Detailed Description

reduced model for non-linear evolution problems as given by a NonlinEvol.DetailedModel.

This is compatible with Greedy.User.IReducedModel and can therefore make use of detailed data objects created by Greedy algorithms.

Definition at line 18 of file ReducedModel.m.

Inheritance diagram for NonlinEvol.ReducedModel:

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Collaboration diagram for NonlinEvol.ReducedModel:

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Public Member Functions
	ReducedModel (NonlinEvol.DetailedModel dmodel,BasisGenDescr bg_descr)
	Constructor for the reduced model. More...

function M =	get_current_M (id)
	returns the collateral reduced basis size for the current parameter and time instant More...

function NonlinEvol.ReducedModel c =	copy ()
	function that deep copies this handle class More...

function rb_sim_data =	rb_simulation_impl (NonlinEvol.EiRbReducedDataNode reduced_data)
	function, which performs a reduced basis online simulation for the parameter vector \(\mu \in {\cal P} \subset \mathbb{R}^p\), which is assumed to be set by IDetailedModel.set_mu() More...

function a0 =	rb_init_values (Greedy.DataTree.Detailed.PODEILeafNode detailed_data, decomp_mode)
	function computing initial values for a reduced simulation. More...

function rb_sim_data =	rb_reconstruction (NonlinEvol.DetailedData detailed_data, rb_sim_data)
	(trivial) function computing a detailed reconstruction by linear combination of the coefficients in the simulation data with the orthonormal reduced basis RB More...

Public Member Functions inherited from Greedy.User.IReducedModel
	IReducedModel (IDetailedModel dmodel,BasisGenDescr bg_descr)
	constructor for this reduced model interface More...

function Greedy.User.ReducedData reduced_data =	gen_reduced_data (Greedy.User.IDetailedData detailed_data)
	Constructs the `reduced_data` object holding low dimensional data needed for efficient reduced simulations with rb_simulation(). More...

function rb_sim_data =	rb_simulation (Greedy.User.ReducedData reduced_data)
	forwards the reduced simulation to the method rb_simulation_impl() after getting a suitable reduced data leaf element. More...

virtual function rb_sim_data =	rb_simulation_impl (Greedy.User.IReducedDataNode reduced_data)
	implementation of the reduced simulation More...

Public Member Functions inherited from IReducedModel
	IReducedModel (IDetailedModel dmodel, bg_descr)
	Constructor of a reduced model. More...

function iseq =	eq (IReducedModel other)
	Comparison operator checking whether the underlying detailed_model members of `this` and `other` are equal. More...

function IReducedData reduced_data =	gen_reduced_data (detailed_data)
	Constructs the `reduced_data` object holding low dimensional data needed for efficient reduced simulations with rb_simulation(). More...

function reduced_data_subset =	extract_reduced_data_subset (IReducedData reduced_data)
	Extracts a subset of the `reduced_data` generated by gen_reduced_data(). More...

virtual function rb_sim_data =	rb_simulation (reduced_data)
	Executes a reduced simulation and optionally an error estimation. More...

virtual function rb_sim_data =	rb_reconstruction (detailed_data, rb_sim_data)
	reconstructs the reduced simulation snapshots generated by rb_simulation() in the reduced space \({\cal W}_{\text{red}}\). More...

function U =	get_dofs_from_sim_data (sim_data)
	extracts the \(H\) dimensional Dof vector from the `sim_data` structure More...

function IDetailedData detailed_data =	gen_detailed_data (model_data)
	initiates the reduced basis generation process More...

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

function model_data =	gen_model_data ()
	generates large model data. More...

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

function this =	set_mu (mu)
	Sets the active parameter vector \(\mu \in {\cal M}\) used for simulations on this model. More...

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

function rb_size =	get_rb_size (detailed_data)
	returns the size of the generated reduced basis by the IDetailedData class. More...

function	couple_N_and_M (detailed_data, ratio, factor)
	sets all the basis sizes for reduced simulations by a ratio with respect to the maximum possible basis size and a factor between RB and EI basis sizes. More...

function this =	set_Mratio (detailed_data, ratio)
	in case of multiple operators subject to empirical interpolation, this sets number of reduced basis functions used for reduced simulations by specifying a ratio. More...

function Mratio =	get_Mratio (detailed_data)
	in case of multiple operators subject to empirical interpolation, this gets the mean of ratio between the number of reduced basis functions used for reduced simulations and the maximum possible. More...

function varargout =	subsref (S)
	forwarding of fieldnames access to the underlying detailed_model description More...

Static Public Member Functions
static function Delta =	get_estimators_from_sim_data (rb_sim_data)

static function Delta =	get_estimator_from_sim_data (rb_sim_data)
	Static helper method returning an error estimator for the whole reduced trajectory \(\{u_{\text{red}}(\cdot, t^k)\}_{k=0}^{K}\) generated by rb_simulation(). More...

Static Public Member Functions inherited from IModel
static function ok =	struct_check (descr, checks)
	executes checks on the fields of a structure object More...

Public Attributes
	enable_error_estimator = true

	compute_conditions = false
	properties (Constant) More...

	stencil_mode = "edge"
	defines how the stencil of the local grid is computed More...

	local_stencil_size = 1
	defines the number of neighbors that shall be added to the stencil of the local grid created for efficient empirical interpolation evalutations. More...

	t
	current time instance More...

	tstep
	current time step More...

Public Attributes inherited from IReducedModel
	descr
	The description structure holding information about the analytical parametrized problem and its discretization. More...

	decomp_mode

	mu_names
	cell array of strings describing the parameters of the model More...

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

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

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

	crb_enabled = false
	flag indicating whether this model depends on collateral reduced basis spaces. More...

::IDetailedModel	detailed_model
	an object which shall be reduced

::BasisGenDescr	bg_descr
	a structure defining the basis generation routines and data structures.

	enable_error_estimator
	boolean flag indicating whether during an rb_simulation() an a posteriori error estimator shall be computed. More...

	N = 0
	control variable for the size of the reduced basis used for reduced simulations. By default this is equal to the size of the generated reduced basis. More...

	M = 0
	control variable for the size of the (collateral) reduced basis used for empirical interpolations. By default this is equal to the size of the generated reduced basis. More...

	Mstrich = 0
	control variable for the number of (collateral) reduced basis vectors used for error estimation. By default this is equal to zero. More...

Public Attributes inherited from IModel
	num_cpus = 4
	The number of CPUs used for parallel sessions. More...

	decomp_mode
	Decomposition operation mode. More...

	mu_names
	cell array of strings describing the parameters of the model More...

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

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

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

Static Public Attributes
static const	ddescr_checks
	This constant is used for a consistency check of the model descr with help of IModel.struct_check() More...

Static Public Attributes inherited from IModel
static const	time_checks
	This constant can be used for a consistency check of time evolution members in the ModelDescr with help of IModel.struct_check() More...

Constructor & Destructor Documentation

NonlinEvol.ReducedModel.ReducedModel	(	NonlinEvol.DetailedModel	dmodel,
		BasisGenDescr	bg_descr
	)

Constructor for the reduced model.

Parameters

dmodel	object specifying how the high dimensional data can be computed.
bg_descr	structure specifying how the reduced basis shall be generated.

Required fields of dmodel:

descr — descr

Definition at line 130 of file ReducedModel.m.

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Member Function Documentation

function NonlinEvol.ReducedModel c = NonlinEvol.ReducedModel.copy ( )

virtual

function that deep copies this handle class

Return values

c	an object which is a deep copy of this object.

Implements IReducedModel.

Definition at line 194 of file ReducedModel.m.

function M = NonlinEvol.ReducedModel.get_current_M ( id )

returns the collateral reduced basis size for the current parameter and time instant

Parameters

id	an optional id in case there are many collateral reduced basis spaces for one parameter and time instant combination.

Return values

M	the size of the collateral reduced basis space

Definition at line 168 of file ReducedModel.m.

function Delta = NonlinEvol.ReducedModel.get_estimator_from_sim_data ( rb_sim_data )

staticvirtual

Static helper method returning an error estimator for the whole reduced trajectory \(\{u_{\text{red}}(\cdot, t^k)\}_{k=0}^{K}\) generated by rb_simulation().

Parameters

rb_sim_data struct holding reduced simulation data returned by IReducedModel.rb_simulation() . struct holding reduced simulation data returned by IReducedModel.rb_simulation() .

Return values

Delta This is a (K+1) x 1 vector of estimates \(\eta^k(\mu)\) Delta = get_estimators_from_sim_data(rb_sim_data); This is a scalar computed from the estimates \(\eta^k(\mu)\). Usually the maximum over \(k=0,\ldots,K\) is returned.

Implements IReducedModel.

Definition at line 290 of file ReducedModel.m.

function Delta = NonlinEvol.ReducedModel.get_estimators_from_sim_data ( rb_sim_data )

static

Definition at line 279 of file ReducedModel.m.

function a0 = NonlinEvol.ReducedModel.rb_init_values	(	Greedy.DataTree.Detailed.PODEILeafNode	detailed_data,
			decomp_mode
	)

function computing initial values for a reduced simulation.

This calls rb_init_values_separable().

Parameters

detailed_data detailed data tree leaf object

decomp_mode

flag indicating the operation mode of the function:

0 (complete) : no affine parameter dependence or decomposition is performed.
1 (components) : for each output argument a cell array of output matrices is returned representing the \(q\)-th component independent of the parameters given in mu_names.
2 (coefficients) : returns a vector where each coordinate represents the \(q\)-the coefficient \(\sigma_{\cdot}^{q}(\mu)\) dependent on the parameters given in mu_names.

Return values

a0	coefficient vector of size `N x 1` for the initial values.

Definition at line 212 of file ReducedModel.m.

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function rb_sim_data = NonlinEvol.ReducedModel.rb_reconstruction	(	NonlinEvol.DetailedData	detailed_data,
			rb_sim_data
	)

(trivial) function computing a detailed reconstruction by linear combination of the coefficients in the simulation data with the orthonormal reduced basis RB

This calls rb_reconstruction_default().

Parameters

detailed_data	object defining the basis generation algorithm and storage for storing high dimensional data, i.e. dependent on dimension \(H\). This data is necessary for detailed simulations, construction of online matrices, `reduced_data` and reconstruction of reduced simulations.
rb_sim_data	struct holding reduced simulation data returned by ReducedModel.rb_simulation().

Return values

rb_sim_data struct holding the reduced simulation results and their reconstructions.

Definition at line 237 of file ReducedModel.m.

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function rb_sim_data = NonlinEvol.ReducedModel.rb_simulation_impl ( NonlinEvol.EiRbReducedDataNode reduced_data )

function, which performs a reduced basis online simulation for the parameter vector \(\mu \in {\cal P} \subset \mathbb{R}^p\), which is assumed to be set by IDetailedModel.set_mu()

allowed dependency of data: Nmax, Mmax, N, M, mu
not allowed dependency of data: H
allowed dependency of computation: Nmax, Mmax, N, M, mu
not allowed dependency of computation: H
Unknown at this stage: —

The behaviour of this simulation is controlled by the ModelDescr structure rmodel.descr.

Parameters

reduced_data an object constructing and storing all (low-dimensional) reduced matrices and vectors needed for reduced simulations.

Return values

rb_sim_data rb sim data

Required fields of descr:

mu_names — the cell array of names of mu-components and for each of these stringt, a corresponding field in model is expected.
T — end-time of simulation
nt — number of timesteps to compute
L_E_local_name — name of the local space-discretization operator evaluation with syntax
INC_local = L_local(U_local_ext, ind_local,

grid_local_ext, model)

where *_local indicates results on a set of elements, *_local_ext includes information including their neighbours, i.e. the grid must be known also for the neighbours, the values of the previous timstep must be known on the neighbours. The subset of elements, which are to be computed are given in ind_local and the values produced are INC_local. Subsequent time-step operator would be defined as NU_local = U(ind_local) - dt * INC_local
rb_operators — function pointer to a method assembling the decomposed discretization operators

Required fields of reduced_data:

a0 — a0
LL_I — LL I
bb_I — bb I

Optional fields of model:

data_const_in_time — if this flag is set, then only operators for first time instance are computed

Generated fields of rb_sim_data:

a — a(:,k) is the coefficient vector of the reduced simulation at time \(t^{k-1}\)
Delta — Delta
reslog — reslog
eilog — eilog
conds.LI — conds.LI
conds.gradLI — conds.gradLI

Definition at line 19 of file rb_simulation_impl.m.

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Member Data Documentation

NonlinEvol.ReducedModel.compute_conditions = false

properties (Constant)

nl_checks = struct('Mstrich',                {{@isscalar, 'minmax', [0, inf]}},...
                   'enable_error_estimator', {{@isscalar, 'own', ...
                                              @(model) ~model.enable_error_estimator || model.Mstrich > 0, ...
                                              'model.Mstrich needs to be positive if error estimator is enabled'}} ...
                  );

copybrief NonlinEvol.DetailedModel.compute_conditions

Default: false

Definition at line 38 of file ReducedModel.m.

NonlinEvol.ReducedModel.ddescr_checks

static

Initial value:

= struct("   \
      'init_values_algorithm', {{\@(x) isequal(class(x), 'function_handle')}},   \
      'error_norm',            {{\@ischar, 'values', {'l2', 'energy'} }},   \
      'stencil_mode',          {{\@ischar, 'values', {'edge', 'vertex'} }},   \
      'local_stencil_size',    {{\@isnumeric}}   
      ")

This constant is used for a consistency check of the model descr with help of IModel.struct_check()

Default: struct(" \ 'init_values_algorithm', {{@(x) isequal(class(x), 'function_handle')}}, \ 'error_norm', {{@ischar, 'values', {'l2', 'energy'} }}, \ 'stencil_mode', {{@ischar, 'values', {'edge', 'vertex'} }}, \ 'local_stencil_size', {{@isnumeric}} ")

Definition at line 107 of file ReducedModel.m.

NonlinEvol.ReducedModel.enable_error_estimator = true

Note: This property has custom functionality when its value is retrieved.

Definition at line 34 of file ReducedModel.m.

NonlinEvol.ReducedModel.local_stencil_size = 1

defines the number of neighbors that shall be added to the stencil of the local grid created for efficient empirical interpolation evalutations.

See also: stencil_mode

Default: 1

Definition at line 69 of file ReducedModel.m.

NonlinEvol.ReducedModel.stencil_mode = "edge"

defines how the stencil of the local grid is computed

Two possibilities

edge for all neighbours over edges
vertex for all neighbours of a grid cell's vertices

See also: local_stencil_size

Default: "edge"

Definition at line 54 of file ReducedModel.m.

NonlinEvol.ReducedModel.t

current time instance

Note: This property has the MATLAB attribute Dependent set to true.; Matlab documentation of property attributes.

Definition at line 83 of file ReducedModel.m.

NonlinEvol.ReducedModel.tstep

current time step

Note: This property has the MATLAB attribute Dependent set to true.; Matlab documentation of property attributes.

Definition at line 94 of file ReducedModel.m.

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

rbasis/problem_types/+NonlinEvol/@ReducedModel/ReducedModel.m
rbasis/problem_types/+NonlinEvol/@ReducedModel/rb_simulation_impl.m

Detailed Description

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation