Application class performing a Newton's iteration as described in newtonBase. More...

#include <newton_w_line_search.h>

Inheritance diagram for FuelCell::ApplicationCore::NewtonLineSearch:

Collaboration diagram for FuelCell::ApplicationCore::NewtonLineSearch:

Public Member Functions
	NewtonLineSearch (ApplicationBase &app)
	Constructor, receiving the application computing the residual and solving the linear problem. More...

virtual void	declare_parameters (ParameterHandler &param)
	Declare the input parameters. More...

void	_initialize (ParameterHandler &param)
	Read the parameters local to NewtonLineSearch. More...

virtual void	initialize (ParameterHandler &param)
	Read the parameters. More...

virtual void	solve (FuelCell::ApplicationCore::FEVector &u, const FuelCell::ApplicationCore::FEVectors &in_vectors)
	The actual Newton solver. More...

Public Member Functions inherited from FuelCell::ApplicationCore::newtonBase
	newtonBase (ApplicationBase &app)
	Constructor, receiving the application computing the residual and solving the linear problem. More...

void	_initialize (ParameterHandler &param)
	Read the parameters local to newtonBase. More...

double	threshold (double new_value)
	Set the maximal residual reduction allowed without triggering assembling in the next step. More...

void	initialize_initial_guess (BlockVector< double > &dst)
	Control object for the Newton iteration. More...

virtual void	assemble ()
	Instead of assembling, this function only sets a flag, such that the inner application will be required to assemble a new derivative matrix next time solve() is called. More...

virtual double	residual (FuelCell::ApplicationCore::FEVector &dst, const FuelCell::ApplicationCore::FEVectors &rhs)
	Returns the L2-norm of the residual and the residual vector in "dst" using the residual function in the ApplicationBase used to initialize the application. More...

Public Member Functions inherited from FuelCell::ApplicationCore::ApplicationWrapper
	ApplicationWrapper (ApplicationBase &app)
	Constructor for a derived application. More...

	~ApplicationWrapper ()
	Destructor. More...

virtual void	remesh ()
	Generate the next mesh depending on the mesh generation parameters. More...

virtual void	init_vector (FEVector &dst) const
	Initialize vector to problem size. More...

virtual double	residual (FEVector &dst, const FEVectors &src, bool apply_boundaries=true)
	Compute residual of `src` and store it into `dst`. More...

virtual void	Tsolve (FEVector &dst, const FEVectors &src)
	Solve the dual system assembled with right hand side `rhs` and return the result in `start`. More...

virtual double	estimate (const FEVectors &src)
	Estimate cell-wise errors. More...

virtual double	evaluate (const FEVectors &src)
	Evaluate a functional. More...

virtual void	grid_out (const std::string &filename) const

virtual void	data_out (const std::string &filename, const FEVectors &src)
	Write data in the format specified by the ParameterHandler. More...

virtual std::string	id () const
	Return a unique identification string for this application. More...

virtual void	notify (const Event &reason)
	Add a reason for assembling. More...

Public Member Functions inherited from FuelCell::ApplicationCore::ApplicationBase
	ApplicationBase (boost::shared_ptr< ApplicationData > data=boost::shared_ptr< ApplicationData >())
	Constructor for an application. More...

	ApplicationBase (const ApplicationBase &other)
	Copy constructor. More...

virtual	~ApplicationBase ()
	Virtual destructor. More...

void	print_parameters_to_file (ParameterHandler &param, const std::string &file_name, const ParameterHandler::OutputStyle &style)
	Print default parameters for the application to a file. More...

virtual void	start_vector (FEVector &dst, std::string) const
	Initialize vector to problem size. More...

virtual void	grid_out (const std::string &)
	Write the mesh in the format specified by the ParameterHandler. More...

boost::shared_ptr < ApplicationData >	get_data ()
	Get access to the protected variable data. More...

const boost::shared_ptr < ApplicationData >	get_data () const
	Get read-only access to the protected variable data. More...

virtual void	clear ()
	All `true` in `notifications`. More...

virtual void	clear_events ()
	All `false` in `notifications`. More...

virtual unsigned int	get_solution_index ()
	Returns solution index. More...

