rb_burgers_fem_online_prep.m

function reduced_data = rb_burgers_fem_online_prep(offline_data,params)
%function reduced_data = rb_burgers_fem_online_prep(offline_data,params)
%
% method which produces reduced_data, which is the data, that will
% be passed to the online-simulation algorithm. 
% Typically, this routine only does a submatrix extraction of the Mmax, Nmax 
% sized offline-objects to produce M, N sized objects for the real simulation.
% Therefore, no quantities or computations dependent on the
% high-dimension H may be included here. Neither may online-data
% include parameter-dependent
% mu-quantities. So no complete grid or detailed solutions 
% or reduced basis vectors may be stored here. 
%
% allowed dependency of data: Nmax, N, M
% not allowed dependency of data: H
% allowed dependency of computation: Nmax, N, M
% not allowed dependency of computation: H
% Unknown at this stage: mu
%
% Required fields of params:
%  N       : number of reduced basis vectors to choose
%
% generated fields of reduced_data:
%  H1{q}    : sequence of N-vector components of initial data projection 
%            ``q = 1... Q_{dir} \quad
%            \verb|H1{q}| = \int u_{dir}^q \xi_i``
%  M       : matrix of N x N mass matrix entries 
%            `M = \int \xi_i \xi_j`
%  B1{q}   : list of N x N stiffness matrix 
%            ``q = 1... Q_{\eta} \qquad
%            \verb|B1{q}| = \int \eta^q (\nabla \xi_i) (\nabla \xi_j)``
%  B2{q1,q2} : array of N x N convection matrices
%            ``\verb|B2{q1,q2)(i,j)|
%              = \int 2 \nabla \cdot (c^{q1} u_{dir}^{q2} \xi_i) \xi_j \qquad
%            q1 = 1... Q_c, q2 = 1.. Q_{dir} ``
%  A{q}:     list of N x N x N tensors
%            ``\verb|A{q}(i,j,k)| = \int \nabla \cdot (c^q \xi_i \xi_j) \xi_k \qquad
%            q = 1,... Q_c``
%  G1{q1,q2}: array of N  vectors
%            ``\verb|G1{q1,q2}(i)|
%              = - \int_{\Gamma_out} \eta^{q1} \nabla u_{dir}^{q2} \cdot n \xi_i \qquad
%            q1 = 1... Q_{\eta}, q2 = 1.. Q_{dir}``
%
%  G2: trivially zero due to missing time dependence
%  G3{q1,q2,q3}: array of N  vectors
%                ``\verb|G3{q1,q2}(i)|
%                  = - \int_{\Omega} 2 c^{q1} u_{dir}^{q2} u_{dir}^{q3} \xi_i \qquad
%                q1 = 1... Q_c, q2 = 1.. Q_{dir}, q3 = 1, ..., Q_{dir}``
%  G4{q1,q2}: array of N  vectors
%             ``\verb|G4{q1,q2}(i)|
%               = - \int_{\Omega} \eta^{q1} \nabla\cdot\nabla u_{dir}^{q2} \xi_i \qquad
%             q1 = 1... Q_{\eta}, q2 = 1.. Q_{dir}``
%
% See the offline-routine for specifications of the fields of offline_data

% Bernard Haasdonk 15.5.2007

% extract correct N-sized submatrices and subvectors from reduced_data
N = params.N;

indices = 1:N;

reduced_data = [];

reduced_data = rb_burgers_fem_offline_subset(offline_data,indices);


% TO BE ADJUSTED TO NEW SYNTAX
%| \docupdate