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rbmatlab
1.16.09
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rbmatlab
1.16.09
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Reduced data implementation for non-linear evolution problems with finite volume discretizations.
See [DHO11] Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation for details on the implementations of the reduced matrices and vectors.
Definition at line 18 of file EiRbReducedDataNode.m.
Public Member Functions | |
| EiRbReducedDataNode (IReducedModel rmodel,TwoPhaseFlow.RbReducedDataNode rb_reduced_data,Greedy.DataTree.Detailed.RbLeafNode rb_detailed_data,TwoPhaseFlow.EiReducedDataNode ei_reduced_data,Greedy.DataTree.Detailed.EiLeafNode ei_detailed_data) | |
| Constructor for the generation of the reduced matrices and vectors. More... | |
| function conds = | get_conds () |
| function yesno = | needs_subset_copy (TwoPhaseFlow.ReducedModel rmodel) |
 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... | |
Public Attributes | |
| BM | |
| empirical interpolation matrix \({\bf B}\) More... | |
| gridbase | grid_local_ext |
| local grid with added neighbours such that a sparse evaluation of the empirically interpolated operators in the interpolation points is possible on this grid. More... | |
| gridbase | grid |
| synonym for grid_local_ext More... | |
| TM_local | |
| indices of grid entities in the grid_local_ext structure where the interpolation points are situated. More... | |
| TM_global | |
| indices of grid entities in the the global grid structure where the interpolation points are situated. More... | |
| gEI | |
| gn_edges | |
| gn_inner_edges | |
| gn_boundary_edges | |
| Mmass | |
| empirical interpolation mass matrix. More... | |
| N | |
| number of reduced basis vectors stored in this data node. More... | |
| M | |
| number of collateral reduced basis vectors stored in this data node. More... | |
| Mstrich | |
| number of collateral reduced basis vectors used for error estimation. More... | |
| ::TwoPhaseFlow.RbReducedDataNode | rb_rd |
| handle of object storing all reduced magnitudes based only on the reduced basis. | |
| ::TwoPhaseFlow.EiReducedDataNode | ei_rd |
| handle of object storing all reduced magnitudes based only on the collateral reduced basis. | |
| opdata | |
| DE | |
| "transition" mass matrix More... | |
| CE | |
| empirical interpolation matrix for operator with projection to reduced basis space with \(M+M'\) basis vectors. More... | |
| CE_red | |
| empirical interpolation matrix for operator with projection to reduced basis space for the empirical interpolation with only \(M\) basis vectors. More... | |
| RB_local_ext | |
| restriction of the reduced basis vectors to interpolation DOFs of the local grid grid_local_ext. | |
| Public Attributes inherited from Greedy.User.IReducedDataNode | |
| methods *function | rdn |
| TwoPhaseFlow.EiRbReducedDataNode.EiRbReducedDataNode | ( | IReducedModel | rmodel, |
| TwoPhaseFlow.RbReducedDataNode | rb_reduced_data, | ||
| Greedy.DataTree.Detailed.RbLeafNode | rb_detailed_data, | ||
| TwoPhaseFlow.EiReducedDataNode | ei_reduced_data, | ||
| Greedy.DataTree.Detailed.EiLeafNode | ei_detailed_data | ||
| ) |
Constructor for the generation of the reduced matrices and vectors.
| rmodel | object specifying how the reduced simulations can be computed. |
| rb_reduced_data | pure reduced basis reduced data structure |
| rb_detailed_data | detailed data structure storing the reduced basis. |
| ei_reduced_data | pure EI reduced data structure |
| ei_detailed_data | detailed data structure storing the collateral reduced basis. |
Definition at line 243 of file EiRbReducedDataNode.m.
| function yesno = TwoPhaseFlow.EiRbReducedDataNode.needs_subset_copy | ( | TwoPhaseFlow.ReducedModel | rmodel | ) |
Definition at line 475 of file EiRbReducedDataNode.m.
| TwoPhaseFlow.EiRbReducedDataNode.BM |
empirical interpolation matrix \({\bf B}\)
\[({\bf B})_{ij} = q_i(x_j)\]
for \(1 \leq i \leq j \leq N\) and vanish elsewhere.
