## Copyright (C) 2013 Marco Vassallo <gedeone-octave@users.sourceforge.net>
##
## This program is free software; you can redistribute it and/or modify it under
## the terms of the GNU General Public License as published by the Free Software
## Foundation; either version 3 of the License, 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 General Public License for more
## details.
##
## You should have received a copy of the GNU General Public License along with
## this program; if not, see <http://www.gnu.org/licenses/>.

pkg load fem-fenics msh

ufl start Evolution
ufl 'element = FiniteElement("Lagrange", triangle, 1)'
ufl
ufl u = TrialFunction(element)
ufl v = TestFunction(element)
ufl
ufl u0 = Coefficient(element)
ufl
ufl dt = Constant(triangle)
ufl
ufl eq = (1/dt)*(u-u0)*v*dx + "inner(grad(u), grad(v))*dx"
ufl a = rhs (eq)
ufl L = lhs (eq)
ufl end

problem = 'Evolution';

mesh = Mesh (msh2m_structured_mesh (0:0.05:1, 0:0.05:1, 1, 1:4));

V = FunctionSpace(problem, mesh);

bc = DirichletBC (V, @(x,y) 1, 1:4);

t = 0;
dt = 0.01;
T = 0.3;

k = Expression ('dt', @(x,y) dt);

u0 = Expression ('u0', @(x,y) 10*exp(-((x - 0.5)^2 + (y - 0.5)^2) / 0.02));

a = BilinearForm (problem, V, V, k);
L = LinearForm (problem, V, k, u0);

A = assemble (a, bc);

# solve the problem for each time step
# We need to update only the lhs
while t < T
  t += dt;

  # we can pass u0 to the lhs indifferently as a fem_coeff or
  # as a fem_func
  L = LinearForm (problem, V, k, u0);
  b = assemble (L, bc);

  u = A \ b;
 
  u0 = Function ('u0', V, u);

  #press Q to make the plot continue
  plot (u0);
end