Detailed Description

reduced model for linear evolution problems as given by a LinEvol.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 LinEvol.ReducedModel:

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Collaboration diagram for LinEvol.ReducedModel:

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

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

function rb_sim_data =	rb_simulation_impl (LinEvol.ReducedData 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 rb_sim_data =	rb_reconstruction (LinEvol.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...

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

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

LinEvol.ReducedModel.ReducedModel	(	LinEvol.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 59 of file ReducedModel.m.

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Member Function Documentation

function LinEvol.ReducedModel c = LinEvol.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.

Reimplemented in LinEvolDune.ReducedModel.

Definition at line 144 of file ReducedModel.m.

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function Delta = LinEvol.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.

Reimplemented in LinEvolDune.ReducedModel.

Definition at line 168 of file ReducedModel.m.

function Delta = LinEvol.ReducedModel.get_estimators_from_sim_data ( rb_sim_data )

static

Definition at line 157 of file ReducedModel.m.

function a0 = LinEvol.ReducedModel.rb_init_values	(	Greedy.DataTree.Detailed.RBLeafNode	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 89 of file ReducedModel.m.

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function rb_sim_data = LinEvol.ReducedModel.rb_reconstruction	(	LinEvol.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 IReducedModel.rb_simulation() .

Return values

rb_sim_data struct holding the reduced simulation results and their reconstructions.

Definition at line 116 of file ReducedModel.m.

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function simulation_data = LinEvol.ReducedModel.rb_simulation_impl ( LinEvol.ReducedData 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, N, M, mu
not allowed dependency of data: H
allowed dependency of computation: Nmax, 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.

if model.name_output_functional is set, then additionally, a sequence of output estimates s(U(:,)) and error bound Delta_s is returned

Parameters

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

Return values

simulation_data struct holding the reduced simulation 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
error_norm — string specifying the used error norm for residual computations. Possible values are l2 or energy.
L_I_inv_norm_bound — upper bound on implicit operator inverse norm constant in time, a single scalar
L_E_norm_bound — upper bounds on explicit operator constant in time, a single scalar
energy_norm_gamma — gamma >= 0 defining the weight in the energy norm

Required fields of reduced_data:

a0 — a0
LL_E — LL E
rb_operators — rb operators
LL_I — LL I
bb — bb
K_II — K II
K_IE — K IE
K_EE — K EE
m_I — m I
m_E — m E
m — m
s_RB — s RB
s_l2norm — s l2norm

Optional fields of descr:

data_const_in_time — if this flag is set, then only operators for first time instance are computed
name_output_functional — if this field is existent, then an output estimation is performed and error.estimtations
starting_time_step — in t-partition case this is the starting time step for the actual t-partitioni time step
stopping_time_step — in t-partition this is the stopping time step for the actual t-partition

Optional fields of reduced_data:

Delta0 — initial error added to the total error

Generated fields of simulation_data:

a — time sequence of solution coefficients, columns are a(:,k) = \(a^{k-1}\)
Delta — time sequence of \(L^2\)-posteriori error estimates Delta(k) = \(\Delta^{k-1}_N\) or energy-norm-posteriori error estimates Delta_energy(k) = \(\bar \Delta^{k-1}_N\) depending on the field error_norm in descr.
Delta_s — (optional) error bounds for the sequence of output estimates s(U(:,)). This is returned if model.name_output_functional is set.
s — (optional) sequence of output estimates s(U(:,)). This is returned if model.name_output_functional is set.
LL_I — \(Q_I\) reduced matrix for implicit operator \({\cal L}_{h,I}\)
LL_E — \(Q_E\)-sequence of reduced matrices for explicit operator \({\cal L}_{h,E}\)
mu — parameter vector of simulation solution

Definition at line 19 of file rb_simulation_impl.m.

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Member Data Documentation

LinEvol.ReducedModel.ddescr_checks

static

Initial value:

= struct("   \
      'operators_ptr',         {{\@(x) isequal(class(x), 'function_handle')}},   \
      'init_values_algorithm', {{\@(x) isequal(class(x), 'function_handle')}},   \
      'error_norm',            {{\@ischar, 'values', {'l2', 'energy'} }}   
      ")

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

Default: struct(" \ 'operators_ptr', {{@(x) isequal(class(x), 'function_handle')}}, \ 'init_values_algorithm', {{@(x) isequal(class(x), 'function_handle')}}, \ 'error_norm', {{@ischar, 'values', {'l2', 'energy'} }} ")

Definition at line 39 of file ReducedModel.m.

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

rbasis/problem_types/+LinEvol/@ReducedModel/ReducedModel.m
rbasis/problem_types/+LinEvol/@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