t_part_rb_simulation.m

function sim_data = t_part_rb_simulation(model, reduced_data)
%function sim_data = t_part_rb_simulation(model, reduced_data)
%
% function performing a reduced basis simulation for t-part models.
% For every time partition a different reduced basis is used. Between the
% t-partitions the initial coefficients of the next partitions are obtained
% by an orthogonal projection of the reduced solution of the last partition
% onto the reduced space of the next partition.
%
% Required fields of reduced_data:
%   t_part_reduced_data: reduced data of the several partitions including a
%                           transormation matrix T to obtian initial
%                           coefficients of the nex partition
%
% Generated fields of sim_data:
%   a: vector of solution coefficients
%
%

% Markus Dihlmann 15.02.2011

if ~isfield(model,'t_part_in_basis_generation')
    model.t_part_in_basis_generation=0;
end


sim_data = [];

base_model = model.base_model;

if ~isfield(reduced_data,'t_part_reduced_data')
    error('No complete t-part model. reduced_data lacks T-partition informations!');
else
    t_part_reduced_data = reduced_data.t_part_reduced_data;
    if model.transition_model
        transition_reduced_data = reduced_data.t_part_transition_reduced_data;
        base_model.transition_model=1;
    end
end

nr_t_parts = length(model.t_part_range); %number of t-partitions

if (isfield(model,'t_part_for_simulation'))&&~isempty(model.t_part_for_simulation)
    stop_part = model.t_part_for_simulation;
else
    stop_part = nr_t_parts;
end

t_part_sim_data = cell(1,stop_part);

for t_part_ind = 1:stop_part

  base_model.starting_time_step = model.t_part_range{t_part_ind}(1);
  base_model.stopping_time_step = model.t_part_range{t_part_ind}(2);

  if t_part_ind>1
    if ~model.transition_model
        %transition between the two reduced models is done by a
        %projection

        %initial data manipulation
        base_model.rb_init_values          = @(model, detailed_data) 1;
        a_end_tp1                          = t_part_sim_data{t_part_ind-1}.a(:,end); %coeficient vector of last time step
        a0_tp2                             = t_part_reduced_data{t_part_ind}.T * a_end_tp1; %first coeffient vector in next time step
        t_part_reduced_data{t_part_ind}.a0 = {a0_tp2};

        %error calculation
        %projection error in t-part transfer

        err_proj = a_end_tp1'*a_end_tp1 - a0_tp2'*a0_tp2 ;
        if err_proj<0
            err_proj=0;
        else
            err_proj = sqrt(err_proj);
        end
        if model.verbose > 5
          disp(['Projection error between partitions: ', num2str(err_proj)]);
        end

        %adding initial error to t_part_reduced_data
        t_part_reduced_data{t_part_ind}.Delta0 = t_part_sim_data{t_part_ind-1}.Delta(end) + err_proj;
        if model.t_part_rb_generation_cut_error ...
            &&...
           model.t_part_in_basis_generation

            %cut the error so that in greedy basis generation only the
            %real "added" error in this t-partition is regarded
            t_part_reduced_data{t_part_ind}.Delta0 = err_proj;
        end
    else
      %transition between the two models is done my a transition
      %time step.

      %transition step
      base_model.rb_init_values = @(model, detailed_data)1;
      transition_reduced_data{t_part_ind-1}.a0{1} = t_part_sim_data{t_part_ind-1}.a(:,end); %coeficient vector of last time step
      transition_reduced_data{t_part_ind-1}.Delta0 = t_part_sim_data{t_part_ind-1}.Delta(end) ;
      %Transition simulation
      base_model.starting_time_step = model.t_part_range{t_part_ind-1}(2);
      base_model.stopping_time_step = model.t_part_range{t_part_ind}(1)+1;
      sim_data_trans = rb_simulation(base_model, transition_reduced_data{t_part_ind-1});

      base_model.starting_time_step = model.t_part_range{t_part_ind}(1)+1; %subtract the transition step
      base_model.stopping_time_step = model.t_part_range{t_part_ind}(2);
      %error
      %...
      t_part_reduced_data{t_part_ind}.Delta0 = sim_data_trans.Delta(end);
      t_part_reduced_data{t_part_ind}.a0{1}  = sim_data_trans.a(:,end);
    end
  end

  if model.verbose > 4
    disp(['rb simulation of partition ',num2str(t_part_ind)]);
  end
  t_part_sim_data{t_part_ind} = rb_simulation(base_model, t_part_reduced_data{t_part_ind});
end


%glue together sim_data
sim_data.t_part_sim_data = t_part_sim_data;
sim_data.a               = [];
sim_data.Delta           = [];
if isfield(t_part_sim_data{1},'s')
    sim_data.s       = [];
    sim_data.Delta_s = [];
end


%sim_data.a=t_part_sim_data{1}.a;
sim_data.Delta = t_part_sim_data{1}.Delta;
if isfield(t_part_sim_data{1},'s')
    sim_data.s       = t_part_sim_data{1}.s;
    sim_data.Delta_s = t_part_sim_data{1}.Delta_s;
end
if stop_part > 1
  for ind=2:stop_part
    len = length(t_part_sim_data{ind}.a(1,:));
    %sim_data.a=[sim_data.a,t_part_sim_data{ind}.a(:,2:len)];
    if ~model.transition_model
      sim_data.Delta = [sim_data.Delta,...
                        t_part_sim_data{ind}.Delta(2:len)];
      if isfield(t_part_sim_data{1},'s')
        sim_data.s       = [sim_data.s,...
                            t_part_sim_data{ind}.s(2:len)];
        sim_data.Delta_s = [sim_data.Delta_s,...
                            t_part_sim_data{ind}.Delta_s(2:len)];
      end
    else
      sim_data.Delta = [sim_data.Delta,...
                        t_part_sim_data{ind}.Delta(1:len)];
      if isfield(t_part_sim_data{1},'s')
        sim_data.s = [sim_data.s,...
                      t_part_sim_data{ind}.s(1:len)];
        sim_data.Delta_s = [sim_data.Delta_s,...
                            t_part_sim_data{ind}.Delta_s(1:len)];
      end
    end
  end
end