Iterative Solvers supporting block recursive matrix and vector classes at compile time. More...

Modules
	Sparse Matrix and Vector classes
	Matrix and Vector classes that support a block recursive structure capable of representing the natural structure from Finite Element discretisations.

	Iterative Solvers

Files
file	superlu.hh
	Classes for using SuperLU with ISTL matrices.

file	umfpack.hh
	Classes for using UMFPack with ISTL matrices.

Classes
class	Dune::ILUSubdomainSolver< M, X, Y >
	base class encapsulating common algorithms of ILU0SubdomainSolver and ILUNSubdomainSolver. More...

class	Dune::ILU0SubdomainSolver< M, X, Y >
	Exact subdomain solver using ILU(p) with appropriate p. More...

class	Dune::ISTLError
	derive error class from the base class in common More...

class	Dune::BCRSMatrixError
	Error specific to BCRSMatrix. More...

class	Dune::ImplicitModeOverflowExhausted
	The overflow error used during implicit BCRSMatrix construction was exhausted. More...

class	Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >
	Sequential overlapping Schwarz preconditioner. More...

class	Dune::SuperLU< BCRSMatrix< FieldMatrix< T, n, m >, A > >
	SuperLu Solver. More...

class	Dune::UMFPack< Matrix >
	Use the UMFPack package to directly solve linear systems – empty default class. More...

class	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >
	The UMFPack direct sparse solver for matrices of type BCRSMatrix. More...

Typedefs
typedef Dune::BCRSMatrix< FieldMatrix< T, n, m >, A >	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::Matrix
	The matrix type.

typedef Dune::ColCompMatrix< Matrix >	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::UMFPackMatrix
	The corresponding SuperLU Matrix type.

typedef ColCompMatrixInitializer< BCRSMatrix< FieldMatrix< T, n, m >, A > >	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::MatrixInitializer
	Type of an associated initializer class.

typedef Dune::BlockVector< FieldVector< T, m >, typename A::template rebind< FieldVector< T, m > >::other >	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::domain_type
	The type of the domain of the solver.

typedef Dune::BlockVector< FieldVector< T, n >, typename A::template rebind< FieldVector< T, n > >::other >	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::range_type
	The type of the range of the solver.

Functions
	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::UMFPack (const Matrix &matrix, int verbose=0)
	Construct a solver object from a BCRSMatrix. More...

	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::UMFPack (const Matrix &matrix, int verbose, bool)
	Constructor for compatibility with SuperLU standard constructor. More...

	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::UMFPack ()
	default constructor

	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::UMFPack (const Matrix &mat_, const char *file, int verbose=0)
	Try loading a decomposition from file and do a decomposition if unsuccessful. More...

	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::UMFPack (const char *file, int verbose=0)
	try loading a decomposition from file More...

virtual void	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::apply (domain_type &x, range_type &b, InverseOperatorResult &res)
	Apply inverse operator,. More...

virtual void	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::apply (domain_type &x, range_type &b, double reduction, InverseOperatorResult &res)
	apply inverse operator, with given convergence criteria. More...

void	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::apply (T x, T b)
	additional apply method with c-arrays in analogy to superlu More...

void	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::setOption (unsigned int option, double value)
	Set UMFPack-specific options. More...

void	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::saveDecomposition (const char *file)
	saves a decomposition to a file More...

void	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::setMatrix (const Matrix &matrix)
	Initialize data from given matrix.

void	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::setVerbosity (int v)
	sets the verbosity level for the UMFPack solver More...

void	Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::free ()
	free allocated space. More...

template<class S >
std::size_t	Dune::ILUSubdomainSolver< M, X, Y >::copyToLocalMatrix (const M &A, S &rowset)
	Copy the local part of the global matrix to ILU. More...

template<class S >
void	Dune::ILU0SubdomainSolver< M, X, Y >::setSubMatrix (const M &A, S &rowset)
	Set the data of the local problem. More...

template<class S >
void	Dune::ILUNSubdomainSolver< M, X, Y >::setSubMatrix (const M &A, S &rowset)
	Set the data of the local problem. More...

void	Dune::SuperLU< BCRSMatrix< FieldMatrix< T, n, m >, A > >::free ()
	free allocated space. More...

	Dune::SuperLU< BCRSMatrix< FieldMatrix< T, n, m >, A > >::SuperLU (const Matrix &mat, bool verbose=false, bool reusevector=true)
	Constructs the SuperLU solver. More...

	Dune::SuperLU< BCRSMatrix< FieldMatrix< T, n, m >, A > >::SuperLU ()
	Empty default constructor. More...

void	Dune::SuperLU< BCRSMatrix< FieldMatrix< T, n, m >, A > >::setMatrix (const Matrix &mat)
	Initialize data from given matrix.

void	Dune::SuperLU< BCRSMatrix< FieldMatrix< T, n, m >, A > >::apply (domain_type &x, range_type &b, InverseOperatorResult &res)
	Apply inverse operator,. More...

void	Dune::SuperLU< BCRSMatrix< FieldMatrix< T, n, m >, A > >::apply (T x, T b)
	Apply SuperLu to C arrays.

