models/thermalblock_descr.m

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function model = thermalblock_descr(params)
% Thermal Block example similar as described in the book of 
% A.T. patera and G. Rozza (just one parameter more)
%
% i.e. 
% - div ( a(x) grad u(x)) = q(x)    on Omega
%                   u(x)) = g_D(x)  on Gamma_D
%     a(x) (grad u(x)) n) = g_N(x)  on Gamma_N
%                       s = l(u) linear output functional
%
% where Omega = [0,1]^2 is divided into B1 * B2 blocks 
% QA := B1*B2. The heat conductivities are given by mu_i:
%
%   -------------------------
%   | ...   | ..... | mu_QA |
%   -------------------------
%   | ....  | ...   | ..... |
%   -------------------------
%   | mu_1  | ...   | mu_B1 |
%   -------------------------
%
% `Gamma_D =` upper edge
% `Gamma_N = boundary(Omega)\Gamma_D`
%
% `a(x) = mu_i(x) if x\in B_i`
% `q(x) = 0`
% `g_D  = 0` on top
% `g_N  = 1` on lower edge, 0 otherwise
% `l(u)` = average over lower edge

% S. Langhof and B. Haasdonk 26.2.2011
% I. Maier 26.04.2011

model.name = 'thermalblock';
model.dmodel_constructor = @ThermalBlock.DetailedModel;
model.rb_problem_type = 'LinStat';

% MD: Mein Vorschlag für simple Basis-Generierungsalgorithmen, verwendet
% die Klasse SimpleDetailedData für die man den Konstruktor mittels eines
% Funktionspointers spezifizieren kann. Genauso könnte man Simple* Klassen
% für die anderen Interfaces, also DetailedModel, ReducedModel und
% ReducedData implementieren. Das fände ich aber ehrlich gesagt unschön...
% Die Basisgenerierung kann so simpel sein, dass es vielleicht Sinn macht,
% die in eine kleine Funktion auszulagern, aber die anderen Klassen haben
% meistens komplexere Datenstrukturen oder mehr Methoden, so dass die
% "Description" Klasse wieder sehr unübersichtlich und intransparent wird,
% wenn man das alles hier hinein packt...
model.detailed_data_constructor = @SimpleDetailedData;

model.RB_customized_basis_generation_ptr = @my_RB_basisgen;
model.RB_train_rand_seed = 100;
model.RB_train_size = 1000;
model.RB_stop_epsilon = 1e-3;
model.RB_stop_Nmax = 100;

if nargin == 0
    params.B1=3;
    params.B2=3;
%    model.default = '3x3 demo version';
end
% number of blocks in X and Y direction
model.B1 = params.B1;
model.B2 = params.B2;
model.number_of_blocks = params.B1*params.B2;

% each block has a different heat conductivity
% upper left has conductivity 1
mu_names = {};
mu_ranges = {};
mu_range = [0.1,10];
for p = 1:model.number_of_blocks
  mu_names = [mu_names,{['mu',num2str(p)]}];
  mu_ranges = [mu_ranges,{mu_range}];
end;
model.mu_names = mu_names;
model.mu_ranges = mu_ranges;

%default values 1 everywhere
model.mus = ones(model.number_of_blocks,1);

% simple snapshots without orthogonalization
model.RB_generation_mode = 'lagrangian';
model.RB_mu_list = {[0.1,1,1,1,1,1,1,1,1],...
                    [1,0.1,1,1,1,1,1,1,1],...
                    [1,1,0.1,1,1,1,1,1,1],...
                    [1,1,1,0.1,1,1,1,1,1],...
                    [1,1,1,1,0.1,1,1,1,1],...
                    [1,1,1,1,1,0.1,1,1,1],...
                    [1,1,1,1,1,1,0.1,1,1],...
                    [1,1,1,1,1,1,1,0.1,1],...
                    [1,1,1,1,1,1,1,1,0.1]};

%model.RB_generation_mode = 'model_RB_basisgen';



%%%%%%%%% set data functions
model.has_diffusivity = 1;
model.has_output_functional = 1;
model.has_dirichlet_values = 1;
model.has_neumann_values = 1;

% zero dirichlet values, i.e. 1 component, Q_dir = 1
dirichlet_values_coefficients = @(dummy,params) [0];
dirichlet_values_components = @(glob,params) {zeros(size(glob,1),1)};
model.local_dirichlet_values = @(glob,params) ...
    eval_affine_decomp_general(dirichlet_values_components, ...
                               dirichlet_values_coefficients,glob,params);

% 1/0 neumann values depending on edge, non parametric, i.e Q_neu = 1;
neumann_values_coefficients = @(dummy,params) 1; % single component
model.local_neumann_values = @(glob,params) ...
    eval_affine_decomp_general(@thermalblock_neumann_values_components, ...
                               neumann_values_coefficients, glob, params);

% diffusion tensor: each row four entries a11,a_21,a_12,a_22. 
% a11(x)=a22(x) = mu_i if x in block i, a12=a21 = 0. 
diffusivity_tensor_coefficients = @(dummy,params) ...
    params.mus(:);
model.local_diffusivity_tensor = @(glob,params) ...
    eval_affine_decomp_general(...
        @thermalblock_diffusivity_tensor_components, ...
        diffusivity_tensor_coefficients, glob,params);

