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Reference documentation for deal.II version 9.3.3
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#include <deal.II/lac/solver_fire.h>
Classes | |
struct | AdditionalData |
Public Types | |
using | vector_type = Vector< double > |
Public Member Functions | |
SolverFIRE (SolverControl &solver_control, VectorMemory< VectorType > &vector_memory, const AdditionalData &data=AdditionalData()) | |
SolverFIRE (SolverControl &solver_control, const AdditionalData &data=AdditionalData()) | |
template<typename PreconditionerType = DiagonalMatrix<VectorType>> | |
void | solve (const std::function< double(VectorType &, const VectorType &)> &compute, VectorType &x, const PreconditionerType &inverse_mass_matrix) |
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 Member Functions | |
virtual void | print_vectors (const unsigned int, const VectorType &x, const VectorType &v, const VectorType &g) const |
Protected Attributes | |
const AdditionalData | additional_data |
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 |
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 |
FIRE (Fast Inertial Relaxation Engine) for minimization of (potentially non-linear) objective function E(\mathbf x), \mathbf x is a vector of n variables ( n is the number of variables of the objective function). Like all other solver classes, it can work on any kind of vector and matrix as long as they satisfy certain requirements (for the requirements on matrices and vectors in order to work with this class, see the documentation of the Solver base class). The type of the solution vector must be passed as template argument, and defaults to Vector<double>.
FIRE is a damped dynamics method described in Structural Relaxation Made Simple by Bitzek et al. 2006, typically used to find stable equilibrium configurations of atomistic systems in computational material science. Starting from a given initial configuration of the atomistic system, the algorithm relies on inertia to obtain (nearest) configuration with least potential energy.
Notation:
Given initial values for \Delta t, \alpha = \alpha_0, \epsilon, \mathbf x = \mathbf x_0 and \mathbf v= \mathbf 0 along with a given mass matrix \mathbf M, FIRE algorithm is as follows,
Also see Energy-Minimization in Atomic-to-Continuum Scale-Bridging Methods by Eidel et al. 2011.
Definition at line 89 of file solver_fire.h.
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inherited |
SolverFIRE< VectorType >::SolverFIRE | ( | SolverControl & | solver_control, |
VectorMemory< VectorType > & | vector_memory, | ||
const AdditionalData & | data = AdditionalData() |
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Constructor.
SolverFIRE< VectorType >::SolverFIRE | ( | SolverControl & | solver_control, |
const AdditionalData & | data = AdditionalData() |
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Constructor. Use an object of type GrowingVectorMemory as a default to allocate memory.
void SolverFIRE< VectorType >::solve | ( | const std::function< double(VectorType &, const VectorType &)> & | compute, |
VectorType & | x, | ||
const PreconditionerType & | inverse_mass_matrix | ||
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Obtain a set of variables x
that minimize an objective function described by the polymorphic function wrapper compute
, with a given preconditioner inverse_mass_matrix
and initial x
values. The function compute
returns the objective function's value and updates the objective function's gradient (with respect to the variables) when passed in as first argument based on the second argument– the state of variables.
void SolverFIRE< VectorType >::solve | ( | const MatrixType & | A, |
VectorType & | x, | ||
const VectorType & | b, | ||
const PreconditionerType & | preconditioner | ||
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Solve for x that minimizes E(\mathbf x) for the special case when E(\mathbf x) = \frac{1}{2} \mathbf x^{T} \mathbf A \mathbf x - \mathbf x^{T} \mathbf b.
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protectedvirtual |
Interface for derived class. This function gets the current iteration x
(variables), v
(x's time derivative) and g
(the gradient) in each step. It can be used for graphical output of the convergence history.
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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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protected |
Additional data to the solver.
Definition at line 179 of file solver_fire.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.