#include <theta_scheme.h>

Inheritance diagram for FuelCell::ApplicationCore::ThetaScheme:

Collaboration diagram for FuelCell::ApplicationCore::ThetaScheme:

Public Member Functions
	ThetaScheme (ApplicationBase &app)
	Constructor, receiving an application with transient model and a data object. More...

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

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

virtual void	solve (FuelCell::ApplicationCore::FEVector &u, const FuelCell::ApplicationCore::FEVectors &in_vectors)
	Actual transient solver. More...

Public Member Functions inherited from FuelCell::ApplicationCore::TransientBase
	TransientBase (ApplicationBase &app)
	Constructor, receiving an application with transient model and a data object. 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	new_assembly
	Event used to make application reassemble its system matrix and rhs. More...

Private Member Functions
void	solve_operations (FuelCell::ApplicationCore::FEVector &u, const FuelCell::ApplicationCore::FEVectors &in_vectors, bool print_solution)
	Performs one transient iteration with the given time step `tau`. More...

Private Attributes
double	theta
	Parameter $\theta \in [0,\,1]$ . More...

double	current_time

float	current_layer
	Variable that contains current time layer. More...

unsigned short int	scheme_order

Additional Inherited Members
Protected Member Functions inherited from FuelCell::ApplicationCore::TransientBase
void	debug_output (const FEVector &sol)
	Function used to output any necessary information at each time layer for debugging purposes. More...

void	responses_output ()
	Function used to output boundary responses computed by application. More...

void	error_output (const double &err)
	Function used to output the solution error on each layer. More...

void	tau_output ()
	Function used to output time step on each time layer. More...

void	initialize_u_old (const FEVector u, const double n_ref, const FEVector old_solution, const bool force=true)
	If we are inside the adaptive refinement loop, then we receive the old solution from class since it was transferred to a finer mesh and has now a different size. More...

void	ats_Richardson (FEVector &u, const FEVector u1, const FEVector u2, int scheme_order, bool &solution_accepted)
	This routine estimates solution error and changes the time step using Richardson extrapolation. More...

bool	file_exists (const std::string &file)

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::TransientBase
bool	print_last_layer_only
	If this variable is set to true, then only the last time layer data will be printed. More...

bool	debug_solution
	Print updated solution after each step into file `solution_NNNNN.dat`. More...

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

unsigned int	step
	Number of the current time layer. More...

std::string	ats_method
	Decision varible for selecting the adaptive time stepping method. More...

double	tau
	Initial time step size. More...

double	max_tau
	Maximal time step size. More...

double	min_tau
	Minimal time step size. More...

int	max_ats_it
	Maximal number of adaptive time step iterations used to resolve each time layer. More...

FEVector	u_old
	A vector to store the solution from the previous time layer in. More...

int	ar_freq
	If adaptive refinement is selected, then it will be performed at each `ar_freq`-th layer. More...

double	total_time
	Total time of simulation in seconds. More...

double	time
	Current time of simulation. More...

double	abs_err_estimate

double	rel_err_estimate

double	abs_error_tolerance

double	rel_error_tolerance

bool	output_error

bool	output_tau

std::ofstream	responses_outfile
	Variable used in printing responses data into a file. More...

std::ofstream	error_outfile
	Variable used in printing solution error data into a file. More...

std::ofstream	tau_outfile
	Variable used in printing time step into a file. More...

const std::string	fname_err ="Solution_error.dat"
	File name for solution error output. More...

const std::string	fname_tau ="Time_step.dat"
	File name for solution error output. More...

std::vector< double >	all_time_values
	A vector of all time values. More...

bool	everything_is_fine =true

unsigned int	n_ref

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

Theta scheme

Theta scheme is a time discretization method for PDEs arising from finite difference approximation of temporal derivative and implicit-explicit treatment of spatial operators and source terms.

