Reference documentation for deal.II version Git 4e68a80cad 20211022 15:50:12 0600

#include <deal.II/lac/solver_bicgstab.h>
Classes  
struct  AdditionalData 
struct  IterationResult 
Public Types  
using  vector_type = VectorType 
Public Member Functions  
SolverBicgstab (SolverControl &cn, VectorMemory< VectorType > &mem, const AdditionalData &data=AdditionalData())  
SolverBicgstab (SolverControl &cn, const AdditionalData &data=AdditionalData())  
virtual  ~SolverBicgstab () override=default 
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 VectorType ¤t_iterate)> &slot) 
template<class Archive >  
void  serialize (Archive &ar, const unsigned int version) 
Subscriptor functionality  
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.  
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 
Static Public Member Functions  
static ::ExceptionBase &  ExcInUse (int arg1, std::string arg2, std::string arg3) 
static ::ExceptionBase &  ExcNoSubscriber (std::string arg1, std::string arg2) 
Protected Member Functions  
template<typename MatrixType >  
double  criterion (const MatrixType &A, const VectorType &x, const VectorType &b) 
virtual void  print_vectors (const unsigned int step, const VectorType &x, const VectorType &r, const VectorType &d) const 
Protected Attributes  
VectorType *  Vx 
VectorMemory< VectorType >::Pointer  Vr 
VectorMemory< VectorType >::Pointer  Vrbar 
VectorMemory< VectorType >::Pointer  Vp 
VectorMemory< VectorType >::Pointer  Vy 
VectorMemory< VectorType >::Pointer  Vz 
VectorMemory< VectorType >::Pointer  Vt 
VectorMemory< VectorType >::Pointer  Vv 
const VectorType *  Vb 
AdditionalData  additional_data 
GrowingVectorMemory< VectorType >  static_vector_memory 
VectorMemory< VectorType > &  memory 
boost::signals2::signal< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType ¤t_iterate), StateCombiner >  iteration_status 
double  alpha 
double  beta 
double  omega 
double  rho 
double  rhobar 
unsigned int  step 
double  res 
Private Member Functions  
template<typename MatrixType , typename PreconditionerType >  
IterationResult  iterate (const MatrixType &A, const PreconditionerType &preconditioner) 
Bicgstab algorithm by van der Vorst.
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.
The Bicgstabmethod has two additional parameters: the first is a boolean, deciding whether to compute the actual residual in each step (true
) or to use the length of the computed orthogonal residual (false
). Note that computing the residual causes a third matrixvectormultiplication, though no additional preconditioning, in each step. The reason for doing this is, that the size of the orthogonalized residual computed during the iteration may be larger by orders of magnitude than the true residual. This is due to numerical instabilities related to badly conditioned matrices. Since this instability results in a bad stopping criterion, the default for this parameter is true
. Whenever the user knows that the estimated residual works reasonably as well, the flag should be set to false
in order to increase the performance of the solver.
The second parameter is the size of a breakdown criterion. It is difficult to find a general good criterion, so if things do not work for you, try to change this value.
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 123 of file solver_bicgstab.h.

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

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

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

overridevirtualdefault 
Virtual destructor.
void SolverBicgstab< VectorType >::solve  (  const MatrixType &  A, 
VectorType &  x,  
const VectorType &  b,  
const PreconditionerType &  preconditioner  
) 
Solve primal problem only.

protected 
Computation of the stopping criterion.

protectedvirtual 
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.

private 
The iteration loop itself. The function returns a structure indicating what happened in this function.

inlineinherited 
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. 

inherited 
Subscribes a user of the object by storing the pointer validity
. The subscriber may be identified by text supplied as identifier
.
Definition at line 136 of file subscriptor.cc.

inherited 
Unsubscribes a user from the object.
identifier
and the validity
pointer must be the same as the one supplied to subscribe(). Definition at line 156 of file subscriptor.cc.

inlineinherited 
Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.
Definition at line 301 of file subscriptor.h.

inlineinherited 
List the subscribers to the input stream
.
Definition at line 318 of file subscriptor.h.

inherited 
List the subscribers to deallog
.
Definition at line 204 of file subscriptor.cc.

inlineinherited 
Read or write the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.
This function does not actually serialize any of the member variables of this class. The reason is that what this class stores is only who subscribes to this object, but who does so at the time of storing the contents of this object does not necessarily have anything to do with who subscribes to the object when it is restored. Consequently, we do not want to overwrite the subscribers at the time of restoring, and then there is no reason to write the subscribers out in the first place.
Definition at line 310 of file subscriptor.h.

protected 
A pointer to the solution vector passed to solve().
Definition at line 196 of file solver_bicgstab.h.

protected 
Auxiliary vector.
Definition at line 201 of file solver_bicgstab.h.

protected 
Auxiliary vector.
Definition at line 206 of file solver_bicgstab.h.

protected 
Auxiliary vector.
Definition at line 211 of file solver_bicgstab.h.

protected 
Auxiliary vector.
Definition at line 216 of file solver_bicgstab.h.

protected 
Auxiliary vector.
Definition at line 221 of file solver_bicgstab.h.

protected 
Auxiliary vector.
Definition at line 226 of file solver_bicgstab.h.

protected 
Auxiliary vector.
Definition at line 231 of file solver_bicgstab.h.

protected 
A pointer to the right hand side vector passed to solve().
Definition at line 236 of file solver_bicgstab.h.

protected 
Additional parameters.
Definition at line 259 of file solver_bicgstab.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.

protectedinherited 
Auxiliary value.
Definition at line 48 of file solver_bicgstab.h.

protectedinherited 
Auxiliary value.
Definition at line 52 of file solver_bicgstab.h.

protectedinherited 
Auxiliary value.
Definition at line 56 of file solver_bicgstab.h.

protectedinherited 
Auxiliary value.
Definition at line 60 of file solver_bicgstab.h.

protectedinherited 
Auxiliary value.
Definition at line 64 of file solver_bicgstab.h.

protectedinherited 
Current iteration step.
Definition at line 69 of file solver_bicgstab.h.

protectedinherited 
Residual.
Definition at line 74 of file solver_bicgstab.h.