Static Public Attributes
static const FuelCell::ApplicationCore::Event	bad_derivative
	The Event set by NewtonLineSearch if convergence is becoming bad and a new matrix should be assembled. More...

Static Public Attributes inherited from FuelCell::ApplicationCore::newtonBase
static const FuelCell::ApplicationCore::Event	bad_derivative
	The Event set if convergence is becoming bad and a new matrix should be assembled. More...

Private Member Functions
bool	find_negative_values (const FEVector &u)
	Routine used to find if there are any negative values on a given solution block. More...

Private Attributes
double	overrelax
	Value used to multiply $\delta u$ , the solution update, from the Newton algorithm during the first overrelax_steps iterations. More...

unsigned int	overrelax_steps
	Number of iterations to which we apply overrelax. More...

bool	line_search
	Do you want to use a line search at each step? More...

unsigned int	block_to_fix
	Block not allowed to be negative: More...

Additional Inherited Members
Public Attributes inherited from FuelCell::ApplicationCore::newtonBase
ReductionControl	control
	Control object for the Newton iteration. More...

double	numIter
	Number of Iterations;. More...

Protected Member Functions inherited from FuelCell::ApplicationCore::newtonBase
void	debug_output (const FEVector &sol, const FEVector &update, const FEVector &residual) const
	Function used to output any necessary information at each Newton iteration for debugging purposes. More...

Protected Member Functions inherited from FuelCell::ApplicationCore::ApplicationWrapper
SmartPointer< ApplicationBase >	get_wrapped_application ()
	Gain access to the inner application. More...

Protected Member Functions inherited from FuelCell::ApplicationCore::ApplicationBase
void	print_caller_name (const std::string &caller_name) const
	Print caller name. More...

Protected Attributes inherited from FuelCell::ApplicationCore::newtonBase
bool	assemble_now
	This flag is set by the function assemble(), indicating that the matrix must be assembled anew upon start. More...

double	assemble_threshold
	Threshold for re-assembling matrix. More...

bool	debug_solution
	Print updated solution after each step into file `Newton_uNNN`? More...

bool	debug_update
	Print Newton update after each step into file `Newton_dNNN`? More...

bool	debug_residual
	Print Newton residual after each step into file `Newton_rNNN`? More...

unsigned int	debug
	Write debug output to FcstUtilities::log; the higher the number, the more output. More...

unsigned int	step
	The number of a basic Newton iteration. More...

std::vector< unsigned int >	blocks
	This vector specifies the blocks of the global solution which are supposed to be treated specially. More...

unsigned int	n_blocks
	The total number of `blocks`. More...

Protected Attributes inherited from FuelCell::ApplicationCore::ApplicationWrapper
SmartPointer< ApplicationBase >	app
	Pointer to the application this one depends upon. More...

Protected Attributes inherited from FuelCell::ApplicationCore::ApplicationBase
boost::shared_ptr < ApplicationData >	data
	Object for auxiliary data. More...

Event	notifications
	Accumulate reasons for assembling here. More...

Detailed Description

Application class performing a Newton's iteration as described in newtonBase.

The implemented algorithm attempts to find a step size length, $ h $ , such that the scalar function

$f (h) = \| \mathbf{F}(\mathbf{x}_{i−1} + h \delta \mathbf{x} ) \|_2^2.$

is reduced at every step. The meaning of $\delta \mathbf{x}$ and how it is obtained is described in the documentation for the base class, i.e. newtonBase.

The method used to determine $ h $ is referred to as the global-convergence strategy. The strategy can greatly affect both the efficiency and versatility of Newton’s method.

This class contains two methods to determine $ h $ . Two options are possible.

Overrelaxation and step size control

If, in the Newton subsection in the parameter file, the option "Line search" is set to false, i.e. set Line search = false, then a normal Netwon iteration is performed where $ h = 1 $ . However, since Newton methods are notorious for overshooting the solution at the initial stages, the algorithm allows the user to specify an overrelaxation constant, $ h $ , for a given number of steps, i.e. overrelax_steps, such that the step size during the initial stages of the algorithm, i.e. for iteration number < overrelax_steps, $ h $ is given as follows:

$h = overrelaxation*step$

where step is the iteration number in the Newton solver. The overrelaxation constant is specified in the Newton subsection in the input file with set Initial Overrelaxation = 0.2. The parameter overrelax_steps is set in the same section with set Number of iterations with overrelaxation = 1.

