test_ei.m

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% small script testing the empirical interpolation 
%
% detailed_data is loaded and single large timestep from 0 to T is
% performed. The linear and nonlinear simulation are opened in the
% gui for comparison and adjusting the parameters

% Bernard Haasdonk 31.5.2007


load demo_nonlin_evol_detailed_data3
params.nt = 1;
params.dt=params.T;
params.k = 0; % deactivate implicit contribution
params.N = size(detailed_data.RB,2);
%params.M = size(detailed_data.QM{1},2);
params.M = 100;
paramslin = params;
paramslin.rb_problem_type = 'lin_evol';

% plot both linear and nonlinear simulation result: should be the same
demo_rb_gui(detailed_data,[],params,'Nonlinear simulation');
demo_rb_gui(detailed_data,[],paramslin,'Linear simulation');

% plot details on nonlinear evolution:

tmp = load('debug_rb_nonlin_evol_simulation');

  % plot computed ll_E values on subgrid

  UN_local_ext = -ones(size(tmp.U_local_ext));

  UN_local_ext(tmp.reduced_data.TM_local) = tmp.U_local;
  
  % plot data before operator evaluation
  figure, plot_element_data(tmp.reduced_data.grid_local_ext,...
                            tmp.U_local_ext, ...
                            tmp.params);
  title('U_local_ext before operator evaluation');
  % plot data after operator evaluation
  figure, plot_element_data(tmp.reduced_data.grid_local_ext,...
                            UN_local_ext,tmp.params);
  ax = gca;
  title('UN_local_ext after operator evaluation');
  
  % plot exact reconstruction before Galerkin projection
  sigma = detailed_data.BM(1:params.M,1:params.M) \ tmp.ll_E;
  UNreconstr = detailed_data.QM(:,1:params.M) * sigma;
  figure, plot_element_data(detailed_data.grid,...
                            UNreconstr,tmp.params);
  title('Exact EI-reconstruction');
%  set(ax,'clim',get(gca,'clim'));
  
% check difference in points: real interpolated values obtained?

mask = zeros(1,detailed_data.grid.nelements);
nbi = detailed_data.grid.NBI(detailed_data.TM,:);
i = find(nbi>0);
mask(nbi(i)) = 1;
mask(detailed_data.TM) = 2;
local_ext_ind = find(mask);
UNreconstr_local_ext = UNreconstr(local_ext_ind);
UNreconstr_local = UNreconstr_local_ext(tmp.reduced_data.TM_local(1:params.M));

figure,plot([UNreconstr_local(:), tmp.ll_E(:)]);
legend({'ei-reconstruction-values','local_eval'});
title(['Comparison of local evaluation values and the values',...
       ' of the resulting interpolant']);

% peform galerkin projection and reconstruction, plot result
A = feval(params.inner_product_matrix_algorithm,detailed_data.grid,params);
a =  detailed_data.RB' * A * UNreconstr;  
UN_RBreconstr = detailed_data.RB * a;
figure, plot_element_data(detailed_data.grid,...
                          UN_RBreconstr,tmp.params);
title('RB-reconstruction of EI-projection');

figure,plot([tmp.rhs, -params.dt * a(:)]);
legend({'reconstr','simulation'});
title(['Comparison of RB-coefficients from explicit reconstruction ', ...
       'and simulation.']);

  
    


% TO BE ADJUSTED TO NEW SYNTAX
%| \docupdate