fv_implicit_space.m

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function [INC, b_I] = fv_implicit_space(model,model_data,U,NU_ind)
% function INC =
%      fv_implicit_space(model, model_data, U, [NU_ind])
%
% function applying an FV-space-discretization operator starting from old
% values U corresponding to the geometry given in grid producing a
% new vector of elementwise scalars NU but only on for the
% subelements with numbers given in NU_ind. If NU_ind is empty, all
% new values NU are determined, i.e. length(NU) = length(U) =
% grid.nelements
%
% By this, the operator evaluation can be performed in a localized
% way, i.e. used for empirical interpolation in rb_nonlin_evol_simulation
%
% usual timestepping can be performed afterwards by (NU = Id - deltat *
% INC). 
%
% required fields of model:
%   verbose                  :   a verbosity level
%   convective_discretization: if set to 'explicit', this operator discretizes
%                              the convective part of the scheme
%   diffusive_discretization : if set to 'explicit', this operator discretizes
%                              the diffusive part of the scheme
%   reaction_discretization  : if set to 'explicit', this operator discretizes
%                              the reaction term of the scheme
%
% optional fields of model_data:
%   implicit_operator : cached operator
%   implicit_constant : cached affine shift vector

% Martin Drohmann 9.12.2007 based on fv_conv_explicit_space by Bernard
% Haasdonk

weights.diff_weight  = model.fv_impl_diff_weight;
weights.conv_weight  = model.fv_impl_conv_weight;
weights.react_weight = model.fv_impl_react_weight;

if isfield(model, 'model_type') ...
        && isequal(model.model_type, 'implicit_nonaffine_linear')
  if isfield(model_data, 'implicit_operator') && isfield(model_data, 'implicit_constant')
    L_I = model_data.implicit_operator;
    b_I = model_data.implicit_constant;
  else
    [L_I, b_I] = model.operators_diff_implicit(model, model_data, NU_ind);
  end
  INC = L_I * U;
else
  [INC, b_I] = fv_space_operator(model,model_data,U,NU_ind,weights);
end