Detailed Description

Interface specialization of an IDetailedModel ready to use with Greedy algorithms for (time dependent) Finite volume discretizations.

Definition at line 19 of file FVDetailedModelDefault.m.

Inheritance diagram for Greedy.User.FVDetailedModelDefault:

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Collaboration diagram for Greedy.User.FVDetailedModelDefault:

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Public Member Functions
	FVDetailedModelDefault (ModelDescr descr)
	Constructor for this class.

function UON =	orthonormalize (ModelData model_data, U)
	orthonormalizes a set of discrete functions \(\{ v_h^l \}_{l=1}^L\)

function U0 =	init_values_algorithm (ModelData model_data)
	computes the Dof vectors for the initial value function \(u_h^0(\cdot;t\mu) = {\cal P}_h[u_0(\mu)]\)

function UV =	inner_product (ModelData model_data, U, V)
	computes the inner project between the Dof vectors of two discrete functions

Public Member Functions inherited from Greedy.User.IDetailedModel
	IDetailedModel (descr)
	constructor

Public Member Functions inherited from IDetailedModel
	IDetailedModel (descr)
	constructor

function isequal =	eq (IDetailedModel other)
	overloaded equality (`==`) operator, by default comparing the descr variables

function IDetailedModel this =	set_mu (mu)
	sets the active parameter vector \(\mu \in {\cal M}\)

function mu =	get_mu ()
	returns the active parameter vector \(\boldsymbol\mu \in {\cal M}\)

virtual function ModelData model_data =	gen_model_data ()
	generates large model data.

virtual function sim_data =	detailed_simulation (model_data)
	executes a detailed simulation for a given parameter

virtual function p =	plot_sim_data (model_data, sim_data, plot_params)
	plots the simulation data as returned by detailed_simulation()

Static Public Member Functions
static function errs =	l2_error_sequence_algorithm (U, Uapprox,ModelData model_data)
	computes the \(L^2(\Omega)\) error for each "snapshot" of a trajectories and returns the sequence of these errors.

static function errs =	linfty_error_sequence_algorithm (U, Uapprox,ModelData model_data)
	computes the \(L^{\infty}(\Omega)\) error for each "snapshot" of a trajectories and returns the sequence of these errors.

static function W =	get_inner_product_matrix (ModelData model_data)
	returns the inner product matrix for efficient computation of inner products on \({\cal W}_h\)

Static Public Member Functions inherited from Greedy.User.IDetailedModel
static function U =	get_dofs_from_sim_data (sim_data)
	extracts the \(H\) dimensional Dof vector from the `sim_data` structure

static function snapshot =	get_dofs_at_time (sim_data, time_index)

Additional Inherited Members
Public Attributes inherited from IDetailedModel
	descr
	The description structure holding information about the analytical parametrized problem and its discretization.

	decomp_mode

	mu_names
	cell array of strings describing the parameters of the model

	mu_ranges
	cell array of vectors of size two defining the allowed interval range for the parameter components

	verbose
	an integer defining the verbosity level of information output during basis generation

	debug
	an integer defining the debugging level controlling error output and extra tests during basis generation

Static Public Attributes inherited from IDetailedModel
static const	base_checks
	this structure holds variable names that need to be defined by the descr structure.

Constructor & Destructor Documentation

Greedy.User.FVDetailedModelDefault.FVDetailedModelDefault ( ModelDescr descr )

Constructor for this class.

Parameters

descr structure

Definition at line 34 of file FVDetailedModelDefault.m.

Member Function Documentation

function W = Greedy.User.FVDetailedModelDefault.get_inner_product_matrix ( ModelData model_data )

staticvirtual

returns the inner product matrix for efficient computation of inner products on \({\cal W}_h\)

The matrix \(W\) returned can be used to compute an inner product

\[\langle u_h, v_h\rangle_{{\cal W}_h} = U^t W V\]

where \(U, V\) are the Dof vectors of the discrete functions \(u_h, v_h\in {\cal W}_h\).

Parameters

model_data Matlab structure storing (possibly) high dimensional data needed by IDetailedModel.detailed_simulation().

Return values

W	The matrix \(W\)

Implements Greedy.User.IDetailedModel.

