fv_operators_output.m

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function [v, l2norm] = fv_operators_output(model,model_data)
%function v = fv_operators_output(model,model_data)
% function returning components, coefficients, and complete
% operator for a linear output functional on fv discrete functions
%
% 'v * U' for a dof vector 'U' gives the desired output of the simulation
% assuming, that the output functional is given by 
%
%      ``int_{\Omega} f(u)dx``
%
% as an integral of a given analytical function multiplied with the
% discrete function.
%
% Function supports affine decomposition, i.e. different operation modes
% guided by optional field decomp_mode in model. See also the
% contents.txt for general explanation

% Bernard Haasdonk 13.7.2006

% determine affine_decomposition_mode as integer
decomp_mode = model.decomp_mode;

grid = [];
if ~isempty(model_data)
  grid = model_data.grid;
end

l2norm = [];
switch decomp_mode
 case 2
   % simply forward coefficients of output_function
   v = model.output_function_ptr([],model);
 case 1
  % simple quadrature quadrature of evaluation of fv function in the midpoints 
  f = model.output_function_ptr([grid.CX(:),grid.CY(:)],model);
  Q_v = length(f);
  v = cell(Q_v,1);
  for q = 1:length(v)
    v{q} = grid.A(:).*(f{q}(:));
  end;
 case 0
  % simple quadrature quadrature of evaluation of fv function in the midpoints 
  f = model.output_function_ptr([grid.CX(:),grid.CY(:)],model);
  % vector that realizes integral over domain of f times U
  % s = \int_Omega f u = sum_e |e| f(c(e)) u(c(e)) = v * U
  % hence v = (|e| f(c(e)))_e;
  v = grid.A(:).*f(:);
  l2norm = sqrt(fv_inner_product(model, model_data, f,f));
end;