetOutputRestriction () 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 Member Functions
	DGMassInverse (FiniteElementSpace &fes_, Coefficient coeff, const IntegrationRule ir, int btype)
	Protected constructor, used internally.

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()

Operator *	SetupRAP (const Operator Pi, const Operator Po)
	Returns RAP Operator of this, using input/output Prolongation matrices Pi corresponds to "P", Po corresponds to "Rt".

Protected Attributes
DG_FECollection	fec
	FE collection in requested basis.

FiniteElementSpace	fes
	FE space in requested basis.

const DofToQuad *	d2q
	Change of basis. Not owned.

Array< real_t >	B_
	Inverse of change of basis.

Array< real_t >	Bt_
	Inverse of change of basis, transposed.

class BilinearForm *	M
	Mass bilinear form, owned.

class MassIntegrator *	m
	Mass integrator, owned by the form M.

Vector	diag_inv
	Jacobi preconditioner.

real_t	rel_tol = 1e-12
	Relative CG tolerance.

real_t	abs_tol = 1e-12
	Absolute CG tolerance.

int	max_iter = 100
	Maximum number of CG iterations;.

Intermediate vectors needed for CG three-term recurrence.
Vector	r_

Vector	d_

Vector	z_

Vector	b2_

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...

Public Attributes inherited from mfem::Solver
bool	iterative_mode
	If true, use the second argument of Mult() as an initial guess.

Detailed Description

Solver for the discontinuous Galerkin mass matrix.

This class performs a local (diagonally preconditioned) conjugate gradient iteration for each element. Optionally, a change of basis is performed to iterate on a better-conditioned system. This class fully supports execution on device (GPU).

Definition at line 27 of file dgmassinv.hpp.

Constructor & Destructor Documentation

◆ DGMassInverse() [1/5]

mfem::DGMassInverse::DGMassInverse	(	FiniteElementSpace &	fes_,
		Coefficient *	coeff,
		const IntegrationRule *	ir,
		int	btype )

protected

Protected constructor, used internally.

Custom coefficient and integration rule are used if coeff and ir are non-NULL.

Definition at line 20 of file dgmassinv.cpp.

◆ DGMassInverse() [2/5]

mfem::DGMassInverse::DGMassInverse	(	FiniteElementSpace &	fes_,
		int	btype = BasisType::GaussLegendre )

Construct the DG inverse mass operator for fes_.

The basis type btype determines which basis should be used internally in the solver. This does not have to be the same basis as fes_. The best choice is typically BasisType::GaussLegendre because it is well-preconditioned by its diagonal.

The solution and right-hand side used for the solver are not affected by this basis (they correspond to the basis of fes_). btype is only used internally, and only has an effect on the convergence rate.

Definition at line 92 of file dgmassinv.cpp.

◆ DGMassInverse() [3/5]

mfem::DGMassInverse::DGMassInverse	(	FiniteElementSpace &	fes_,
		Coefficient &	coeff,
		int	btype = BasisType::GaussLegendre )

Construct the DG inverse mass operator for fes_ with Coefficient coeff.

See also: DGMassInverse(FiniteElementSpace&, int) for information about btype.

Definition at line 80 of file dgmassinv.cpp.

◆ DGMassInverse() [4/5]

mfem::DGMassInverse::DGMassInverse	(	FiniteElementSpace &	fes_,
		Coefficient &	coeff,
		const IntegrationRule &	ir,
		int	btype = BasisType::GaussLegendre )

Construct the DG inverse mass operator for fes_ with Coefficient coeff and IntegrationRule ir.

See also: DGMassInverse(FiniteElementSpace&, int) for information about btype.

Definition at line 84 of file dgmassinv.cpp.

◆ DGMassInverse() [5/5]

mfem::DGMassInverse::DGMassInverse	(	FiniteElementSpace &	fes_,
		const IntegrationRule &	ir,
		int	btype = BasisType::GaussLegendre )

Construct the DG inverse mass operator for fes_ with IntegrationRule ir.

See also: DGMassInverse(FiniteElementSpace&, int) for information about btype.

Definition at line 88 of file dgmassinv.cpp.

◆ ~DGMassInverse()

mfem::DGMassInverse::~DGMassInverse ( )

Definition at line 113 of file dgmassinv.cpp.

Member Function Documentation

◆ DGMassCGIteration()

template<int DIM, int D1D, int Q1D>

void mfem::DGMassInverse::DGMassCGIteration	(	const Vector &	b_,
		Vector &	u_ ) const

Solve the system M b = u. Not part of the public interface.

Note: This member function must be public because it defines an extended lambda used in an mfem::forall kernel (nvcc limitation)

Definition at line 119 of file dgmassinv.cpp.

◆ Mult()

void mfem::DGMassInverse::Mult	(	const Vector &	b,
		Vector &	u ) const

virtual

Solve the system M b = u.

If iterative_mode is true, u is used as an initial guess.

Implements mfem::Operator.

Definition at line 263 of file dgmassinv.cpp.

◆ MultTranspose()

void mfem::DGMassInverse::MultTranspose	(	const Vector &	b,
		Vector &	u ) const

inlinevirtual

Same as Mult() since the mass matrix is symmetric.

Reimplemented from mfem::Operator.

Definition at line 91 of file dgmassinv.hpp.

◆ SetAbsTol()

void mfem::DGMassInverse::SetAbsTol ( const real_t abs_tol_ )

Set the absolute tolerance.

Definition at line 102 of file dgmassinv.cpp.

◆ SetMaxIter()

void mfem::DGMassInverse::SetMaxIter ( const real_t max_iter_ )

Set the maximum number of iterations.

Definition at line 104 of file dgmassinv.cpp.

◆ SetOperator()

void mfem::DGMassInverse::SetOperator ( const Operator & op )

virtual

Not implemented. Aborts.

Implements mfem::Solver.

Definition at line 95 of file dgmassinv.cpp.

◆ SetRelTol()

void mfem::DGMassInverse::SetRelTol ( const real_t rel_tol_ )

Set the relative tolerance.

Definition at line 100 of file dgmassinv.cpp.

◆ Update()

void mfem::DGMassInverse::Update ( )

Recompute operator and preconditioner (when coefficient or mesh changes).

Definition at line 106 of file dgmassinv.cpp.

Member Data Documentation

◆ abs_tol

real_t mfem::DGMassInverse::abs_tol = 1e-12

protected

Absolute CG tolerance.

Definition at line 39 of file dgmassinv.hpp.

◆ b2_

Vector mfem::DGMassInverse::b2_

protected

Definition at line 44 of file dgmassinv.hpp.

◆ B_

Array<real_t> mfem::DGMassInverse::B_

protected

Inverse of change of basis.

Definition at line 33 of file dgmassinv.hpp.

◆ Bt_

Array<real_t> mfem::DGMassInverse::Bt_

protected

Inverse of change of basis, transposed.

Definition at line 34 of file dgmassinv.hpp.

◆ d2q

const DofToQuad* mfem::DGMassInverse::d2q

protected

Change of basis. Not owned.

Definition at line 32 of file dgmassinv.hpp.

◆ d_

Vector mfem::DGMassInverse::d_

protected

Definition at line 44 of file dgmassinv.hpp.

◆ diag_inv

Vector mfem::DGMassInverse::diag_inv

protected

Jacobi preconditioner.

Definition at line 37 of file dgmassinv.hpp.

◆ fec

DG_FECollection mfem::DGMassInverse::fec

protected

FE collection in requested basis.

Definition at line 30 of file dgmassinv.hpp.

◆ fes

FiniteElementSpace mfem::DGMassInverse::fes

protected

FE space in requested basis.

Definition at line 31 of file dgmassinv.hpp.

◆ M

class BilinearForm* mfem::DGMassInverse::M

protected

Mass bilinear form, owned.

Definition at line 35 of file dgmassinv.hpp.

◆ m

class MassIntegrator* mfem::DGMassInverse::m

protected

Mass integrator, owned by the form M.

Definition at line 36 of file dgmassinv.hpp.

◆ max_iter

int mfem::DGMassInverse::max_iter = 100

protected

Maximum number of CG iterations;.

Definition at line 40 of file dgmassinv.hpp.

◆ r_

Vector mfem::DGMassInverse::r_

mutableprotected

Definition at line 44 of file dgmassinv.hpp.

◆ rel_tol

real_t mfem::DGMassInverse::rel_tol = 1e-12

protected

Relative CG tolerance.

Definition at line 38 of file dgmassinv.hpp.

◆ z_

Vector mfem::DGMassInverse::z_

protected

Definition at line 44 of file dgmassinv.hpp.

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

fem/dgmassinv.hpp
fem/dgmassinv.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ DGMassInverse() [1/5]

◆ DGMassInverse() [2/5]

◆ DGMassInverse() [3/5]

◆ DGMassInverse() [4/5]

◆ DGMassInverse() [5/5]

◆ ~DGMassInverse()

Member Function Documentation

◆ DGMassCGIteration()

◆ Mult()

◆ MultTranspose()

◆ SetAbsTol()

◆ SetMaxIter()

◆ SetOperator()

◆ SetRelTol()

◆ Update()

Member Data Documentation

◆ abs_tol

◆ b2_

◆ B_

◆ Bt_

◆ d2q

◆ d_

◆ diag_inv

◆ fec

◆ fes

◆ M

◆ m

◆ max_iter

◆ r_

◆ rel_tol

◆ z_