Detailed Description

Reduced data implementation for linear evolution problems with finite volume discretizations.

See [HO08a] Reduced Basis Method for Finite Volume Approximations of Parametrized Linear Evolution Equations for details on the implementation of the reduced matrices and vectors.

Definition at line 18 of file ReducedData.m.

Inheritance diagram for LinEvol.ReducedData:

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Collaboration diagram for LinEvol.ReducedData:

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Public Member Functions
	ReducedData (LinEvol.ReducedModel rmodel,IDetailedData detailed_data)
	Constructor for the generation of the reduced matrices and vectors. More...

function yesno =	needs_subset_copy (LinEvol.ReducedModel rmodel)

function conds =	get_conds ()

Public Member Functions inherited from Greedy.User.IReducedDataNode
function subset_reduced_data =	extract_reduced_data_subset (Greedy.User.IReducedModel rmodel)
	Changes the size of the offline data matrices. More...

Public Member Functions inherited from DataTree.ILeafNode
function children =	length ()
	Returns the number of children of the node. More...

function index =	get_index (dummy2, dummy3, dummy)
	Obtains the leaf index vector that best fits the child description given by the three arguments. More...

function this =	set (dummy2,DataTree.INode value)
	Sets a child at the given path in the tree hierarchy. More...

function data =	get (index)
	Access to a child of the current node. More...

function DataTree.ILeafNode node =	get_active_leaf (DataTree.IModel model, id)
	retuns the leaf element for the current IDetailedModel configuration. More...

function tree =	create_tree (creator, ids, mu_cube, tslice, basepath)
	Creates a new tree from a subtree specified by ids, parameter and time index regions. More...

Public Member Functions inherited from DataTree.INode
virtual function DataTree.INode tree =	create_tree (DataTree.ICreator creator, ids, mu_cube, tslice, basepath)
	Creates a new tree from a subtree specified by ids, parameter and time index regions. More...

virtual function this =	set (index, value)
	Sets a child at the given path in the tree hierarchy. More...

function	leaf_func (funcptr, ids, mu_cube, tslice)
	applies a function to all leafs of a DataTree More...

function tree =	create_scalar_tree (funcptr, ids, mu_cube, tslice)
	copies the current trees with different leafs. These leafs are computes by a function returning scalar values. More...

function start_index =	traverse_start ()
	Start iterator for a full traverse of the DataTree. More...

function next_index =	traverse_next (this_index)
	iterator for a full traverse of the DataTree. More...

function description =	get_active_leaf_description (IModel model, ids)
	returns an enumeration of all leaves' basepath index vectors with a description of their parents. More...

function description =	get_leaf_description (ids, mu_cube, tslice)
	returns an enumeration of all leaves' basepath index vectors with a description of their parents. More...

function tstop =	index_valid_till (index)
	Returns the last valid time step index of a time slice. More...

function INode data =	get_by_description (id, mu, nt)
	A combination of get_index() and get() More...

function active_leaf_index =	get_active_leaf_index (IModel model, id)
	retuns the leaf element index for the current IDetailedModel configuration. More...

function DataTree.LeafNode active_leaf =	get_active_leaf (IModel model, id)
	retuns the leaf element for the current IDetailedModel configuration. More...

function	display (fn, basepath, name)
	overwrites the standard display method for DataTree objects More...

function lines =	disp_node (basepath, fn)
	returns a cell array of strings with information on the node. More...

Public Member Functions inherited from IReducedData
virtual function IReducedData subset_reduced_data =	extract_reduced_data_subset (rmodel)
	Changes the size of the offline data matrices. More...

Static Public Member Functions
static function [ LL_I , LL_E , bb , K_II , K_IE , K_EE , m_I , m_E , m ] =	rb_operators (LinEvol.ReducedModel rmodel,Greedy.DataTree.Detailed.RBLeafNode detailed_data, decomp_mode)
	function computing the time-dependent reduced basis operators and vectors. More...

Public Attributes
	a0
	Dof vectors of projections \(\left\{{ \cal P }_{\text{red}}[u_0^q] \right\}_{q=1}^{Q_{u_0}}\). More...

	LL_I
	\(Q_I\) reduced matrix for implicit operator \({\cal L}_{h,I}\) More...

	LL_E
	\(Q_E\)-sequence of reduced matrices for explicit operator \({\cal L}_{h,E}\) More...

	bb
	\(Q_b\)-sequence of reduced vectors for constant contributions \(b_h\) More...

	K_II
	\(Q_I \cdot Q_I\)-sequence of gram matrices More...