Detailed Description

Iterative Solvers supporting block recursive matrix and vector classes at compile time.

The Iterative Solver Template Library applies generic programming in C++ to the domain of iterative solvers of linear systems stemming from finite element discretizations. Those discretizations exhibit a lot of structure, e.g:

Certain discretizations for systems of PDEs or higher order methods result in matrices where individual entries are replaced by small blocks, say of size \(2\times 2\) or \(4\times 4\). Dense blocks of different sizes e.g. arise in \(hp\) Discontinuous Galerkin discretization methods. It is straightforward and efficient to treat these small dense blocks as fully coupled and solve them with direct methods within the iterative method.
Equation-wise ordering for systems results in matrices having an \(n\times n\) block structure where \(n\) corresponds to the number of variables in the PDE and the blocks themselves are large and sparse. As an example we mention the Stokes system.
Other discretisation, e.~g. those of reaction/diffusion systems, produce sparse matrices whose blocks are sparse matrices of small dense blocks,

Our matrix and vector interface supports a block recursive structure. Each sparse matrix entry can itself be either a sparse or a small dense matrix.

The solvers use this recursive block structure via template meta programming at compile time.

ISTL consists of the matrix and vector API and the solvers which use the Preconditioners preconditioners.

Function Documentation

◆ apply() [1/4]

template<typename T , typename A , int n, int m>

virtual void Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::apply	(	domain_type &	x,
		range_type &	b,
		double	reduction,
		InverseOperatorResult &	res
	)

inlinevirtual

apply inverse operator, with given convergence criteria.

Warning: Right hand side b may be overwritten!

Parameters

x	The left hand side to store the result in.
b	The right hand side
reduction	The minimum defect reduction to achieve.
res	Object to store the statistics about applying the operator.

References DUNE_UNUSED_PARAMETER.

◆ apply() [2/4]

template<typename T , typename A , int n, int m>

void Dune::SuperLU< BCRSMatrix< FieldMatrix< T, n, m >, A > >::apply	(	domain_type &	x,
		range_type &	b,
		InverseOperatorResult &	res
	)

Apply inverse operator,.

Warning: Note: right hand side b may be overwritten!

Parameters

x	The left hand side to store the result in.
b	The right hand side
res	Object to store the statistics about applying the operator.

◆ apply() [3/4]

template<typename T , typename A , int n, int m>

virtual void Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::apply	(	domain_type &	x,
		range_type &	b,
		InverseOperatorResult &	res
	)

inlinevirtual

Apply inverse operator,.

Warning: Note: right hand side b may be overwritten!

Parameters

x	The left hand side to store the result in.
b	The right hand side
res	Object to store the statistics about applying the operator.

References Dune::InverseOperatorResult::converged, Dune::block_vector_unmanaged< B, A >::dim(), DUNE_THROW, Dune::InverseOperatorResult::elapsed, and Dune::InverseOperatorResult::iterations.

◆ apply() [4/4]

template<typename T , typename A , int n, int m>

void Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::apply	(	T *	x,
		T *	b
	)

inline

additional apply method with c-arrays in analogy to superlu

Parameters

x	solution array
b	rhs array

◆ copyToLocalMatrix()

template<class M , class X , class Y >

template<class S >

std::size_t Dune::ILUSubdomainSolver< M, X, Y >::copyToLocalMatrix	(	const M &	A,
		S &	rowset
	)

protected

Copy the local part of the global matrix to ILU.

Parameters

A	The global matrix.
rowset	The global indices of the local problem.

◆ free() [1/2]

template<typename T , typename A , int n, int m>

void Dune::SuperLU< BCRSMatrix< FieldMatrix< T, n, m >, A > >::free

free allocated space.

Warning: later calling apply will result in an error.

◆ free() [2/2]

template<typename T , typename A , int n, int m>

void Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::free ( )

inline

free allocated space.

Warning: later calling apply will result in an error.

◆ saveDecomposition()

template<typename T , typename A , int n, int m>

void Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::saveDecomposition ( const char * file )

inline

saves a decomposition to a file

Parameters

file	the filename to save to

References DUNE_THROW.

◆ setOption()

template<typename T , typename A , int n, int m>

void Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::setOption	(	unsigned int	option,
		double	value
	)

inline

Set UMFPack-specific options.

This method allows to set various options that control the UMFPack solver. More specifically, it allows to set values in the UMF_Control array. Please see the UMFPack documentation for a list of possible options and values.

Parameters

option	Entry in the UMF_Control array, e.g., UMFPACK_IRSTEP
value	Corresponding value

Exceptions

RangeError If nonexisting option was requested

References DUNE_THROW.

