scripts/riemann_burgers.m

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% script demonstrating the burgers equation with explicit fv
% discretization, empirical interpolation and RB model reduction
%
% a step needs to be selected in this script, default is 1.
%
% example is meant to demonstrate automatic space dimension reduction
% of the algorithm.
% The interpolation basis functions are nicely vertical stripes.
% The error convergence in ei however is constant until 100 basis
% functions then drops to zero. Interesting fact, but clearly M not
% variable afterwards!!!
% As a reduced basis, two shock-trajectories are used.

% Bernard Haasdonk 16.6.2008

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% Select here, what is to be performed with the burgers data %%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%step = 1 % single detailed simulation with given data and plot. Run
         % this with varying parameters mu until sure that scheme
         % is stable. Modify dt or the data-functions accordingly,
         % until a nice parameter-domain with uniformly stable
         % detailed scheme is obtained.
%step = 2 % generate colateral reduced basis of L_E operator
         % takes still 20 minutes if snapshots are already computed!!
%step = 3 % compare single detailed simulation with and without
         % interpolated space operator
%step = 4 % generate dummy reduced basis from trajectories and check, if
         % ei_interpolation with projection on this space maintains
         % result. A simple reduced simulation can also be
         % performed. All results should be visually identical
%step = 5 % generate reduced basis
%step = 6 % time measurement of reduced simulation

%step = 7 % generate error-landscape over varying N (and eventually M)
          % can take several hours!!!
%step = 8 % generate different Figures for presentation and time measurement
step = 9 % start demo_rb_gui with error estimator
%step = 10 % start demo_rb_gui without error estimator

% output-filenames in rbmatlabtemp
CRBfname = 'riemann_burgers_CRB.mat';
detailedfname = 'riemann_burgers_detailed.mat';
testdir = 'riemann_burgers_test_10';
results_fname_base = 'riemann_burgers_step7_result';
ei_detailed_savepath = 'riemann_burgers_ei_detailed';
ei_operator_savepath = 'riemann_burgers_detailed';

% old settings, now in riemann_burgers_model:

switch step
 case 1 % single detailed simulation and plot

  descr = riemann_burgers_descr([]);
  dmodel = gen_detailed_model(descr);
  model_data = gen_model_data(dmodel);

  disp('performing single detailed simulation')
  % grid = construct_grid(dmodel);
  % shock moving to left:
  % dmodel = set_mu(dmodel,[-0.5,1,-1]); % cdir_left, c_dir_right, vx
  % non-moving shock:
  % dmodel = set_mu(dmodel,[-1,1,-1]); % cdir_left, c_dir_right, vx
  % symmetric rarefaction wave:
  % dmodel = set_mu(dmodel,[1,-1,-1]); % cdir_left, c_dir_right, vx
  % moving shock with velocity 0.5:
  dmodel = set_mu(dmodel,[0,1,-1]); % cdir_left, c_dir_right, vx
  sim_data = detailed_simulation(dmodel, model_data);
  plot_params = [];
  plot_sim_data(dmodel,model_data,sim_data,plot_params);
  save(fullfile(rbmatlabtemp,detailedfname),...
       'model_data','dmodel');
% case 4 % construct dummy reduced basis by single trajectory and simulate
%  load(fullfile(rbmatlabtemp,CRBfname));
%  descr = riemann_burgers_descr;
%  [dmodel, rmodel] = gen_models(descr);
%  % set mu values new, as may be different in stored file
%  dmodel.c_dir_left  = 1.0;
%  dmodel.c_dir_right = 0.0;
%  dmodel.dir_middle  = 0.5;

%  disp('detailed interpolated simulation for basis construction:')
%  rmodel.M = size(detailed_data.QM{1},2);
%  sim_data_interpol =  ...
%      nonlin_evol_detailed_ei_simulation(dmodel,detailed_data);
%  %  A = feval(params.inner_product_matrix_algorithm, ...
%  %           detailed_data.grid,params);
%  UON = dmodel.orthonormalize(dmodel,model_data,sim_data_interpol.U,1e-4);
%  %  UON = dmodel.orthonormalize(dmodel,model_data,sim_data_interpol.U,1e-4);
%  detailed_data.RB = UON;
%  dmodel.N = size(detailed_data.RB,2);
%  dmodel.M = size(detailed_data.QM{1},2);
%  save(fullfile(rbmatlabtemp,'riemann_burgers_temp'),'dmodel','detailed_data')
%  disp('reduced simulation:')
%  reduced_data = gen_reduced_data(dmodel,detailed_data);
%  sim_data = rb_simulation(dmodel,reduced_data);
%  sim_data = rb_reconstruction(dmodel,detailed_data,sim_data);

%  disp('detailed interpolated and rb-projected simulation:')
%  dmodel.M = size(detailed_data.QM{1},2);
%  dmodel.N = size(detailed_data.RB,2);
%  sim_data_ei_rb_proj = ...
%      nonlin_evol_detailed_ei_rb_proj_simulation(dmodel,detailed_data);

%  plot_params.title = 'reduced simulation result';
%  plot_sim_data(dmodel,model_data,sim_data,plot_params);
%  plot_params.title = 'detailed ei_interpol simulation result';
%  plot_sim_data(dmodel,model_data,sim_data_interpol,plot_params);
%  plot_params.title = 'detailed ei_interpol and rb_projected simulation result';
%  plot_sim_data(dmodel,model_data,sim_data_ei_rb_proj,plot_params);
 case 5 % reduced basis construction
  disp('constructing reduced basis')
  descr = riemann_burgers_descr;
  [dmodel,rmodel] = gen_models(descr);
  model_data = gen_model_data(dmodel);

  detailed_data = gen_detailed_data(rmodel, model_data);
  % set these fields such that demo_rb_gui works nicely
  rmodel.N = get_rb_size(detailed_data, rmodel);
  rmodel.M = get_ei_size(detailed_data, rmodel);

  save(fullfile(rbmatlabtemp,detailedfname),...
       'detailed_data','dmodel','rmodel');

  max_err_sequence = get_field(detailed_data.datatree, 'max_err_sequence');
  plot(max_err_sequence);
  set(gca,'Yscale','log');
  title('RB-generation error convergence');

 case 6 % time measurement of reduced simulation

  load(fullfile(rbmatlabtemp,detailedfname));
  disp('reduced simulation:')
  rmodel.N = get_rb_size(detailed_data, rmodel);
  rmodel.M = get_ei_size(detailed_data, rmodel)-rmodel.Mstrich;
  reduced_data = gen_reduced_data(rmodel,detailed_data);
  tic;
  rb_sim_data = rb_simulation(rmodel,reduced_data);
  t = toc;
  disp(['time for online phase: t = ',num2str(t)]);

  disp('full simulation:')
  tic;
  sim_data = detailed_simulation(dmodel,model_data);
  t = toc;
  disp(['time for detailed simulation: t = ',num2str(t)]);
 case 9 % start demo_rb_gui with error estimation
  load(fullfile(rbmatlabtemp,detailedfname));
  %  dmodel = riemann_burgers_model;
  %  dmodel.show_colorbar = 1;
  dmodel.c_dir_left = -1;
  dmodel.c_dir_right = 0;
  dmodel.flux_vx = -1;
  rmodel.M = get_ei_size(detailed_data, rmodel) - 1;
  rmodel.Mstrich = 1;
  rmodel.N = get_rb_size(detailed_data, rmodel);
  rmodel.enable_error_estimator = 1;
  demo_rb_gui(rmodel,detailed_data);

 case 10 % start demo_rb_gui without error estimation
  load(fullfile(rbmatlabtemp,detailedfname));
  %  dmodel = riemann_burgers_model;
  %  dmodel.show_colorbar = 1;
  rmodel.M = get_ei_size(detailed_data, rmodel);
  rmodel.Mstrich = 0;
  rmodel.N = get_rb_size(detailed_data, rmodel);
  rmodel.enable_error_estimator = 0;
  demo_rb_gui(rmodel,detailed_data);

 otherwise
  error('step-number is unknown!');
end;