% only useful for detailed simulation or nonlinear outputs:
%model.output_functional = @output_functional_boundary_integral;

model.operators_output = @fem_operators_output_boundary_integral;
% output weight function: simply 1 on lower edge, 0 else => Ql = 1 component
output_function_components = @(glob,model) {1.0*(glob(:,2)<eps)};
output_function_coefficients = @(glob,model) 1;
model.output_function = @(glob,params) ...
    eval_affine_decomp_general(...
        output_function_components,...
        output_function_coefficients, glob,params);

model.output_integral_qdeg = 2; %

%%%%%%%%%% discretization settings

if ~isfield(params,'numintervals_per_block')
  params.numintervals_per_block = 5;
end;

model.gridtype = 'triagrid';
model.xnumintervals = params.numintervals_per_block*params.B1;
model.ynumintervals = params.numintervals_per_block*params.B2;
model.xrange = [0,1];
model.yrange = [0,1];

if ~isfield(params,'pdeg')
  params.pdeg = 1; 
end;

if ~isfield(params,'qdeg')
  params.qdeg = 2; 
end;

% numerics settings:
model.pdeg = params.pdeg; % degree of polynomial functions
model.qdeg = params.qdeg; % quadrature degree
model.dimrange = 1; % scalar solution

model.boundary_type = @thermalblock_boundary_type;
%model.normals = @my_normals;

% new plot routine, additional block boundaries are plotted
model.compute_output_functional = 1;
model.yscale_uicontrols = 0.2;

% for error estimation:
model.coercivity_alpha = @(model) min(model.mus(:));
model.continuity_gamma = @(model) max(model.mus(:));
model.enable_error_estimator = 1;

% for making work with current dmodel/rmodel/descr decomposition
model.crb_enabled = 0;

% local data functions:
%model = elliptic_discrete_model(model);

%%%%%%% auxiliary functions %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function res = thermalblock_boundary_type(glob,params)
  % returns the boundary type
res = zeros(size(glob,1),1);
i  = find(glob(:,1)<=1e-10);
res(i) = -2;
i  = find(glob(:,1)>=1-1e-10);
res(i) = -2;
i  = find(glob(:,2)<=1e-10);
res(i) = -2;
i  = find(glob(:,2)>=1-1e-10);
res(i) = -1;

function model = thermalblock_set_mu(model,mu)
if length(mu)~=model.number_of_blocks
  error('length of mu does not fit to number of blocks!');
end;
model.mus = [mu(:)];

function comp = thermalblock_neumann_values_components(glob,params) 
  % Neumann values component function
res = zeros(size(glob,1),1);
i = find(glob(:,2)<eps);
res(i) = 1;
comp = {res};

function res = thermalblock_diffusivity_tensor_components(glob,params)
  % diffusivity tensor component function

% for each point in glob find global block number
% xi: range 0 ... B1-1
xi = floor(glob(:,1)*params.B1);
i = find(xi>=params.B1);
if ~isempty(i)
  xi(i) = params.B1-1; 
end;
% xi: range 0 ... B1-1
yi = floor(glob(:,2)*params.B2);
i = find(yi>=params.B2);
if ~isempty(i);
  yi(i) = params.B2-1; 
end;
block_index = yi*params.B1+xi+1;
zeroblock = zeros(size(glob,1),4);
res = cell(1,params.number_of_blocks);
for q = 1:params.number_of_blocks;
  block = zeroblock;
  i = find(block_index==q);
  if ~isempty(i)
    block(i,1) = 1;
    block(i,4) = 1;
  end;
  res{q} = block;
end;
% check!
%block = zeroblock;
%for q=1:params.number_of_blocks;
%  block = block + res{q};
%end;
%disp('check diffusivity matrix!')
%keyboard;

function alpha = thermalblock_coercivity_alpha(model)
alpha = min(model.get_mu(model))

%function [RBinit] = my_init_data_basis(model, ...
%                                          detailed_data)

function RB = my_RB_basisgen(rmodel,detailed_data)
% simple greedy

disp('entered my_RB_basisgen');

sim_data = detailed_simulation(rmodel, detailed_data.model_data);
n = fem_h10_norm(sim_data.uh);
detailed_data.RB = sim_data.uh.dofs / n;
reduced_data = gen_reduced_data(rmodel, detailed_data);
h10_matrix = sim_data.uh.df_info.h10_inner_product_matrix;

rng('default');
mus = rand_uniform(rmodel.train_size,rmodel.mu_ranges);
max_err_est = 1e10;

while( max_err_est> rmodel.stop_epsilon) && ...
      (size(detailed_data.RB,2)< rmodel.stop_Nmax)
  max_err_est = 0;
  mu_max = [];
  tic;
  for i = 1:size(mus,2);
    set_mu(rmodel, mus(:,i));
    rb_sim_data = rb_simulation(rmodel,reduced_data);
    if rb_sim_data.Delta > max_err_est
      mu_max = mus(:,i);
      max_err_est = rb_sim_data.Delta; 
    end;
  end;
  toc
  disp(['max error estimator: ',num2str(max_err_est),...
        ' for mu = ',num2str(mu_max')]);
  set_mu(rmodel,mu_max);
  sim_data = detailed_simulation(rmodel,detailed_data.model_data);
  pr = sim_data.uh.dofs - ...
       detailed_data.RB * (detailed_data.RB' * h10_matrix * ...
                           sim_data.uh.dofs);
  n = sqrt(max(pr'*h10_matrix*pr,0));
  detailed_data.RB = [detailed_data.RB,pr/n];  
  reduced_data = gen_reduced_data(rmodel,detailed_data);
  disp(['new basis size: ',num2str(size(detailed_data.RB,2))]);
end;

RB = detailed_data.RB;