Dependent set to true. SetAccess = Private, GetAccess = Public Definition at line 33 of file EiRbReducedDataNode.m.
| TwoPhaseFlow.EiRbReducedDataNode.CE |
empirical interpolation matrix for operator with projection to reduced basis space with \(M+M'\) basis vectors.
This matrix is the solution \({\bf C}\)of the equation system
\[{ \bf B C } = { \bf D }\]
with empirical interpolation matrix \({ \bf B }\) and transition matrix \({\bf D}\).
In case you have a vector of interpolation evaluations \(\bf l\) at interpolation points, the interpolation can the be calculated as
\[{\bf C l}\]
.
Definition at line 203 of file EiRbReducedDataNode.m.
| TwoPhaseFlow.EiRbReducedDataNode.CE_red |
empirical interpolation matrix for operator with projection to reduced basis space for the empirical interpolation with only \(M\) basis vectors.
Definition at line 221 of file EiRbReducedDataNode.m.
| TwoPhaseFlow.EiRbReducedDataNode.DE |
"transition" mass matrix
\[({ \bf D })_{ij} = \int q_i \varphi_j\]
for \(i=1,\ldots,M, j=1,\ldots,N\)Definition at line 191 of file EiRbReducedDataNode.m.
| TwoPhaseFlow.EiRbReducedDataNode.gEI |
Definition at line 101 of file EiRbReducedDataNode.m.
| TwoPhaseFlow.EiRbReducedDataNode.gn_boundary_edges |
Definition at line 110 of file EiRbReducedDataNode.m.
| TwoPhaseFlow.EiRbReducedDataNode.gn_edges |
Definition at line 104 of file EiRbReducedDataNode.m.
| TwoPhaseFlow.EiRbReducedDataNode.gn_inner_edges |
Definition at line 107 of file EiRbReducedDataNode.m.
| TwoPhaseFlow.EiRbReducedDataNode.grid |
synonym for grid_local_ext
Dependent set to true. SetAccess = Private, GetAccess = Public Definition at line 63 of file EiRbReducedDataNode.m.
| TwoPhaseFlow.EiRbReducedDataNode.grid_local_ext |
local grid with added neighbours such that a sparse evaluation of the empirically interpolated operators in the interpolation points is possible on this grid.
Dependent set to true. SetAccess = Private, GetAccess = Public Definition at line 49 of file EiRbReducedDataNode.m.
| TwoPhaseFlow.EiRbReducedDataNode.M |
number of collateral reduced basis vectors stored in this data node.
Dependent set to true. SetAccess = Private, GetAccess = Public Definition at line 144 of file EiRbReducedDataNode.m.
| TwoPhaseFlow.EiRbReducedDataNode.Mmass |
empirical interpolation mass matrix.
\[({ \bf M })_{ij} = \int q_i q_j\]
for \(i,j=1,\ldots,M\)Dependent set to true. SetAccess = Private, GetAccess = Public Definition at line 113 of file EiRbReducedDataNode.m.
| TwoPhaseFlow.EiRbReducedDataNode.Mstrich |
number of collateral reduced basis vectors used for error estimation.
Dependent set to true. SetAccess = Private, GetAccess = Public Definition at line 156 of file EiRbReducedDataNode.m.
| TwoPhaseFlow.EiRbReducedDataNode.N |
number of reduced basis vectors stored in this data node.
Dependent set to true. SetAccess = Private, GetAccess = Public Definition at line 132 of file EiRbReducedDataNode.m.
| TwoPhaseFlow.EiRbReducedDataNode.TM_global |
indices of grid entities in the the global grid structure where the interpolation points are situated.
Dependent set to true. SetAccess = Private, GetAccess = Public Definition at line 88 of file EiRbReducedDataNode.m.
| TwoPhaseFlow.EiRbReducedDataNode.TM_local |
indices of grid entities in the grid_local_ext structure where the interpolation points are situated.
Dependent set to true. SetAccess = Private, GetAccess = Public Definition at line 75 of file EiRbReducedDataNode.m.
1.8.8