preconditioned conjugate gradient method More...

#include <apcg.hh>

Detailed Description

template<class X, class Xstar>
class Kaskade::Pcg< X, Xstar >

preconditioned conjugate gradient method

This implements a preconditioned IterateType::CG iteration for an operator \( A: X\to X^* \), preconditioned by a preconditioner \( B^{-1}: X^* \to X \). The termination is policy-based.

The implementation follows Deuflhard/Weiser, Section 5.3.3.

Template Parameters

X	the type of vectors from the primal space
Xstar	the type of vectors from the dual space

See also: PCGEnergyErrorTerminationCriterion

Definition at line 280 of file linalg/apcg.hh.

Inheritance diagram for Kaskade::Pcg< X, Xstar >:

Public Types
typedef X	domain_type
	The domain type of the operator to be inverted. More...

typedef Xstar	range_type
	The range type of the operator to be inverted. More...

typedef X::field_type	field_type
	The field type of the operator to be inverted. More...

typedef ScalarTraits< field_type >::Real	Real
	the real field type corresponding to field_type More...

Public Member Functions
	Pcg (SymmetricLinearOperator< X, Xstar > &op_, SymmetricPreconditioner< X, Xstar > &prec_, PCGTerminationCriterion< Real > &terminate_, int verbose_=0)
	Set up conjugate gradient solver. More...

	Pcg (Dune::LinearOperator< X, Xstar > &op_, Dune::Preconditioner< X, Xstar > &prec_, DualPairing< X, Xstar > const &dp_, PCGTerminationCriterion< Real > &terminate_, int verbose_=0)
	Set up conjugate gradient solver. More...

virtual void	apply (X &u, Xstar &b, Dune::InverseOperatorResult &res)
	Apply inverse operator by performing a number of IterateType::PCG iterations. More...

virtual void	apply (X &x, Xstar &b, double tol, Dune::InverseOperatorResult &res)
	Apply inverse operator with given tolerance. More...

virtual Dune::SolverCategory::Category	category () const override
	returns the category of the operator More...

Member Typedef Documentation

◆ domain_type

template<class X , class Xstar >

typedef X Kaskade::Pcg< X, Xstar >::domain_type

The domain type of the operator to be inverted.

Definition at line 284 of file linalg/apcg.hh.

◆ field_type

template<class X , class Xstar >

typedef X::field_type Kaskade::Pcg< X, Xstar >::field_type

The field type of the operator to be inverted.

Definition at line 288 of file linalg/apcg.hh.

◆ range_type

template<class X , class Xstar >

typedef Xstar Kaskade::Pcg< X, Xstar >::range_type

The range type of the operator to be inverted.

Definition at line 286 of file linalg/apcg.hh.

◆ Real

template<class X , class Xstar >

typedef ScalarTraits<field_type>::Real Kaskade::Pcg< X, Xstar >::Real

the real field type corresponding to field_type

Definition at line 293 of file linalg/apcg.hh.

Constructor & Destructor Documentation

◆ Pcg() [1/2]

template<class X , class Xstar >

Kaskade::Pcg< X, Xstar >::Pcg	(	SymmetricLinearOperator< X, Xstar > &	op_,
		SymmetricPreconditioner< X, Xstar > &	prec_,
		PCGTerminationCriterion< Real > &	terminate_,
		int	verbose_ = `0`
	)

inline

Set up conjugate gradient solver.

Parameters

op	the operator
prec	the preconditioner
terminate	the termination criterion. The object has to exist during the lifetime of the pcg object as it is referenced.
verbose	controls the verbosity of logging to std::cout. 0 means no output at all (default). Values in 0,1,2 are valid.

Definition at line 303 of file linalg/apcg.hh.

◆ Pcg() [2/2]

template<class X , class Xstar >

Kaskade::Pcg< X, Xstar >::Pcg	(	Dune::LinearOperator< X, Xstar > &	op_,
		Dune::Preconditioner< X, Xstar > &	prec_,
		DualPairing< X, Xstar > const &	dp_,
		PCGTerminationCriterion< Real > &	terminate_,
		int	verbose_ = `0`
	)

inline

Set up conjugate gradient solver.

Parameters

op	the operator
prec	the preconditioner
dp	the dual pairing with respect to which the operator is symmetric
terminate	the termination criterion. The object has to exist during the lifetime of the pcg object as it is referenced.
verbose	controls the verbosity of logging to std::cout. 0 means no output at all (default). Values in 0,1,2 are valid.

Definition at line 321 of file linalg/apcg.hh.

Member Function Documentation

◆ apply() [1/2]

template<class X , class Xstar >

virtual void Kaskade::Pcg< X, Xstar >::apply	(	X &	u,
		Xstar &	b,
		Dune::InverseOperatorResult &	res
	)

inlinevirtual

Apply inverse operator by performing a number of IterateType::PCG iterations.

Parameters

u	the initial value (starting iterate)
b	the right hand side (which will not be modified)

Definition at line 334 of file linalg/apcg.hh.

◆ apply() [2/2]

template<class X , class Xstar >

virtual void Kaskade::Pcg< X, Xstar >::apply	(	X &	x,
		Xstar &	b,
		double	tol,
		Dune::InverseOperatorResult &	res
	)

inlinevirtual

Apply inverse operator with given tolerance.

This method is equivalent to setting first the tolerance in the termination criterion, then calling apply().

Definition at line 481 of file linalg/apcg.hh.

◆ category()

template<class X , class Xstar >

virtual Dune::SolverCategory::Category Kaskade::Pcg< X, Xstar >::category ( ) const

inlineoverridevirtual

returns the category of the operator

From the Dune doxygen documentation it is unclear what this is supposed to mean. We return a dummy here.

Definition at line 493 of file linalg/apcg.hh.

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

linalg/apcg.hh

Detailed Description

Public Types

Public Member Functions

Member Typedef Documentation

◆ domain_type

◆ field_type

◆ range_type

◆ Real

Constructor & Destructor Documentation

◆ Pcg() [1/2]

◆ Pcg() [2/2]

Member Function Documentation

◆ apply() [1/2]

◆ apply() [2/2]

◆ category()