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"""This demo program solves Poisson's equation
- div grad u(x, y) = f(x, y)
on the unit square with source f given by
f(x, y) = -1.0 if (x - 0.33)^2 + (y - 0.67)^2 < 0.015
5.0 if 0.015 < (x - 0.33)^2 + (y - 0.67)^2 < 0.025
-1.0 if (x,y) in triangle( (0.55, 0.05), (0.95, 0.45), (0.55, 0.45) )
0.0 otherwise
and homogeneous Dirichlet boundary conditions.
"""
# Copyright (C) 2010 Kristian B. Oelgaard
#
# 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/>.
#
# Modified by Anders Logg 2011
#
# First added: 2010-07-23
# Last changed: 2012-11-12
from dolfin import *
import matplotlib.pyplot as plt
# Create mesh and define function space
mesh = UnitSquareMesh(64, 64)
V = FunctionSpace(mesh, "CG", 2)
# Define Dirichlet boundary (x = 0 or x = 1)
def boundary(x):
return x[0] < DOLFIN_EPS or x[0] > 1.0 - DOLFIN_EPS or x[1] < DOLFIN_EPS or x[1] > 1.0 - DOLFIN_EPS
# Define boundary condition
u0 = Constant(0.0)
bc = DirichletBC(V, u0, boundary)
# Define variational problem
u = TrialFunction(V)
v = TestFunction(V)
x = SpatialCoordinate(mesh)
c0 = conditional(le( (x[0]-0.33)**2 + (x[1]-0.67)**2, 0.015), -1.0, 5.0)
c = conditional( le( (x[0]-0.33)**2 + (x[1]-0.67)**2, 0.025), c0, 0.0 )
t0 = conditional(ge( x[0], 0.55), -1.0, 0.0)
t1 = conditional(le( x[0], 0.95), t0, 0.0)
t2 = conditional(ge( x[1], 0.05), t1, 0.0)
t3 = conditional(le( x[1], 0.45), t2, 0.0)
t = conditional(ge( x[1] - x[0] - 0.05 + 0.55, 0.0), t3, 0.0)
f = c + t
a = inner(grad(u), grad(v))*dx
L = f*v*dx
# Compute solution
u = Function(V)
solve(a == L, u, bc)
# Save solution in VTK format
file = File("conditional.pvd")
file << u
# Plot solution
plot(u)
plt.show()
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