demo_dom_dec.m

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function demo_dom_dec()
%function demo_dom_dec()
% Demo showing the functionality of the dom_dec routines.
% 
% some solutions of the iterative procedure are plotted,
% the detailed and reduced simulation are compared.

% I.Maier 19.07.2011

disp('start domain decomposition demo');
disp('-------------------------------');
disp('visualize detailed simulation');
disp('-----------------------------');

params = [];
% specify geometrical decomposition
params.dd_rect_corner1 = {[0,0],[0.25,0],[0.75,0]};
params.dd_rect_corner2 = {[0.25,0.25],[0.75,0.75],[1,0.5]};

params.numintervals = 24; % discretization parameter
params.RB_numintervals = 2;
params.subsampling_level = 4; % for plotting

% create models
base_model = thermalblock_dd_model(params);
model = dom_dec_model(base_model,params);
disp('models created');

dir = model.dirichlet_side;
no_dir = mod(dir,2)+1;

% generate model_data
model_data = gen_model_data(model);
disp('model_data created');

%%%%%%%%%%%%%%% visualize detailed simulation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

model = set_mu(model,[1.843,2.878,8.879,0.874]);

% plot source function
disp('plot source function');
source = femdiscfunc([],model_data.base_model_data.df_info);
source = fem_interpol_local(model.base_model.source,source, ...
                            model.base_model);
figure,
plot(source,params);
title('source function');

% perform detailed simulation
sim_data = detailed_simulation(model,model_data);

disp('plotting');
for i = [1 5 10]
  figure,
  
  for j = 1:2
    sim_data.uh{j}.dofs = sim_data.all_dofs{j}(:,i);
    plot(sim_data.uh{j},params);
  end;
  
  title(['iterative solution, ', num2str(i),' iterations']);
end;

for j = 1:2
  sim_data.uh{j}.dofs = sim_data.all_dofs{j}(:,end);
end;

% compute un-decomposed solution - perform detailed simulation of
% base_model
disp('perform detailed simulation of base_model');
base_sim_data = detailed_simulation(model.base_model, ...
                                    model_data.base_model_data);
disp(['output: s = ', num2str(base_sim_data.s), ', iterative: s = ', ...
    num2str(sim_data.s)]);
fprintf('\n');
figure,
plot_sim_data(model.base_model,model_data.base_model_data, ...
                  base_sim_data,params);
title('monolithic solution');

disp('press enter to continue');
pause;

%%%%%%%%%%%%%% compare detailed and reduced simulation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('---------------------------------------');
disp('compare detailed und reduced simulation');
disp('---------------------------------------');
model.det_sim_tol = 1e-07;
model.RB_sim_tol = 1e-07;
model.N_max = {12 12};
model.RB_generation_mode = 'PCA_trajectories';
model.RB_generation_epsilon = 1e-7;

% build reduced basis
disp('generate detailed_data');
model.verbose = 0;
detailed_data = gen_detailed_data(model,model_data);
model.base_model.dual_mode = 1;
detailed_data.dual_detailed_data = gen_detailed_data(model,model_data);
model.base_model.dual_mode = 0;
model.verbose = 1;
disp('dimensions of reduced basis:');
disp(['  N_1^0 = ',num2str(length(detailed_data.I_0{dir}))]);
disp(['  N_1^G = ',num2str(length(detailed_data.I_G{dir}))]);
disp(['  N_2^0 = ',num2str(length(detailed_data.I_0{no_dir}))]);
disp(['  N_2^G = ',num2str(length(detailed_data.I_G{no_dir}))]);
disp(['  M_1^0 = ',num2str(length(detailed_data.dual_detailed_data.I_0{dir}))]);
disp(['  M_1^G = ',num2str(length(detailed_data.dual_detailed_data.I_G{dir}))]);
disp(['  M_2^0 = ',num2str(length(detailed_data.dual_detailed_data.I_0{no_dir}))]);
disp(['  M_2^G = ',num2str(length(detailed_data.dual_detailed_data.I_G{no_dir}))]);

disp('generate reduced_data');
reduced_data = gen_reduced_data(model,detailed_data);

% perform detailed simulation
tic;
sim_data = detailed_simulation(model,model_data);
det_sim_time = toc;

sim_data = model.compute_error(model,model_data,sim_data);

disp('------------------------------------------');
disp(['elapsed time of detailed simulation: ', ...
      num2str(det_sim_time,3),'s']);
disp(['error of iterative solution: ',num2str(sim_data.X_err(end),3)]);
disp(['error of iterative output: ', ...
    num2str(abs(sim_data.s - sim_data.base_sim_data.s))]);

% perform reduced simulation
tic;
rb_sim_data = rb_simulation(model,reduced_data);
rb_sim_data = rb_reconstruction(model,detailed_data,rb_sim_data);
rb_sim_time = toc;

rb_sim_data = model.compute_error(model,detailed_data,rb_sim_data);

model.base_model.compute_output_functional = 0;
rb_sim_data_no = rb_simulation(model, reduced_data);

disp('------------------------------------------');
disp(['elapsed time of reduced simulation: ',num2str(rb_sim_time,3), ...
      's']);
disp(['error of reduced iterative solution: ', ...
      num2str(rb_sim_data.X_err(end),3)]);
disp(['error estimate of reduced iterative solution: ', ...
      num2str(rb_sim_data_no.Delta(end),3)]);
disp(['error of reduced iterative output: ', ...
    num2str(abs(rb_sim_data.sN - sim_data.base_sim_data.s))]);
disp(['error estimate of reduced iterative output: ', ...
    num2str(rb_sim_data.Delta_s)]);

plot_sim_data(model, model_data, sim_data, params);
title('detailed solution');
plot_sim_data(model, model_data, rb_sim_data, params);
title('reduced solution');