In addition to the overrelaxation option, the algorithm makes sure that after every iteration the residual is reduced. If the residual is not reduced, then the step size, $ h = 1 $ , is discarded and updated with

$h = 2^{-i}$

where $ i $ is the number of failed attempts.

Line search

If, in the Newton subsection in the parameter file, the option "Line search" is set to true, i.e. set Line search = true, then a line search is performed at every iteration in order to estimate the value of $ h $ .

In this case, the line search simply involves evaluating the residual at several points, by default 5 points, with $h_i = 2^{-i}$ and $ i = 1,...,5 $ .

At each iteration a line search is performed by evaluating the L2 norm of the residual for each $ h_i $ and then the best step size is selected.

Parameters

The parameters that control all Newton solvers are defined in the subsection Newton in the data input file. The parameters are the following:

* subsection Newton
*  //NewtonLineSearch specific parameters
*  set Line search = false                # Specify if the code should perform a line search
*  set Initial Overrelaxation = 1         # Specify the over-relaxation length, \alpha, for the initial step, i.e. u_i = u_{i-1} + \alpha \delta u
*  set Number of iterations with overrelaxation = 1 # Specify for how many steps should the code overrelax the update ()
*  // All the parameters below are from NetwonBase:
*  set Max steps          = 100           # Maximum number of iterations
*  set Tolerance          = 1.e-8         # Absolute tolerance
*  set Reduction          = 1.e-20        # Maximum allowed reduction during line search. If the residual is not reduced by at least this number the iteration is discarded.
*  set Assemble threshold = 0.0           # Used as a threshold to state if the Jacobian needs to be re-evaluated
*  set Debug level        = 0
*  set Debug residual     = false         # Would you like the code to output the residual at every Newton iteration?
*  set Debug solution     = false         # Would you like the code to output the solution at every Newton iteration?
*  set Debug update       = false
* end
* 

Author: Marc Secanell, 2007

Constructor & Destructor Documentation

FuelCell::ApplicationCore::NewtonLineSearch::NewtonLineSearch ( ApplicationBase & app )

Constructor, receiving the application computing the residual and solving the linear problem.

Member Function Documentation

void FuelCell::ApplicationCore::NewtonLineSearch::_initialize ( ParameterHandler & param )

Read the parameters local to NewtonLineSearch.

virtual void FuelCell::ApplicationCore::NewtonLineSearch::declare_parameters ( ParameterHandler & param )

virtual

Declare the input parameters.

Reimplemented from FuelCell::ApplicationCore::newtonBase.

bool FuelCell::ApplicationCore::NewtonLineSearch::find_negative_values ( const FEVector & u )

private

Routine used to find if there are any negative values on a given solution block.

The block searched is given in

Solution variable not allowed to be negative

If you do not want to search any block, provide a negative value.

virtual void FuelCell::ApplicationCore::NewtonLineSearch::initialize ( ParameterHandler & param )

virtual

Read the parameters.

Reimplemented from FuelCell::ApplicationCore::newtonBase.

virtual void FuelCell::ApplicationCore::NewtonLineSearch::solve	(	FuelCell::ApplicationCore::FEVector &	u,
		const FuelCell::ApplicationCore::FEVectors &	in_vectors
	)

virtual

The actual Newton solver.

Implements FuelCell::ApplicationCore::newtonBase.

Member Data Documentation

const FuelCell::ApplicationCore::Event FuelCell::ApplicationCore::NewtonLineSearch::bad_derivative

static

The Event set by NewtonLineSearch if convergence is becoming bad and a new matrix should be assembled.

unsigned int FuelCell::ApplicationCore::NewtonLineSearch::block_to_fix

private

Block not allowed to be negative:

bool FuelCell::ApplicationCore::NewtonLineSearch::line_search

private

Do you want to use a line search at each step?

double FuelCell::ApplicationCore::NewtonLineSearch::overrelax

private

Value used to multiply $\delta u$ , the solution update, from the Newton algorithm during the first overrelax_steps iterations.

We will multiply the first iteration by $\alpha \delta u$ , where $\alpha$ is the value of overrelax and then the following iterations by $it \alpha \delta u$ where $ it $ is the iteration number