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# Copyright (C) 2011-2013 Marie E. Rognes, Martin S. Alnaes
#
# This file is part of DOLFIN.
#
# DOLFIN 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.
#
# DOLFIN 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 for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with DOLFIN. If not, see <http://www.gnu.org/licenses/>.
#
# First added: 2011-11-09
# Last changed: 2013-01-29
# Begin demo
#
# NB! This demo is work in progress and will be updated as we get further in the multidomain features implementation.
#
from dolfin import *
import matplotlib.pyplot as plt
class Left(SubDomain):
def inside(self, x, on_boundary):
return (x[0] <= 0.25+DOLFIN_EPS)
class Mid(SubDomain):
def inside(self, x, on_boundary):
return (x[0] >= 0.375-DOLFIN_EPS) and (x[0] <= 0.625+DOLFIN_EPS)
class Right(SubDomain):
def inside(self, x, on_boundary):
return (x[0] >= 0.75-DOLFIN_EPS)
# Define mesh and subdomains
mesh = UnitSquareMesh(64, 64)
domains = MeshFunction("size_t", mesh, mesh.topology().dim())
domains.set_all(0)
Left().mark(domains, 1)
Mid().mark(domains, 2)
Right().mark(domains, 3)
# Define input data
alpha = Constant(1e-3)
f = Constant(3.0)
g = Constant(5.0)
# Define function space and basis functions
V = FunctionSpace(mesh, "CG", 2)
u = TrialFunction(V)
v = TestFunction(V)
# Define regions as tuples of subdomain labels
DL, DM, DR = (1,2), (2,), (2,3) # ***
# Define new measures associated with the interior domains
dx = Measure('dx', domain=mesh, subdomain_data=domains)
# Make forms for equation
a = u*v*dx() + alpha*dot(grad(u), grad(v))*dx() # ***
L = f*v*dx(DR) + g*v*dx(DL) - (f+g)/2*v*dx(DM) # ***
# Solve problem
u = Function(V)
solve(a == L, u)
# Plot solution and gradient
plt.figure()
plot(domains, title='domains')
plt.figure()
plot(u, title="u")
plt.show()
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