SolverFIRE< VectorType > Class Template Reference

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

Inheritance diagram for SolverFIRE< VectorType >:

Classes
struct	AdditionalData

Public Types
using	vector_type = VectorType

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 VectorType &current_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
virtual void	print_vectors (const unsigned int, const VectorType &x, const VectorType &v, const VectorType &g) const

Protected Attributes
const 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 &current_iterate), StateCombiner >	iteration_status

Private Types
using	map_value_type = decltype(counter_map)::value_type
using	map_iterator = decltype(counter_map)::iterator

Private Member Functions
void	check_no_subscribers () const noexcept

Private Attributes
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 Private Attributes
static std::mutex	mutex

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:

• The global vector of unknown variables: \(\mathbf x\).
• Objective function: \(E(\mathbf x)\).
• Rate of change of unknowns: \(\mathbf v\).
• Gradient of the objective function w.r.t unknowns: \(\mathbf g = \nabla E(\mathbf x)\).
• Mass matrix: \(\mathbf M\).
• Initial guess of unknowns: \(\mathbf x_0\).
• Time step: \(\Delta t\).

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 92 of file solver_fire.h.

Member Typedef Documentation

vector_type

template<typename VectorType = Vector<double>>

using SolverBase< VectorType >::vector_type = VectorType

inherited

An alias for the underlying vector type

Definition at line 347 of file solver.h.

map_value_type

using Subscriptor::map_value_type = decltype(counter_map)::value_type

privateinherited

The data type used in counter_map.

Definition at line 229 of file subscriptor.h.

map_iterator

using Subscriptor::map_iterator = decltype(counter_map)::iterator

privateinherited

The iterator type used in counter_map.

Definition at line 234 of file subscriptor.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()

template<typename VectorType = Vector<double>>

boost::signals2::connection SolverBase< VectorType >::connect ( const std::function< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType &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

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.

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.

subscribe()

void Subscriptor::subscribe ( std::atomic< bool > *const validity, const std::string & identifier = "" ) const

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 135 of file subscriptor.cc.

unsubscribe()

void Subscriptor::unsubscribe ( std::atomic< bool > *const validity, const std::string & identifier = "" ) const

inherited

Unsubscribes a user from the object.

Note

The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 155 of file subscriptor.cc.

n_subscriptions()

unsigned int Subscriptor::n_subscriptions ( ) const

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 300 of file subscriptor.h.

list_subscribers() [1/2]

template<typename StreamType >

void Subscriptor::list_subscribers ( StreamType & stream ) const

inlineinherited

List the subscribers to the input stream.

Definition at line 317 of file subscriptor.h.

list_subscribers() [2/2]

void Subscriptor::list_subscribers ( ) const

inherited

List the subscribers to deallog.

Definition at line 203 of file subscriptor.cc.

serialize()

template<class Archive >

void Subscriptor::serialize ( Archive & ar, const unsigned int version )

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 309 of file subscriptor.h.

check_no_subscribers()

void Subscriptor::check_no_subscribers ( ) const

privatenoexceptinherited

Check that there are no objects subscribing to this object. If this check passes then it is safe to destroy the current object. It this check fails then this function will either abort or print an error message to deallog (by using the AssertNothrow mechanism), but will not throw an exception.

Note

Since this function is just a consistency check it does nothing in release mode.

If this function is called when there is an uncaught exception then, rather than aborting, this function prints an error message to the standard error stream and returns.

Definition at line 52 of file subscriptor.cc.

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 184 of file solver_fire.h.

static_vector_memory

template<typename VectorType = Vector<double>>

GrowingVectorMemory<VectorType> SolverBase< VectorType >::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 415 of file solver.h.

memory

template<typename VectorType = Vector<double>>

VectorMemory<VectorType>& SolverBase< VectorType >::memory

protectedinherited

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

Definition at line 420 of file solver.h.

iteration_status

template<typename VectorType = Vector<double>>

boost::signals2::signal< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType &current_iterate), StateCombiner> SolverBase< VectorType >::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 471 of file solver.h.

counter

std::atomic<unsigned int> Subscriptor::counter

mutableprivateinherited

Store the number of objects which subscribed to this object. Initially, this number is zero, and upon destruction it shall be zero again (i.e. all objects which subscribed should have unsubscribed again).

The creator (and owner) of an object is counted in the map below if HE manages to supply identification.

We use the mutable keyword in order to allow subscription to constant objects also.

This counter may be read from and written to concurrently in multithreaded code: hence we use the std::atomic class template.

Definition at line 218 of file subscriptor.h.

counter_map

std::map<std::string, unsigned int> Subscriptor::counter_map

mutableprivateinherited

In this map, we count subscriptions for each different identification string supplied to subscribe().

Definition at line 224 of file subscriptor.h.

validity_pointers

std::vector<std::atomic<bool> *> Subscriptor::validity_pointers

mutableprivateinherited

In this vector, we store pointers to the validity bool in the SmartPointer objects that subscribe to this class.

Definition at line 240 of file subscriptor.h.

object_info

const std::type_info* Subscriptor::object_info

mutableprivateinherited

Pointer to the typeinfo object of this object, from which we can later deduce the class name. Since this information on the derived class is neither available in the destructor, nor in the constructor, we obtain it in between and store it here.

Definition at line 248 of file subscriptor.h.

mutex

std::mutex Subscriptor::mutex

staticprivateinherited

A mutex used to ensure data consistency when accessing the mutable members of this class. This lock is used in the subscribe() and unsubscribe() functions, as well as in list_subscribers().

Definition at line 271 of file subscriptor.h.

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

• include/deal.II/lac/solver_fire.h