Sequential overlapping Schwarz preconditioner. More...

#include <dune/istl/overlappingschwarz.hh>

Public Types
typedef M	matrix_type
	The type of the matrix to precondition.

typedef X	domain_type
	The domain type of the preconditioner.

typedef X	range_type
	The range type of the preconditioner.

typedef TM	Mode
	The mode (additive or multiplicative) of the Schwarz method. More...

typedef X::field_type	field_type
	The field type of the preconditioner.

typedef matrix_type::size_type	size_type
	The return type of the size method.

typedef TA	allocator
	The allocator to use.

typedef std::set< size_type, std::less< size_type >, typename std::allocator_traits< TA >::template rebind_alloc< size_type > >	subdomain_type
	The type for the subdomain to row index mapping.

typedef std::vector< subdomain_type, typename std::allocator_traits< TA >::template rebind_alloc< subdomain_type > >	subdomain_vector
	The vector type containing the subdomain to row index mapping.

typedef SLList< size_type, typename std::allocator_traits< TA >::template rebind_alloc< size_type > >	subdomain_list
	The type for the row to subdomain mapping.

typedef std::vector< subdomain_list, typename std::allocator_traits< TA >::template rebind_alloc< subdomain_list > >	rowtodomain_vector
	The vector type containing the row index to subdomain mapping.

typedef TD	slu
	The type for the subdomain solver in use.

typedef std::vector< slu, typename std::allocator_traits< TA >::template rebind_alloc< slu > >	slu_vector
	The vector type containing subdomain solvers.

Public Member Functions
	SeqOverlappingSchwarz (const matrix_type &mat, const subdomain_vector &subDomains, field_type relaxationFactor=1, bool onTheFly_=true)
	Construct the overlapping Schwarz method. More...

	SeqOverlappingSchwarz (const matrix_type &mat, const rowtodomain_vector &rowToDomain, field_type relaxationFactor=1, bool onTheFly_=true)

void	pre (X &x, X &b) override
	Prepare the preconditioner. More...

void	apply (X &v, const X &d) override
	Apply the preconditioner. More...

void	post (X &x) override
	Postprocess the preconditioner. More...

template<bool forward>
void	apply (X &v, const X &d)
	Apply one step of the preconditioner to the system A(v)=d. More...

SolverCategory::Category	category () const override
	Category of the preconditioner (see SolverCategory::Category)

Detailed Description

template<class M, class X, class TM = AdditiveSchwarzMode, class TD = ILU0SubdomainSolver<M,X,X>, class TA = std::allocator<X>>
class Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >

Sequential overlapping Schwarz preconditioner.

Template Parameters

M	The matrix type.
X	The range and domain type.
TM	The Schwarz mode. Currently supported modes are AdditiveSchwarzMode, MultiplicativeSchwarzMode, and SymmetricMultiplicativeSchwarzMode. (Default values is AdditiveSchwarzMode)
TD	The type of the local subdomain solver to be used.
TA	The type of the allocator to use.

Member Typedef Documentation

◆ Mode

template<class M , class X , class TM = AdditiveSchwarzMode, class TD = ILU0SubdomainSolver<M,X,X>, class TA = std::allocator<X>>

typedef TM Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >::Mode

The mode (additive or multiplicative) of the Schwarz method.

Either AdditiveSchwarzMode or MultiplicativeSchwarzMode

Member Function Documentation

◆ apply()

template<class M , class X , class TM = AdditiveSchwarzMode, class TD = ILU0SubdomainSolver<M,X,X>, class TA = std::allocator<X>>

template<bool forward>

void Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >::apply	(	X &	v,
		const X &	d
	)

virtual

Apply one step of the preconditioner to the system A(v)=d.

On entry v=0 and d=b-A(x) (although this might not be computed in that way. On exit v contains the update, i.e one step computes \( v = M^{-1} d \) where \( M \) is the approximate inverse of the operator \( A \) characterizing the preconditioner.

Parameters

[out]	v	The update to be computed
	d	The current defect.

Implements Dune::Preconditioner< X, X >.

◆ post()

template<class M , class X , class TM = AdditiveSchwarzMode, class TD = ILU0SubdomainSolver<M,X,X>, class TA = std::allocator<X>>

void Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >::post ( X & x )

inlineoverridevirtual

Postprocess the preconditioner.

Clean up.

This method is called after the last apply call for the linear system to be solved. Memory may be deallocated safely here. x is the solution of the linear equation.

Parameters

x	The right hand side of the equation.

Implements Dune::Preconditioner< X, X >.

◆ pre()

template<class M , class X , class TM = AdditiveSchwarzMode, class TD = ILU0SubdomainSolver<M,X,X>, class TA = std::allocator<X>>

void Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >::pre	(	X &	x,
		X &	b
	)

inlineoverridevirtual

Prepare the preconditioner.

A solver solves a linear operator equation A(x)=b by applying one or several steps of the preconditioner. The method pre() is called before the first apply operation. b and x are right hand side and solution vector of the linear system respectively. It may. e.g., scale the system, allocate memory or compute a (I)LU decomposition. Note: The ILU decomposition could also be computed in the constructor or with a separate method of the derived method if several linear systems with the same matrix are to be solved.

Note: if a preconditioner is copied (e.g. for a second thread) again the pre() method has to be called to ensure proper memory management.

X x(0.0);
Y b = ...; // rhs
Preconditioner<X,Y> prec(...);
prec.pre(x,b);   // prepare the preconditioner
prec.apply(x,b); // can be called multiple times now...
prec.post(x);    // cleanup internal state