	K_IE
	\(Q_I \cdot Q_E\)-sequence of gram matrices More...

	K_EE
	\(Q_E \cdot Q_E\)-sequence of gram matrices More...

	m_I
	\(Q_I \cdot Q_b\)-sequence of vectors More...

	m_E
	\(Q_E \cdot Q_b\)-sequence of vectors More...

	m
	\(Q_b \cdot Q_b\)-sequence of scalars More...

	s_RB
	in case of output functional this is a \(Q_s\)-sequence of vectors. More...

	s_l2norm
	in case of output functional this is a \(Q_s\)-sequence of scalars. More...

	N
	number of reduced basis vectors stored in this data node. More...

	M = 0
	number of collateral reduced basis vectors stored in this data node. More...

	Mstrich = 0
	number of collateral reduced basis vectors used for error estimation More...

Public Attributes inherited from Greedy.User.IReducedDataNode
methods *function	rdn

Constructor & Destructor Documentation

LinEvol.ReducedData.ReducedData	(	LinEvol.ReducedModel	rmodel,
		IDetailedData	detailed_data
	)

Constructor for the generation of the reduced matrices and vectors.

Parameters

rmodel	object specifying how the reduced simulations can be computed.
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.

Definition at line 219 of file ReducedData.m.

Member Function Documentation

function yesno = LinEvol.ReducedData.needs_subset_copy ( LinEvol.ReducedModel rmodel )

Definition at line 261 of file ReducedData.m.

function [ LL_I , LL_E , bb , K_II , K_IE , K_EE , m_I , m_E , m ] = LinEvol.ReducedData.rb_operators	(	LinEvol.ReducedModel	rmodel,
		Greedy.DataTree.Detailed.RBLeafNode	detailed_data,
			decomp_mode
	)

static

function computing the time-dependent reduced basis operators and vectors.

In coefficients mode the detailed data is empty.

Parameters

rmodel	object specifying how the reduced simulations can be computed.
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.
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

LL_I	\(Q_I\) reduced matrix for implicit operator \({\cal L}_{h,I}\)
LL_E	\(Q_E\)-sequence of reduced matrices for explicit operator \({\cal L}_{h,E}\)
bb	\(Q_b\)-sequence of reduced vectors for constant contributions \(b_h\)
K_II	\(Q_I \cdot Q_I\)-sequence of gram matrices
K_IE	\(Q_I \cdot Q_E\)-sequence of gram matrices
K_EE	\(Q_E \cdot Q_E\)-sequence of gram matrices
m_I	\(Q_I \cdot Q_b\)-sequence of vectors
m_E	\(Q_E \cdot Q_b\)-sequence of vectors
m	\(Q_b \cdot Q_b\)-sequence of scalars

Required fields of rmodel:

descr — descr

Required fields of detailed_data:

model_data — model data
RB — RB

Definition at line 19 of file rb_operators.m.

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Member Data Documentation

LinEvol.ReducedData.a0

Dof vectors of projections \(\left\{{ \cal P }_{\text{red}}[u_0^q] \right\}_{q=1}^{Q_{u_0}}\).

See also: LinEvol.ReducedModel.rb_init_values() for details.

Definition at line 34 of file ReducedData.m.

LinEvol.ReducedData.bb

\(Q_b\)-sequence of reduced vectors for constant contributions \(b_h\)

The matrix entries are: \[({ \bf b})_{i} = \int \varphi_i b^q_h\]
for \(i=1,\ldots,N\) and \(q=1,\ldots,Q_b\).

Definition at line 69 of file ReducedData.m.

LinEvol.ReducedData.K_EE

\(Q_E \cdot Q_E\)-sequence of gram matrices

The matrix entries are: \[({ \bf K}_{EE}^{q_1,q_2})_{ij} = \int {\cal L}^{q_1}_{h,E}[\varphi_i] {\cal L}^{q_2}_{h,E}[\varphi_j]\]
for \(i,j=1,\ldots,N\) and \(q_1,q_2=1,\ldots,Q_E\).

Definition at line 105 of file ReducedData.m.

LinEvol.ReducedData.K_IE

\(Q_I \cdot Q_E\)-sequence of gram matrices

The matrix entries are: \[({ \bf K}_{IE}^{q_1,q_2})_{ij} = \int {\cal L}^{q_1}_{h,I}[\varphi_i] {\cal L}^{q_2}_{h,E}[\varphi_j]\]
for \(i,j=1,\ldots,N\) and \(q_1=1,\ldots,Q_I, q_2=1,\ldots,Q_E\).

