Reference documentation for deal.II version Git 1dafe5d 2017-11-23 14:01:03 +0100
Classes | Public Member Functions | Protected Member Functions | Protected Attributes | List of all members
SolverRichardson< VectorType > Class Template Reference

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

Inheritance diagram for SolverRichardson< VectorType >:
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Classes

struct  AdditionalData
 

Public Member Functions

 SolverRichardson (SolverControl &cn, VectorMemory< VectorType > &mem, const AdditionalData &data=AdditionalData())
 
 SolverRichardson (SolverControl &cn, const AdditionalData &data=AdditionalData())
 
virtual ~SolverRichardson ()=default
 
template<typename MatrixType , typename PreconditionerType >
void solve (const MatrixType &A, VectorType &x, const VectorType &b, const PreconditionerType &preconditioner)
 
template<typename MatrixType , typename PreconditionerType >
void Tsolve (const MatrixType &A, VectorType &x, const VectorType &b, const PreconditionerType &preconditioner)
 
void set_omega (const double om=1.)
 
virtual void print_vectors (const unsigned int step, const VectorType &x, const VectorType &r, const VectorType &d) const
 
- Public Member Functions inherited from Solver< VectorType >
 Solver (SolverControl &solver_control, VectorMemory< VectorType > &vector_memory)
 
 Solver (SolverControl &solver_control)
 
boost::signals2::connection connect (const std::function< SolverControl::State(const unsigned int iteration, const doublecheck_value, const VectorType &current_iterate)> &slot)
 
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
 Subscriptor (Subscriptor &&)
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
Subscriptoroperator= (Subscriptor &&)
 
void subscribe (const char *identifier=nullptr) const
 
void unsubscribe (const char *identifier=nullptr) const
 
unsigned int n_subscriptions () const
 
void list_subscribers () const
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 

Protected Member Functions

virtual VectorType::value_type criterion (const VectorType &r, const VectorType &d) const
 

Protected Attributes

AdditionalData additional_data
 
- Protected Attributes inherited from Solver< VectorType >
GrowingVectorMemory< VectorType > static_vector_memory
 
VectorMemory< VectorType > & memory
 
boost::signals2::signal< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType &current_iterate), StateCombineriteration_status
 

Additional Inherited Members

- Public Types inherited from Solver< VectorType >
typedef VectorType vector_type
 
- Static Public Member Functions inherited from Subscriptor
static::ExceptionBase & ExcInUse (int arg1, char *arg2, std::string &arg3)
 
static::ExceptionBase & ExcNoSubscriber (char *arg1, char *arg2)
 

Detailed Description

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

Implementation of the preconditioned Richardson iteration method. The stopping criterion is the norm of the residual.

For the requirements on matrices and vectors in order to work with this class, see the documentation of the Solver base class.

Like all other solver classes, this class has a local structure called AdditionalData which is used to pass additional parameters to the solver, like damping parameters or the number of temporary vectors. We use this additional structure instead of passing these values directly to the constructor because this makes the use of the SolverSelector and other classes much easier and guarantees that these will continue to work even if number or type of the additional parameters for a certain solver changes.

For the Richardson method, the additional data is the damping parameter, which is the only content of the AdditionalData structure. By default, the constructor of the structure sets it to one.

Observing the progress of linear solver iterations

The solve() function of this class uses the mechanism described in the Solver base class to determine convergence. This mechanism can also be used to observe the progress of the iteration.

Author
Ralf Hartmann

Definition at line 61 of file solver_richardson.h.

Constructor & Destructor Documentation

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

Constructor.

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

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

template<class VectorType = Vector<double>>
virtual SolverRichardson< VectorType >::~SolverRichardson ( )
virtualdefault

Virtual destructor.

Member Function Documentation

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

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

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

Solve \(A^Tx=b\) for \(x\).

template<class VectorType = Vector<double>>
void SolverRichardson< VectorType >::set_omega ( const double  om = 1.)

Set the damping-coefficient. Default is 1., i.e. no damping.

template<class VectorType = Vector<double>>
virtual void SolverRichardson< VectorType >::print_vectors ( const unsigned int  step,
const VectorType &  x,
const VectorType &  r,
const VectorType &  d 
) const
virtual

Interface for derived class. This function gets the current iteration vector, the residual and the update vector in each step. It can be used for graphical output of the convergence history.

template<class VectorType = Vector<double>>
virtual VectorType::value_type SolverRichardson< VectorType >::criterion ( const VectorType &  r,
const VectorType &  d 
) const
protectedvirtual

Implementation of the computation of the norm of the residual. Depending on the flags given to the solver, the default implementation of this function uses either the actual residual, r, or the preconditioned residual, d.

Member Data Documentation

template<class VectorType = Vector<double>>
AdditionalData SolverRichardson< VectorType >::additional_data
protected

Control parameters.

Definition at line 155 of file solver_richardson.h.


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