stokes_rb_supremizer_extension.m

function [RBext, dummy] = stokes_rb_supremizer_extension(model, detailed_data)
%function [RBext, dummy] = stokes_rb_supremizer_extension(model, detailed_data)
%
% Simple routine computing snapshot and supremizer enrichment for basis
% generation.

% IM 19.06.2013

dummy = [];

sim_data = detailed_simulation(model, detailed_data);

U = model.get_dofs_from_sim_data(sim_data);

ndofs = detailed_data.df_info.ndofs;
vel_ndofs = detailed_data.df_info.values{1}.ndofs;
dirichlet_gids = detailed_data.bc_info.dirichlet_gids;
vel_dofinds = 1:vel_ndofs;

U(dirichlet_gids) = 0;

% inner product on velocity space
if isfield(detailed_data, 'W')
    K = detailed_data.W;
else
    K = model.get_inner_product_matrix(detailed_data);
end

K = getMatrix(K) + eps*speye(ndofs);
K(dirichlet_gids, :) = 0;
K(:, dirichlet_gids) = 0;
K_dirichlet = sparse(dirichlet_gids, dirichlet_gids, ones(length(dirichlet_gids), 1), ndofs, ndofs);
K = K + K_dirichlet;

% further matrices
A = detailed_data.operators(model, detailed_data);

% compute supremizer function
U_pre = U;
U_pre(vel_dofinds) = 0;

r = A * U_pre;
spF = K \ r;

spF = spF(vel_dofinds);
U_pre(vel_dofinds) = [];
% return results
RBext = VecMat.CompositeMatrixDefault(2);

RBext = set(RBext, [U(vel_dofinds), spF], 1);
RBext = set(RBext, U_pre, 2);
end