In general, a theta scheme for a PDE

$u_{,t}+L(u)=f(u,\,t),$

where $ L(u) $ is a spatial differential operator and $f(u,\,t)$ is a source term, will look like

$\frac{u^{n+1}-u^n}{\tau}+\theta L(u^{n+1}) + (1-\theta) L(u^n) = \theta f(u^{n+1},\,t) + (1-\theta) f(u^n,\,t).$

Here we used first order approximation of $u_{,t}$ . After finite element method is applied, resulting equation is of the form

$[ M + \tau \theta A ] u^{n+1} = [ M + \tau (1-\theta) A ] u^n + \tau \theta f(u^{n+1},\,t) + \tau (1-\theta) f(u^n,\,t),$

where $ M $ is a mass matrix and $ A $ is a matrix corresponding to operator $ L(u) $ . Depending on parameter $\theta \in [0,\,1]$ , one can obtain explicit Euler scheme ( $\theta = 0$ ), Crank-Nicolson scheme ( $\theta = 0.5$ ), implicit Euler scheme ( $\theta = 1$ ), or anything inbetween.

Parameters

Parameters that control theta scheme solver are defined in Theta_Scheme subsection in the data input file. Default parameters are as follows:

subsection Transient
 set Total time of simulation, [s] = 10       
 subsection Theta Scheme
  set Theta = 0.5        
 end       
end

Usage

In order to use the class, first create an object passing in a linear application and data application

boost::shared_ptr< FuelCell::ApplicationCore::ApplicationData >  data = FuelCell::ApplicationCore::ApplicationData ();
FuelCell::Application::AppDiffusion<dim> app_lin (data);
FuelCell::ApplicationCore::ThetaScheme> transient_solver (app_lin,data);

Then, read data and initialize code using a ParameterHandler object:

transient_solver.declare_parameters(param);
// Use ParameterHandler param to read from file ...
transient_solver.initialize(param);

Finally, execute:

transient_solver.solve(u_out, in_vectors)

Author: Aslan Kosakian and Marc Secanell, 2015

Constructor & Destructor Documentation

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

Constructor, receiving an application with transient model and a data object.

Member Function Documentation

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

virtual

Declare input parameters.

The following are the parameters used and their default values in section "Transient".

Total time of simulation, [s] = 10;
Theta = 0.5.

These values are set in parameter file.

Reimplemented from FuelCell::ApplicationCore::TransientBase.

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

virtual

Read parameters.

Reimplemented from FuelCell::ApplicationCore::TransientBase.

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

virtual

Actual transient solver.

Performs loop over time layers.

Parameters:

u : Output solution at the next time step
in_vectors : collection of vectors with information at each DOF.

Implements FuelCell::ApplicationCore::TransientBase.

void FuelCell::ApplicationCore::ThetaScheme::solve_operations	(	FuelCell::ApplicationCore::FEVector &	u,
		const FuelCell::ApplicationCore::FEVectors &	in_vectors,
		bool	print_solution
	)

private

Performs one transient iteration with the given time step tau.

Member Data Documentation

float FuelCell::ApplicationCore::ThetaScheme::current_layer

private

Variable that contains current time layer.

Note: The type is float so that partial steps can be shown, e.g. step .

double FuelCell::ApplicationCore::ThetaScheme::current_time

private

const FuelCell::ApplicationCore::Event FuelCell::ApplicationCore::ThetaScheme::new_assembly

static

Event used to make application reassemble its system matrix and rhs.

unsigned short int FuelCell::ApplicationCore::ThetaScheme::scheme_order

private

double FuelCell::ApplicationCore::ThetaScheme::theta

private

Parameter $\theta \in [0,\,1]$ .

Depending on parameter $\theta \in [0,\,1]$ , one can obtain explicit Euler scheme ( $\theta = 0$ ), Crank-Nicolson scheme ( $\theta = 0.5$ ), implicit Euler scheme ( $\theta = 1$ ), or anything inbetween.

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

theta_scheme.h

Public Member Functions

Static Public Attributes

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Theta scheme

Parameters

Usage

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation