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flux_test_1D.py
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flux_test_1D.py
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from pylab import *
from fenics import *
from matrices import plot_matrix
n = 200
mesh = UnitIntervalMesh(3)
# refine mesh :
origin = Point(0.0,0.0,0.0)
for i in range(1,1):
cell_markers = CellFunction("bool", mesh)
cell_markers.set_all(False)
for cell in cells(mesh):
p = cell.midpoint()
if p.distance(origin) < 1.0/i:
cell_markers[cell] = True
mesh = refine(mesh, cell_markers)
Q = FunctionSpace(mesh, 'CG', 1)
w = TrialFunction(Q)
v = TestFunction(Q)
u = Function(Q, name='u')
f = Constant(1.0)
a = w.dx(0) * v.dx(0) * dx
l = f * v * dx
def left(x, on_boundary):
return x[0] == 0 and on_boundary
bc = DirichletBC(Q, 0.0, left)
solve(a == l, u, bc)
File('output/u.pvd') << u
uv = u.vector().array()
b = assemble(l).array()
A = assemble(a).array()
t = np.dot(A,uv) - b
q = Function(Q, name='q')
q.vector().set_local(t)
q.vector().apply('insert')
File('output/q.pvd') << q
fig = figure()
ax = fig.add_subplot(111)
plot_matrix(A, ax, r'stiffness matrix $K$', continuous=False)
tight_layout()
show()