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Reference documentation for deal.II version 9.4.1
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Reference documentation for deal.II version 9.4.1
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#include <deal.II/lac/solver_cg.h>
Classes | |
| struct | AdditionalData |
Public Types | |
| using | size_type = types::global_dof_index |
| using | vector_type = VectorType |
Public Member Functions | |
| SolverFlexibleCG (SolverControl &cn, VectorMemory< VectorType > &mem, const AdditionalData &data=AdditionalData()) | |
| SolverFlexibleCG (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_coefficients_slot (const std::function< void(typename VectorType::value_type, typename VectorType::value_type)> &slot) |
| boost::signals2::connection | connect_condition_number_slot (const std::function< void(double)> &slot, const bool every_iteration=false) |
| boost::signals2::connection | connect_eigenvalues_slot (const std::function< void(const std::vector< double > &)> &slot, const bool every_iteration=false) |
| boost::signals2::connection | connect (const std::function< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType ¤t_iterate)> &slot) |
Protected Member Functions | |
| virtual void | print_vectors (const unsigned int step, const VectorType &x, const VectorType &r, const VectorType &d) const |
Static Protected Member Functions | |
| static void | compute_eigs_and_cond (const std::vector< typename VectorType::value_type > &diagonal, const std::vector< typename VectorType::value_type > &offdiagonal, const boost::signals2::signal< void(const std::vector< double > &)> &eigenvalues_signal, const boost::signals2::signal< void(double)> &cond_signal) |
Protected Attributes | |
| AdditionalData | additional_data |
| boost::signals2::signal< void(typename VectorType::value_type, typename VectorType::value_type)> | coefficients_signal |
| boost::signals2::signal< void(double)> | condition_number_signal |
| boost::signals2::signal< void(double)> | all_condition_numbers_signal |
| boost::signals2::signal< void(const std::vector< double > &)> | eigenvalues_signal |
| boost::signals2::signal< void(const std::vector< double > &)> | all_eigenvalues_signal |
| bool | determine_beta_by_flexible_formula |
| 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 |
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 |
| 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 |
| 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 |
| 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 |
This class implements a flexible variant of the conjugate gradient method, which is based on a different formula to compute \(\beta_k\) in the process of constructing a new search direction that is A-orthogonal against the previous one. Rather than using the Fletcher–Reeves update formula with \(\beta_k = \frac{\mathbf{r}^T_{k+1} \mathbf{z}_{k+1}}{\mathbf{r}^T_{k} \mathbf{z}_{k}}\) for computing the new search direction (here \(\mathbf{r}_{k+1}\) is the residual in step \(k+1\) and \(\mathbf{z}_{k+1} = P^{-1} \mathbf{r}_{k+1}\)) as in the classical conjugate gradient algorithm, this class selects the Polak-Ribiere formula \(\beta_k = \frac{\mathbf{r}^T_{k+1} \left(\mathbf{z}_{k+1} - \mathbf{z}_{k}\right)}{\mathbf{r}^T_{k} \mathbf{z}_{k}}\). The additional term \(\mathbf{r}^T_{k+1} \mathbf{z}_{k}\) is zero for linear symmetric-positive definite preconditioners due to the construction of the search directions, so the behavior of SolverFlexibleCG is equivalent for those kinds of situations and merely increases costs by requiring an additional stored vector and associated vector operations. While there are no theoretical guarantees for convergence as in the classical CG algorithm, the current class has been documented to be much more robust for variable preconditioners (e.g., involving some iterative inverse that is not fully converged) or a preconditioner with some slight non-symmetry (like weighted Schwarz methods), which results from the local optimality of the search direction with at least as good progress as the locally optimal steepest descent method.
Definition at line 354 of file solver_cg.h.
| using SolverFlexibleCG< VectorType >::size_type = types::global_dof_index |
Declare type for container size.
Definition at line 360 of file solver_cg.h.
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inherited |
| SolverFlexibleCG< VectorType >::SolverFlexibleCG | ( | SolverControl & | cn, |
| VectorMemory< VectorType > & | mem, | ||
| const AdditionalData & | data = AdditionalData() |
||
| ) |
Constructor.
| SolverFlexibleCG< VectorType >::SolverFlexibleCG | ( | SolverControl & | cn, |
| const AdditionalData & | data = AdditionalData() |
||
| ) |
Constructor. Use an object of type GrowingVectorMemory as a default to allocate memory.
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inherited |
Solve the linear system \(Ax=b\) for x.
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inherited |
Connect a slot to retrieve the CG coefficients. The slot will be called with alpha as the first argument and with beta as the second argument, where alpha and beta follow the notation in Y. Saad: "Iterative methods for Sparse Linear Systems", section 6.7. Called once per iteration
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inherited |
Connect a slot to retrieve the estimated condition number. Called on each iteration if every_iteration=true, otherwise called once when iterations are ended (i.e., either because convergence has been achieved, or because divergence has been detected).
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inherited |
Connect a slot to retrieve the estimated eigenvalues. Called on each iteration if every_iteration=true, otherwise called once when iterations are ended (i.e., either because convergence has been achieved, or because divergence has been detected).
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protectedvirtualinherited |
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.
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staticprotectedinherited |
Estimates the eigenvalues from diagonal and offdiagonal. Uses these estimate to compute the condition number. Calls the signals eigenvalues_signal and cond_signal with these estimates as arguments.
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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. |
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protectedinherited |
Additional parameters.
Definition at line 281 of file solver_cg.h.
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protectedinherited |
Signal used to retrieve the CG coefficients. Called on each iteration.
Definition at line 288 of file solver_cg.h.
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protectedinherited |
Signal used to retrieve the estimated condition number. Called once when all iterations are ended.
Definition at line 294 of file solver_cg.h.
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protectedinherited |
Signal used to retrieve the estimated condition numbers. Called on each iteration.
Definition at line 300 of file solver_cg.h.
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protectedinherited |
Signal used to retrieve the estimated eigenvalues. Called once when all iterations are ended.
Definition at line 306 of file solver_cg.h.
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protectedinherited |
Signal used to retrieve the estimated eigenvalues. Called on each iteration.
Definition at line 313 of file solver_cg.h.
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protectedinherited |
Flag to indicate whether the classical Fletcher–Reeves update formula for the parameter \(\beta_k\) (standard CG algorithm, minimal storage needs) or the flexible conjugate gradient method with Polak-Ribiere formula for \(\beta_k\) should be used. This base class implementation of SolverCG will always use the former method, whereas the derived class SolverFlexibleCG will use the latter.
Definition at line 323 of file solver_cg.h.
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mutableprotectedinherited |
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protectedinherited |
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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.
1.9.5