Reference documentation for deal.II version Git df0d004539 2020-05-25 12:18:57 +0200
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Classes | Public Member Functions | Private Attributes | List of all members
SolverFGMRES< VectorType > Class Template Reference

#include <deal.II/lac/solver_gmres.h>

Inheritance diagram for SolverFGMRES< VectorType >:
[legend]

Classes

struct  AdditionalData
 

Public Member Functions

 SolverFGMRES (SolverControl &cn, VectorMemory< VectorType > &mem, const AdditionalData &data=AdditionalData())
 
 SolverFGMRES (SolverControl &cn, const AdditionalData &data=AdditionalData())
 
template<typename MatrixType , typename PreconditionerType >
void solve (const MatrixType &A, VectorType &x, const VectorType &b, const PreconditionerType &preconditioner)
 
- Public Member Functions inherited from SolverBase< VectorType >
 SolverBase (SolverControl &solver_control, VectorMemory< VectorType > &vector_memory)
 
 SolverBase (SolverControl &solver_control)
 
boost::signals2::connection connect (const std::function< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType &current_iterate)> &slot)
 
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
 Subscriptor (Subscriptor &&) noexcept
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
Subscriptoroperator= (Subscriptor &&) noexcept
 
void subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
 
void unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
 
unsigned int n_subscriptions () const
 
template<typename StreamType >
void list_subscribers (StreamType &stream) const
 
void list_subscribers () const
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 

Private Attributes

AdditionalData additional_data
 
FullMatrix< doubleH
 
FullMatrix< doubleH1
 

Additional Inherited Members

- Public Types inherited from SolverBase< VectorType >
using vector_type = VectorType
 
- Static Public Member Functions inherited from Subscriptor
static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
 
static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)
 
- Protected Attributes inherited from SolverBase< VectorType >
GrowingVectorMemory< VectorTypestatic_vector_memory
 
VectorMemory< VectorType > & memory
 
boost::signals2::signal< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType &current_iterate), StateCombineriteration_status
 

Detailed Description

template<class VectorType = Vector<double>>
class SolverFGMRES< VectorType >

Implementation of the Generalized minimal residual method with flexible preconditioning (flexible GMRES or FGMRES).

This flexible version of the GMRES method allows for the use of a different preconditioner in each iteration step. Therefore, it is also more robust with respect to inaccurate evaluation of the preconditioner. An important application is the use of a Krylov space method inside the preconditioner. As opposed to SolverGMRES which allows one to choose between left and right preconditioning, this solver always applies the preconditioner from the right.

FGMRES needs two vectors in each iteration steps yielding a total of 2*SolverFGMRES::AdditionalData::max_basis_size+1 auxiliary vectors. Otherwise, FGMRES requires roughly the same number of operations per iteration compared to GMRES, except one application of the preconditioner less at each restart and at the end of solve().

For more details see [59].

Author
Guido Kanschat, 2003

Definition at line 464 of file solver_gmres.h.

Constructor & Destructor Documentation

◆ SolverFGMRES() [1/2]

template<class VectorType = Vector<double>>
SolverFGMRES< VectorType >::SolverFGMRES ( SolverControl cn,
VectorMemory< VectorType > &  mem,
const AdditionalData data = AdditionalData() 
)

Constructor.

◆ SolverFGMRES() [2/2]

template<class VectorType = Vector<double>>
SolverFGMRES< VectorType >::SolverFGMRES ( SolverControl cn,
const AdditionalData data = AdditionalData() 
)

Constructor. Use an object of type GrowingVectorMemory as a default to allocate memory.

Member Function Documentation

◆ solve()

template<class VectorType = Vector<double>>
template<typename MatrixType , typename PreconditionerType >
void SolverFGMRES< VectorType >::solve ( const MatrixType &  A,
VectorType x,
const VectorType b,
const PreconditionerType &  preconditioner 
)

Solve the linear system \(Ax=b\) for x.

Member Data Documentation

◆ additional_data

template<class VectorType = Vector<double>>
AdditionalData SolverFGMRES< VectorType >::additional_data
private

Additional flags.

Definition at line 525 of file solver_gmres.h.

◆ H

template<class VectorType = Vector<double>>
FullMatrix<double> SolverFGMRES< VectorType >::H
private

Projected system matrix

Definition at line 530 of file solver_gmres.h.

◆ H1

template<class VectorType = Vector<double>>
FullMatrix<double> SolverFGMRES< VectorType >::H1
private

Auxiliary matrix for inverting H

Definition at line 535 of file solver_gmres.h.


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