Reference documentation for deal.II version Git 409ee4b167 2020-08-14 09:46:12 -0400
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Classes | Public Member Functions | Static Public Member Functions | Protected Member Functions | Protected Attributes | List of all members
SolverMinRes< VectorType > Class Template Reference

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

Inheritance diagram for SolverMinRes< VectorType >:


struct  AdditionalData

Public Member Functions

 SolverMinRes (SolverControl &cn, VectorMemory< VectorType > &mem, const AdditionalData &data=AdditionalData())
 SolverMinRes (SolverControl &cn, const AdditionalData &data=AdditionalData())
virtual ~SolverMinRes () override=default
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)

Static Public Member Functions

static ::ExceptionBaseExcPreconditionerNotDefinite ()
- 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 Member Functions

virtual double criterion ()
virtual void print_vectors (const unsigned int step, const VectorType &x, const VectorType &r, const VectorType &d) const

Protected Attributes

double res2
- 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

Additional Inherited Members

- Public Types inherited from SolverBase< VectorType >
using vector_type = VectorType

Detailed Description

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

Minimal residual method for symmetric matrices.

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.

However, since the MinRes method does not need additional data, the respective structure is empty and does not offer any functionality. The constructor has a default argument, so you may call it without the additional parameter.

The preconditioner has to be positive definite and symmetric

The algorithm is taken from the Master thesis of Astrid Battermann with some changes. The full text can be found at

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.

Definition at line 69 of file solver_minres.h.

Constructor & Destructor Documentation

◆ SolverMinRes() [1/2]

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


◆ SolverMinRes() [2/2]

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

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

◆ ~SolverMinRes()

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

Virtual destructor.

Member Function Documentation

◆ solve()

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

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

◆ criterion()

template<class VectorType = Vector<double>>
virtual double SolverMinRes< VectorType >::criterion ( )

Implementation of the computation of the norm of the residual.

◆ print_vectors()

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

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.

Member Data Documentation

◆ res2

template<class VectorType = Vector<double>>
double SolverMinRes< VectorType >::res2

Within the iteration loop, the square of the residual vector is stored in this variable. The function criterion uses this variable to compute the convergence value, which in this class is the norm of the residual vector and thus the square root of the res2 value.

Definition at line 143 of file solver_minres.h.

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