evol_TB_2D_weak_form_model_script.m

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% This Script computes the comsol 2D-evol-ThermalBlock_weak_form model
% in detailed form and reduced form and compares the errors!
%
% It shall show two things:
% 1. How evolution problems can be treated using COMSOL and rbmatlab.
% 2. Not only a "COMSOL coefficient form model" can be used but also a
%   "COMSOL weak form model"!
%
% Oliver Zeeb, 2013/11/21

fprintf('loading evol_TB_2D_weak_form_model...\n')
model = evol_TB_2D_weak_form_model;
fprintf('done!\n')

fprintf('generating model_data...\n')
model_data = gen_model_data(model);
fprintf('done!\n')

%after generation of model data all the needed matrices are stored in
%model_data --> now Comsol is only needed for plotting the results but no
%longer for calculating! Using Matlab instead of Comsol for the calculation
%speeds up things (really much, especially on a Mac!!!)
model.use_comsol=0;

fprintf('generating detailed_data...\n')
detailed_data = gen_detailed_data(model,model_data);
fprintf('done!\n')

fprintf('generating reduced_data...\n')
reduced_data = gen_reduced_data(model,detailed_data);
fprintf('done!\n')

mu=[1,2,1,2];
fprintf(['calculating detailed solution for mu = ' num2str(mu),'...\n']);
model = set_mu(model,mu);
sim_data = detailed_simulation(model,model_data);
fprintf('done!\n')


fprintf(['calculating reduced solution for mu = ' num2str(mu),'...\n']);
rb_sim_data = rb_simulation(model,reduced_data);
rb_sim_data = rb_reconstruction(model,detailed_data,rb_sim_data);
fprintf('done!\n')


fprintf('comparing the L2-error Udet - Ured.\n')
Udet = sim_data.U;
Ured = rb_sim_data.U;
U_diff = abs(Udet-Ured);
L2_error = diag(U_diff' * model_data.inner_product_matrices.L2 * U_diff);
plot(L2_error);
title('L_2 error Udet - Ured')

fprintf('comparing the output error: sdet - sred.\n')
figure
plot(rb_sim_data.s)
hold on
plot(sim_data.s,'r')
plot(sim_data.s-(rb_sim_data.s)','g')
title('detailed and reduced output')


fprintf('adding the initial values to the (rb_)sim_data.\n')
sim_data_with_init_values = sim_data;
rb_sim_data_with_init_values = rb_sim_data;
sim_data_with_init_values.U=sim_data.U + repmat(model_data.operators.init_values,1,size(sim_data.U,2));
rb_sim_data_with_init_values.U=rb_sim_data.U + repmat(model_data.operators.init_values,1,size(sim_data.U,2));

fprintf('Plotting the detailed simulation.\n')
plot_sim_data(model,model_data,sim_data,[]);
%after the rb_reconstruction plotting of the rb_sim_data can be done via:
%plot_sim_data(model,model_data,rb_sim_data,[]);