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% Copyright (C) 2009-2016 Alassane SY, Yves Renard.
%
% This file is a part of GetFEM++
%
% GetFEM++ is free software; you can redistribute it and/or modify it
% under the terms of the GNU Lesser General Public License as published
% by the Free Software Foundation; either version 3 of the License, or
% (at your option) any later version along with the GCC Runtime Library
% Exception either version 3.1 or (at your option) any later version.
% This program is distributed in the hope that it will be useful, but
% WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
% or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
% License and GCC Runtime Library Exception for more details.
% You should have received a copy of the GNU Lesser General Public License
% along with this program; if not, write to the Free Software Foundation,
% Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
%
% Shape optimization with topological gradient
% (with a fictitious domain approach).
%
% This program is used to check that matlab-getfem is working. This is
% also a good example of use of GetFEM++.
%
gf_workspace('clear all');
% parameters
NX=30;
ls_degree = 1;
alpha = 1;
beta = 1;
rayon_trous = 0.2;
% Finite element and integration methods definition
m=gfMesh('cartesian', -.5:(1/NX):.5, -.5:(1/NX):.5);
% m=gfMesh('triangles grid', -.5:(1/NX):.5, -.5:(1/NX):.5);
% mim=gfMeshIm(m, gf_integ('IM_GAUSS_PARALLELEPIPED(2,4)'));
mf_basic=gfMeshFem(m, 1);
gf_mesh_fem_set(mf_basic,'fem',gf_fem('FEM_QK(2,2)'));
mls=gfMeshLevelSet(m);
ls=gfLevelSet(m, ls_degree);
set(mls, 'add', ls);
mf_ls=gfObject(get(ls, 'mf'));
P=get(mf_ls, 'basic dof nodes');
x = P(1,:); y = P(2,:);
ULS=1000*ones(1,numel(x));
% Loop on the topological optimization
while(1)
gf_workspace('push');
set(ls, 'values', ULS);
set(mls, 'adapt');
mim_bound = gfMeshIm('levelset',mls,'boundary', gf_integ('IM_TRIANGLE(6)'));
mim = gfMeshIm('levelset',mls,'outside', gf_integ('IM_TRIANGLE(6)'));
set(mim, 'integ', 4);
mf_mult=gfMeshFem(m); set(mf_mult, 'fem', gf_fem('FEM_QK(2,1)'));
M = gf_asm('mass matrix', mim, mf_basic);
D = abs(full(diag(M)));
ind = find(D > 1E-8);
mf = gf_mesh_fem('partial', mf_basic, ind);
S = gf_asm('volumic','V()+=comp()',mim);
disp('remaining surface :'); disp(S);
% Problem definition (Laplace(u) + u = f)
md=gf_model('real');
gf_model_set(md, 'add fem variable', 'u', mf);
gf_model_set(md, 'add Laplacian brick', mim, 'u');
gf_model_set(md, 'add fem data', 'VolumicData', mf_basic);
gf_model_set(md, 'add source term brick', mim, 'u', 'VolumicData');
gf_model_set(md, 'add initialized data', 'rho', [1.]);
gf_model_set(md, 'add mass brick', mim, 'u', 'rho');
gf_model_set(md, 'add multiplier', 'mult_dir', mf_mult, 'u');
% To be completely robust, a stabilization should be used on the Dirichlet
% boundary to ensure the inf-sup condition (Nitsche or Barbosa-Hughes)
gf_model_set(md, 'add Dirichlet condition with multipliers', ...
mim_bound, 'u', 'mult_dir', -1);
% Solving the direct problem.
U0 = gf_mesh_fem_get(mf_basic, 'eval', ...
{ '0.4*(3.*sin(pi*(x+y)) + ((x-0.5).^10 + (y-0.5).^10 + (x+0.5).^10 + (y+0.5).^10))' });
gf_model_set(md, 'variable', 'VolumicData', U0);
gf_model_get(md, 'solve');
U = gf_model_get(md, 'variable', 'u');
subplot(2,1,1);
gf_plot(mf, U);
hold on;
[h1,h2]=gf_plot(mf_ls, get(ls,'values'), 'contour', 0,'pcolor','off');
set(h2{1},'LineWidth',2);
set(h2{1},'Color','green');
colorbar;
title('u');
hold off;
% Solving the adjoint problem.
UBASIC = gf_compute(mf, U, 'interpolate on', mf_basic);
F = 2*(UBASIC-U0);
gf_model_set(md, 'variable', 'VolumicData', F);
gf_model_get(md, 'solve');
W = gf_model_get(md, 'variable', 'u');
% Computation of the topological gradient
mf_g=gfMeshFem(m, 1);
gf_mesh_fem_set(mf_g,'fem', ...
gf_fem('FEM_PRODUCT(FEM_PK_DISCONTINUOUS(1,2),FEM_PK_DISCONTINUOUS(1,2))'));
DU = gf_compute(mf, U, 'gradient', mf_g);
DW = gf_compute(mf, W, 'gradient', mf_g);
nbdof = gf_mesh_fem_get(mf_g, 'nbdof');
DU = reshape(DU, 2, nbdof);
DW = reshape(DW, 2, nbdof);
UU = gf_compute(mf, U, 'interpolate on', mf_g);
UU0 = gf_compute(mf_basic, U0, 'interpolate on', mf_g);
LS = gf_compute(mf_ls, ULS, 'interpolate on', mf_g);
G = (-4*pi*( alpha*(DU(1,:).^2 + DU(2,:).^2 + DU(1,:).*DW(1,:) + ...
DU(2,:).*DW(2,:)) + beta*(UU-UU0).^2)) .* (sign(LS)+1.)/2;
subplot(2,1,2);
gf_plot(mf_g, G);
title('Topological gradient');
colorbar;
pause(0.01);
% Find the point where the topological gradient is minimum
[val, i] = min(G);
if (val >= -12)
disp('Topological optimization finished.');
return;
end;
point = gf_mesh_fem_get(mf_g, 'basic dof nodes', [i]);
gf_workspace('pop');
% Updating the level set to add the hole
R = -(val+7) / 200;
xc = point(1);
yc = point(2);
ULS = min(ULS, ((x - xc).^2 + (y - yc).^2) - R^2);
end;
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