Reference documentation for deal.II version 9.3.3

#include <deal.II/lac/solver_gmres.h>
Classes  
struct  AdditionalData 
Public Types  
using  vector_type = Vector< double > 
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) 
boost::signals2::connection  connect (const std::function< SolverControl::State(const unsigned int iteration, const double check_value, const Vector< double > ¤t_iterate)> &slot) 
Protected Attributes  
GrowingVectorMemory< Vector< double > >  static_vector_memory 
VectorMemory< Vector< double > > &  memory 
boost::signals2::signal< SolverControl::State(const unsigned int iteration, const double check_value, const Vector< double > ¤t_iterate), StateCombiner >  iteration_status 
Private Attributes  
AdditionalData  additional_data 
FullMatrix< double >  H 
FullMatrix< double >  H1 
Subscriptor functionality  
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.  
std::atomic< unsigned int >  counter 
std::map< std::string, unsigned int >  counter_map 
std::vector< std::atomic< bool > * >  validity_pointers 
const std::type_info *  object_info 
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) 
using  map_value_type = decltype(counter_map)::value_type 
using  map_iterator = decltype(counter_map)::iterator 
static std::mutex  mutex 
static ::ExceptionBase &  ExcInUse (int arg1, std::string arg2, std::string arg3) 
static ::ExceptionBase &  ExcNoSubscriber (std::string arg1, std::string arg2) 
void  check_no_subscribers () const noexcept 
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 [106].
Definition at line 459 of file solver_gmres.h.

inherited 
SolverFGMRES< VectorType >::SolverFGMRES  (  SolverControl &  cn, 
VectorMemory< VectorType > &  mem,  
const AdditionalData &  data = AdditionalData() 

) 
Constructor.
SolverFGMRES< VectorType >::SolverFGMRES  (  SolverControl &  cn, 
const AdditionalData &  data = AdditionalData() 

) 
Constructor. Use an object of type GrowingVectorMemory as a default to allocate memory.
void SolverFGMRES< VectorType >::solve  (  const MatrixType &  A, 
VectorType &  x,  
const VectorType &  b,  
const PreconditionerType &  preconditioner  
) 
Solve the linear system \(Ax=b\) for x.

inherited 
Connect a function object that will be called periodically within iterative solvers. This function is used to attach monitors to iterative solvers, either to determine when convergence has happened, or simply to observe the progress of an iteration. See the documentation of this class for more information.
slot  A function object specified here will, with each call, receive the number of the current iteration, the value that is used to check for convergence (typically the residual of the current iterate with respect to the linear system to be solved) and the currently best available guess for the current iterate. Note that some solvers do not update the approximate solution in every iteration but only after convergence or failure has been determined (GMRES is an example); in such cases, the vector passed as the last argument to the signal is simply the best approximate at the time the signal is called, but not the vector that will be returned if the signal's return value indicates that the iteration should be terminated. The function object must return a SolverControl::State value that indicates whether the iteration should continue, has failed, or has succeeded. The results of all connected functions will then be combined to determine what should happen with the iteration. 

private 
Additional flags.
Definition at line 508 of file solver_gmres.h.

private 
Projected system matrix
Definition at line 513 of file solver_gmres.h.

private 
Auxiliary matrix for inverting H
Definition at line 518 of file solver_gmres.h.

mutableprotectedinherited 

protectedinherited 

protectedinherited 
A signal that iterative solvers can execute at the end of every iteration (or in an otherwise periodic fashion) to find out whether we should continue iterating or not. The signal may call one or more slots that each will make this determination by themselves, and the result over all slots (function calls) will be determined by the StateCombiner object.
The arguments passed to the signal are (i) the number of the current iteration; (ii) the value that is used to determine convergence (oftentimes the residual, but in other cases other quantities may be used as long as they converge to zero as the iterate approaches the solution of the linear system); and (iii) a vector that corresponds to the current best guess for the solution at the point where the signal is called. Note that some solvers do not update the approximate solution in every iteration but only after convergence or failure has been determined (GMRES is an example); in such cases, the vector passed as the last argument to the signal is simply the best approximate at the time the signal is called, but not the vector that will be returned if the signal's return value indicates that the iteration should be terminated.