Reference documentation for deal.II version 9.4.0
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Classes | Public Types | Public Member Functions | Protected Member Functions | Protected Attributes | List of all members
SolverFIRE< VectorType > Class Template Reference

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

Inheritance diagram for SolverFIRE< VectorType >:
[legend]

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 > &current_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 > &current_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 intcounter
 
std::map< std::string, unsigned intcounter_map
 
std::vector< std::atomic< bool > * > validity_pointers
 
const std::type_info * object_info
 
static std::mutex mutex
 
static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
 
static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)
 
void check_no_subscribers () const noexcept
 

Detailed Description

template<typename VectorType = Vector<double>>
class SolverFIRE< VectorType >

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,

  1. Calculate \(\mathbf g = \nabla E(\mathbf x)\) and check for convergence ( \(\mathbf g \cdot \mathbf g < \epsilon^2 \)).
  2. Update \(\mathbf x\) and \(V\) using simple (forward) Euler integration step,
    \(\mathbf x = \mathbf x + \Delta t \mathbf v\),
    \(\mathbf v = \mathbf v + \Delta t \mathbf M^{-1} \cdot \mathbf g\).
  3. Calculate \(p = \mathbf g \cdot \mathbf v\).
  4. Set \(\mathbf v = (1-\alpha) \mathbf v + \alpha \frac{|\mathbf v|}{|\mathbf g|} \mathbf g\).
  5. If \(p<0\) and number of steps since \(p\) was last negative is larger than certain value, then increase time step \(\Delta t\) and decrease \(\alpha\).
  6. If \(p>0\), then decrease the time step, freeze the system i.e., \(\mathbf v = \mathbf 0\) and reset \(\alpha = \alpha_0\).
  7. Return to 1.

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.

Member Typedef Documentation

◆ vector_type

using SolverBase< Vector< double > >::vector_type = Vector< double >
inherited

An alias for the underlying vector type

Definition at line 346 of file solver.h.

Constructor & Destructor Documentation

◆ SolverFIRE() [1/2]

template<typename VectorType = Vector<double>>
SolverFIRE< VectorType >::SolverFIRE ( SolverControl solver_control,
VectorMemory< VectorType > &  vector_memory,
const AdditionalData data = AdditionalData() 
)

Constructor.

◆ SolverFIRE() [2/2]

template<typename VectorType = Vector<double>>
SolverFIRE< VectorType >::SolverFIRE ( SolverControl solver_control,
const AdditionalData data = AdditionalData() 
)

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

Member Function Documentation

◆ solve() [1/2]

template<typename VectorType = Vector<double>>
template<typename PreconditionerType = DiagonalMatrix<VectorType>>
void SolverFIRE< VectorType >::solve ( const std::function< double(VectorType &, const VectorType &)> &  compute,
VectorType &  x,
const PreconditionerType &  inverse_mass_matrix 
)

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.

◆ solve() [2/2]

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

Solve for x that minimizes \(E(\mathbf x)\) for the special case when \(E(\mathbf x) = \frac{1}{2} \mathbf x^{T} \mathbf A \mathbf x - \mathbf x^{T} \mathbf b\).

◆ print_vectors()

template<typename VectorType = Vector<double>>
virtual void SolverFIRE< VectorType >::print_vectors ( const unsigned int  ,
const VectorType &  x,
const VectorType &  v,
const VectorType &  g 
) const
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.

◆ connect()

boost::signals2::connection SolverBase< Vector< double > >::connect ( const std::function< SolverControl::State(const unsigned int iteration, const double check_value, const Vector< double > &current_iterate)> &  slot)
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.

Parameters
slotA 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.
Returns
A connection object that represents the connection from the signal to the function object. It can be used to disconnect the function object again from the signal. See the documentation of the BOOST Signals2 library for more information on connection management.

Member Data Documentation

◆ additional_data

template<typename VectorType = Vector<double>>
const AdditionalData SolverFIRE< VectorType >::additional_data
protected

Additional data to the solver.

Definition at line 179 of file solver_fire.h.

◆ static_vector_memory

GrowingVectorMemory<Vector< double > > SolverBase< Vector< double > >::static_vector_memory
mutableprotectedinherited

A static vector memory object to be used whenever no such object has been given to the constructor.

Definition at line 414 of file solver.h.

◆ memory

VectorMemory<Vector< double > >& SolverBase< Vector< double > >::memory
protectedinherited

A reference to an object that provides memory for auxiliary vectors.

Definition at line 419 of file solver.h.

◆ iteration_status

boost::signals2::signal< SolverControl::State(const unsigned int iteration, const double check_value, const Vector< double > & current_iterate), StateCombiner> SolverBase< Vector< double > >::iteration_status
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.

Definition at line 470 of file solver.h.


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