◆ setSubMatrix() [1/2]

template<class M , class X , class Y >

template<class S >

void Dune::ILU0SubdomainSolver< M, X, Y >::setSubMatrix	(	const M &	A,
		S &	rowset
	)

Set the data of the local problem.

Parameters

A	The global matrix.
rowset	The global indices of the local problem.

Template Parameters

S	The type of the set with the indices.

◆ setSubMatrix() [2/2]

template<class M , class X , class Y >

template<class S >

void Dune::ILUNSubdomainSolver< M, X, Y >::setSubMatrix	(	const M &	A,
		S &	rowset
	)

Set the data of the local problem.

Parameters

A	The global matrix.
rowset	The global indices of the local problem.

Template Parameters

S	The type of the set with the indices.

◆ setVerbosity()

template<typename T , typename A , int n, int m>

void Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::setVerbosity ( int v )

inline

sets the verbosity level for the UMFPack solver

Parameters

v	verbosity level The following levels are implemented: 0 - only error messages 1 - a bit of statistics on decomposition and solution 2 - lots of statistics on decomposition and solution

◆ SuperLU() [1/2]

template<typename T , typename A , int n, int m>

Dune::SuperLU< BCRSMatrix< FieldMatrix< T, n, m >, A > >::SuperLU

Empty default constructor.

Use setMatrix to tell SuperLU for what matrix it solves. Using this constructor no vectors will be reused.

◆ SuperLU() [2/2]

template<typename T , typename A , int n, int m>

Dune::SuperLU< BCRSMatrix< FieldMatrix< T, n, m >, A > >::SuperLU	(	const Matrix &	mat,
		bool	verbose = `false`,
		bool	reusevector = `true`
	)

explicit

Constructs the SuperLU solver.

During the construction the matrix will be decomposed. That means that in each apply call forward and backward substitutions take place (and no decomposition).

Parameters

mat	The matrix of the system to solve.
verbose	If true some statistics are printed.
reusevector	Default value is true. If true the two vectors are allocate in the first call to apply. These get resused in subsequent calls to apply and are deallocated in the destructor. If false these vectors are allocated at the beginning and deallocated at the end of each apply method. This allows using the same instance of superlu from different threads.

◆ UMFPack() [1/4]

template<typename T , typename A , int n, int m>

Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::UMFPack	(	const char *	file,
		int	verbose = `0`
	)

inline

try loading a decomposition from file

Parameters

file	the decomposition file
verbose	the verbosity level

Exceptions

Dune::Exception When not being able to load the file. Does not need knowledge of the actual matrix!

References DUNE_THROW.

◆ UMFPack() [2/4]

template<typename T , typename A , int n, int m>

Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::UMFPack	(	const Matrix &	mat_,
		const char *	file,
		int	verbose = `0`
	)

inline

Try loading a decomposition from file and do a decomposition if unsuccessful.

Parameters

mat_	the matrix to decompose when no decoposition file found
file	the decomposition file
verbose	the verbosity level

Use saveDecomposition(char* file) for manually storing a decomposition. This constructor will decompose mat_ and store the result to file if no file wasn't found in the first place. Thus, if you always use this you will only compute the decomposition once (and when you manually deleted the decomposition file).

◆ UMFPack() [3/4]

template<typename T , typename A , int n, int m>

Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::UMFPack	(	const Matrix &	matrix,
		int	verbose,
		bool
	)

inline

Constructor for compatibility with SuperLU standard constructor.

This computes the matrix decomposition, and may take a long time (and use a lot of memory).

Parameters

mat_	the matrix to solve for
verbose	[0..2] set the verbosity level, defaults to 0

◆ UMFPack() [4/4]

template<typename T , typename A , int n, int m>

Dune::UMFPack< BCRSMatrix< FieldMatrix< T, n, m >, A > >::UMFPack	(	const Matrix &	matrix,
		int	verbose = `0`
	)

inline

Construct a solver object from a BCRSMatrix.

This computes the matrix decomposition, and may take a long time (and use a lot of memory).

Parameters

mat_	the matrix to solve for
verbose	[0..2] set the verbosity level, defaults to 0

DUNE Distributed and Unified Numerics Environment

Dune Core Modules (2.4.1)

Modules

Files

Classes

Typedefs

Functions

Detailed Description

Function Documentation

◆ apply() [1/4]

◆ apply() [2/4]

◆ apply() [3/4]

◆ apply() [4/4]

◆ copyToLocalMatrix()

◆ free() [1/2]

◆ free() [2/2]

◆ saveDecomposition()

◆ setOption()

◆ setSubMatrix() [1/2]

◆ setSubMatrix() [2/2]

◆ setVerbosity()

◆ SuperLU() [1/2]

◆ SuperLU() [2/2]

◆ UMFPack() [1/4]

◆ UMFPack() [2/4]

◆ UMFPack() [3/4]

◆ UMFPack() [4/4]