Dirichlet condition which is a function

[Toomyalla]

I am trying to solve Poisson's equationwith non trivial boun dary conditions but it does not work . I need help how to code the conditions and this is my attempt.

from firedrake import *

mesh = UnitSquareMesh(10, 10)

V = FunctionSpace(mesh, "CG", 1)

u = TrialFunction(V)
v = TestFunction(V)

a = (inner(grad(u), grad(v)) + inner(u, v)) * dx
L = Constant(0)*v*dx

x =SpatialCoordinate(mesh)

g = Function(V)
g.interpolate(min(4*x[0],4-4*x[0]))
bc1=DirichletBC(V, g ,1)

boundary_ids={2, 3, 4}
bc2=DirichletBC(V,0, boundary_ids)

u = Function(V)

solve(a == L, u,bcs=[bc1,bc2], solver_parameters={'ksp_type': 'cg', 'pc_type': 'none'})

Thank you in advance,

[dham]

Thanks for the question. I notice a couple of things immediately:

• The equation being solved is Helmholtz, not Poisson. Is this intentional?
• For a small problem like this, changing the default solver parameters probably isn't desirable.

You haven't specified what you mean by "it does not work". Could you please detail what the observed output is and what you expect.

[Toomyalla]

Sorry, I mean a to be
a = dot(grad(u), grad(v))* dx

I get the error
UFL:ERROR UFL conditions cannot be evaluated as bool in a Python context.
Traceback (most recent call last):
File "/home/firedrake/mycode/poisson.py", line 26, in
g.interpolate((min(4y,4-4y)))
File "/home/firedrake/firedrake/src/ufl/ufl/conditional.py", line 34, in bool
error("UFL conditions cannot be evaluated as bool in a Python context.")
File "/home/firedrake/firedrake/src/ufl/ufl/log.py", line 158, in error
raise self._exception_type(self._format_raw(*message))
ufl.log.UFLException: UFL conditions cannot be evaluated as bool in a Python context.

I expect an answer of approximately 0.325 when I ask for the solution at the center.
print(u.at([0.5,0.5]))

[ksagiyam]

I think you want g.interpolate(conditional(4*x[0] > 4-4*x[0], 4-4*x[0], 4*x[0])) instead of g.interpolate(min(4*x[0],4-4*x[0])).

[Toomyalla]

Thank you. It is solved but without the use of the index 0.

g.interpolate(conditional(4y > 4-4y, 4-4y, 4y))