duneconvdiff.m

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% small script demonstrating the convdiff example from the M2AN Paper, that is
% also implemented in Dune. Later it will be possible to use the Dune
% implementation through a mex interface.  
% Martin Drohmann 06.05.2009
% based on burgers_fv.m by
% Bernard Haasdonk 14.8.2007

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% Select here, what is to be performed                        %%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%step = 0 % initialize the model_data structure. This step needs to be executed
          % once per Matlab session only
%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 reduced basis
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%old steps:
%step = 6 % time measurement of reduced simulation and 
          % use reduced basis in rb_demo_gui
%step = 7 % generate error-landscape over varying N and M
          % can take several hours!!!
%step = 9 % test one simulation
%step = 10 % generate dummy reduced basis from single trajectory.
          % A simple reduced simulation can also be
          % performed. All results should be visually identical

%steps = {2,5,7,8}
steps = [0,1,2];

for si=1:length(steps)

step = steps(si);

params.model_type = 'default';

detailedfname = ['duneconvdiff_', params.model_type, '_detailed_interpol.mat'];
% $$$ params.verbose = 5;
% $$$ 
% $$$ %% parameters for visualization
% $$$ plot_params.show_colorbar = 1;
% $$$ plot_params.colorbar_mode = 'EastOutside';                 

switch step
 case 0 % initialize model data
  descr               = convdiff_dune_descr('init_model');
  descr.detailedfname = fullfile(rbmatlabtemp, detailedfname);
  params.mu_ranges    = descr.mu_ranges;
  params.mu_names     = descr.mu_names;

  [dmodel, rmodel] = gen_models(descr);

  model_data = gen_model_data(dmodel);
% $$$   grid       = model_data.grid;
 case 1 % single detailed simulation and plot
  disp('performing single detailed simulation')
  tic
%  mu_test  = cellfun(@mean, model.mu_ranges);
%  mu_test = [0,1,0.2]
%  model    = model.set_mu(model, mu_test);
  sim_data = detailed_simulation(dmodel, model_data);
  toc
%  plot_sim_data(model, model_data, sim_data, plot_params);
%      Uname = [getenv('RBMATLABTEMP'),'/U',num2str(temp)];
%      temp = temp + 1;
%      disp(['save solution U in ', Uname]);
%      save(Uname, 'U');
%  end

 case 2 % reduced basis
  disp('constructing reduced basis')
% $$$   mu_test   = cellfun(@mean, params.mu_ranges);
% $$$   params.mu = mu_test;
% $$$   sim_data  = detailed_simulation(model, model_data, params);

  tic;
  detailed_data = gen_detailed_data(rmodel, model_data);
  t = toc;
%  detailed_data = rb_basis_generation(detailed_data, ...
%                  params);
  % reconstruct 
  reduced_data = gen_reduced_data(rmodel, detailed_data);

  rmodel.N = get_rb_size(detailed_data, rmodel);
  reduced_data = extract_reduced_data_subset(rmodel, reduced_data);

  %dunerbconvdiff('dune_keyboard');
  params.mu = [0.001, 0.5, 0.5];
  set_mu(rmodel, params.mu);
  rb_sim_data = rb_simulation(rmodel, reduced_data);
  %  reconstruct_and_compare(model, rb_sim_data);
  set_mu(dmodel, params.mu);
  dmodel.descr.mexptr('reconstruct_and_compare', rb_sim_data.a);

  save(fullfile(rbmatlabresult, detailedfname),...
       'detailed_data','params');
  plot(detailed_data.datatree.get_field_on_active_child('max_err_sequence', rmodel));
  set(gca,'Yscale','log');
  title('RB-generation error convergence');
 
 case 4
  load(fullfile(rbmatlabresult,detailedfname));
  disp('reduced simulation:')
  reduced_data = gen_reduced_data(model, detailed_data);
  params.N = size(detailed_data.RB,2);
  params.M = params.N;
  reduced_data = extract_reduced_data_subset(model, reduced_data);
  tic;
  params.mu = mu_test;
  rb_sim_data = rb_simulation(model,reduced_data,params);
  t = toc;
  disp(['time for online phase: t = ',num2str(t)]);

  disp('full simulation:')
  tic;
  sim_data = detailed_simulation(model,model_data,params);
  t = toc;
  disp(['time for detailed simulation: t = ',num2str(t)]);

  dune_demo_rb_gui(model,detailed_data,[],params,plot_params);

 case 7 % training-error landscape
  disp('warning: takes a few hours!');
  load(fullfile(rbmatlabresult,detailedfname));

  model.N = model.RB_stop_Nmax;

  offline_data = gen_reduced_data(model,detailed_data);
  range_params.plot_fields = { 'N', 'M' };
  range_params.max         = [ size(detailed_data.RB,2), ...
                               size(detailed_data.BM{1},2) ];
  range_params.sample_size = [ 10, 12 ];
  range_params.Msamples    = 12;
  range_params.mu_set_size = 100;

  testdir = [ 'duneconvdiff_test_', range_params.mu_set_size ];

  params.run_name    = ['_', testdir, '_step7'];
  params.tictoctable = true;

  output=stochastic_error_estimation(model, detailed_data, offline_data,...
                                     testdir, range_params, params);

  case 9
   tmp=load(fullfile(rbmatlabresult,detailedfname));
   detailed_data = tmp.detailed_data;

   reduced_data = gen_reduced_data(model, detailed_data, params);

   params.N = get_rb_size(model, detailed_data);
   reduced_data = extract_reduced_data_subset(model, reduced_data, ...
                                            params);

   params.mu = [0.5, 0.5, 0.5];
   rb_sim_data = rb_simulation(model, reduced_data, params);

   plot(rb_sim_data.a);
 
 case 10 % construct dummy reduced basis by single trajectory and simulate
  disp('old, to be adjusted:')
  disp('detailed interpolated simulation for basis construction:')
  mu_test   = cellfun(@mean, params.mu_ranges);
%  mu_test2  = cellfun(@min, params.mu_ranges);
  params.mu = mu_test;
  sim_data  = detailed_simulation(model, model_data);
  UON       = model.orthonormalize(model, model_data, sim_data.U);
  detailed_data.grid = model_data.grid;
  detailed_data.W = model_data.W;
  detailed_data.RB = UON;
  disp('reduced simulation:')
  reduced_data = gen_reduced_data(model, detailed_data);
  params.N = size(detailed_data.RB,2);
  reduced_data = extract_reduced_data_subset(reduced_data);
  params.mu = mu_test;
  rb_sim_data = rb_simulation(model, reduced_data);
  rb_sim_data = rb_reconstruction(model, detailed_data, rb_sim_data);
  
  plot_params.title = 'reduced simulation result';
  plot_sim_data(model, model_data, rb_sim_data, plot_params);
  plot_params.title = 'detailed simulation result';
  plot_sim_data(model, model_data, sim_data, plot_params);

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

end;

%| \docupdate