Definition at line 127 of file FVDetailedModelDefault.m.

function U0 = Greedy.User.FVDetailedModelDefault.init_values_algorithm ( ModelData model_data )

virtual

computes the Dof vectors for the initial value function \(u_h^0(\cdot;t\mu) = {\cal P}_h[u_0(\mu)]\)

Parameters

model_data Matlab structure storing (possibly) high dimensional data needed by IDetailedModel.detailed_simulation().

Return values

U0	the Dof vector of the initial value projection

This calls the function pointer defined in the descr structure field init_values_algorithm.

Implements Greedy.User.IDetailedModel.

Definition at line 69 of file FVDetailedModelDefault.m.

function UV = Greedy.User.FVDetailedModelDefault.inner_product	(	ModelData	model_data,
			U,
			V
	)

virtual

computes the inner project between the Dof vectors of two discrete functions

Parameters

U	Dof vector of first discrete function \(u_h\)
V	Dof vector of second discrete function \(v_h\)
model_data	Matlab structure storing (possibly) high dimensional data needed by IDetailedModel.detailed_simulation().

Return values

UV	Dof vector of innter product \(\langle u_h, v_h \rangle_{{\cal W}_h}\)

This uses the W=get_inner_product_matrix() method in order to compute the inner product \(\langle u_h, v_h \rangle = U' W V\)

Implements Greedy.User.IDetailedModel.

Definition at line 83 of file FVDetailedModelDefault.m.

function errs = Greedy.User.FVDetailedModelDefault.l2_error_sequence_algorithm	(		U,
			Uapprox,
		ModelData	model_data
	)

staticvirtual

computes the \(L^2(\Omega)\) error for each "snapshot" of a trajectories and returns the sequence of these errors.

Parameters

U	first sequence of Dof vectors of discrete functions \(\{u_h^k\}_{k=0}^K\) stored in a `H x K+1` matrix
Uapprox	second sequence of Dof vectors of functions \(\{v_h^k\}_{k=0}^K\) stored in a `H x K+1` matrix
model_data	Matlab structure storing (possibly) high dimensional data needed by IDetailedModel.detailed_simulation().

Return values

errs	sequence of errors \(\{ \\| u_h^k - v_h^k \\|_{L^2(\Omega)} \}_{k=0}^{K}\) stored in a `K+1 x 1` vector

This function calls fv_l2_error()

Implements Greedy.User.IDetailedModel.

Reimplemented in TwoPhaseFlow.DetailedModel.

Definition at line 101 of file FVDetailedModelDefault.m.

function errs = Greedy.User.FVDetailedModelDefault.linfty_error_sequence_algorithm	(		U,
			Uapprox,
		ModelData	model_data
	)

staticvirtual

computes the \(L^{\infty}(\Omega)\) error for each "snapshot" of a trajectories and returns the sequence of these errors.

Parameters

U	first sequence of Dof vectors of discrete functions \(\{u_h^k\}_{k=0}^K\) stored in a `H x K+1` matrix
Uapprox	second sequence of Dof vectors of functions \(\{v_h^k\}_{k=0}^K\) stored in a `H x K+1` matrix
model_data	Matlab structure storing (possibly) high dimensional data needed by IDetailedModel.detailed_simulation().

Return values

errs	sequence of errors \(\{ \\| u_h^k - v_h^k \\|_{L^{\infty}(\Omega)} \}_{k=0}^{K}\) stored in a `K+1 x 1` vector

This function calls fv_linfty_error();

Implements Greedy.User.IDetailedModel.

Definition at line 114 of file FVDetailedModelDefault.m.

function UON = Greedy.User.FVDetailedModelDefault.orthonormalize	(	ModelData	model_data,
			U
	)

virtual

orthonormalizes a set of discrete functions \(\{ v_h^l \}_{l=1}^L\)

Parameters

U	The Dof vectors for the set of discrete functions
model_data	Matlab structure storing (possibly) high dimensional data needed by IDetailedModel.detailed_simulation().

Return values

UON	The Dof vectors of the orthonormalized set of discrete functions.

This implements an orthonormalization with help of the QR method.

Implements Greedy.User.IDetailedModel.

Definition at line 53 of file FVDetailedModelDefault.m.

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

rbasis/basisgen/oop/+Greedy/+User/FVDetailedModelDefault.m

Detailed Description

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

Member Function Documentation