Definition at line 93 of file ReducedData.m.

LinEvol.ReducedData.K_II

\(Q_I \cdot Q_I\)-sequence of gram matrices

The matrix entries are: \[({ \bf K}_{II}^{q_1,q_2})_{ij} = \int {\cal L}^{q_1}_{h,I}[\varphi_i] {\cal L}^{q_2}_{h,I}[\varphi_j]\]
for \(i,j=1,\ldots,N\) and \(q_1,q_2=1,\ldots,Q_I\).

Definition at line 81 of file ReducedData.m.

LinEvol.ReducedData.LL_E

\(Q_E\)-sequence of reduced matrices for explicit operator \({\cal L}_{h,E}\)

The matrix entries are: \[({ \bf L}_E^q)_{ij} = \int \varphi_i {\cal L}^q_{h,E}[\varphi_j]\]
for \(i,j=1,\ldots,N\) and \(q=1,\ldots,Q_E\).

Definition at line 57 of file ReducedData.m.

LinEvol.ReducedData.LL_I

\(Q_I\) reduced matrix for implicit operator \({\cal L}_{h,I}\)

The matrix entries are: \[({ \bf L}_I^q)_{ij} = \int \varphi_i {\cal L}^q_{h,I}[\varphi_j]\]
for \(i,j=1,\ldots,N\) and \(q=1,\ldots,Q_I\).

Definition at line 45 of file ReducedData.m.

LinEvol.ReducedData.m

\(Q_b \cdot Q_b\)-sequence of scalars

The scalars are: \[{ \bf m}^{q_1,q_2} = \int b_h^{q_1} b_h^{q_2}\]
and \(q_1,q_2=1,\ldots,Q_b\).

Definition at line 141 of file ReducedData.m.

LinEvol.ReducedData.M = 0

number of collateral reduced basis vectors stored in this data node.

Note: This property has non-standard access specifiers: SetAccess = Private, GetAccess = Public; Matlab documentation of property attributes.
Default: 0

Definition at line 193 of file ReducedData.m.

LinEvol.ReducedData.m_E

\(Q_E \cdot Q_b\)-sequence of vectors

The vector entries are: \[({ \bf m}_E^{q_1,q_2})_i = \int {\cal L}^{q_1}_{h,E}[\varphi_i] b_h^{q_2}\]
for \(i=1,\ldots,N\) and \(q_1=1,\ldots,Q_E, q_2=1,\ldots,Q_b\).

Definition at line 129 of file ReducedData.m.

LinEvol.ReducedData.m_I

\(Q_I \cdot Q_b\)-sequence of vectors

The vector entries are: \[({ \bf m}_I^{q_1,q_2})_i = \int {\cal L}^{q_1}_{h,I}[\varphi_i] b_h^{q_2}\]
for \(i=1,\ldots,N\) and \(q_1=1,\ldots,Q_I, q_2=1,\ldots,Q_b\).

Definition at line 117 of file ReducedData.m.

LinEvol.ReducedData.Mstrich = 0

number of collateral reduced basis vectors used for error estimation

Note: This property has non-standard access specifiers: SetAccess = Private, GetAccess = Public; Matlab documentation of property attributes.
Default: 0

Definition at line 204 of file ReducedData.m.

LinEvol.ReducedData.N

number of reduced basis vectors stored in this data node.

Note: This property has the MATLAB attribute Dependent set to true.; This property has non-standard access specifiers: SetAccess = Private, GetAccess = Public; Matlab documentation of property attributes.; [readonly]

Definition at line 179 of file ReducedData.m.

LinEvol.ReducedData.s_l2norm

in case of output functional this is a \(Q_s\)-sequence of scalars.

The scalars are: \[{ \bf s}_{l^2}^q = \|s(\varphi_1), \ldots, s(\varphi_N)\|_{l^2}\]
for \(q_1=1,\ldots,Q_s\)

Definition at line 165 of file ReducedData.m.

LinEvol.ReducedData.s_RB

in case of output functional this is a \(Q_s\)-sequence of vectors.

The vector entries are: \[({ \bf s}^q)_i = s(\varphi_i)\]
for \(i=1,\ldots,N\) and \(q_1=1,\ldots,Q_s\)

Definition at line 153 of file ReducedData.m.

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

rbasis/problem_types/+LinEvol/@ReducedData/ReducedData.m
rbasis/problem_types/+LinEvol/@ReducedData/rb_operators.m

Detailed Description

Public Member Functions

Static Public Member Functions

Public Attributes

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation