[firedrake] Specify boundary conditions at a corner

[Justin Chang]

Andrew,

That actually did the trick, thank you very much.

But I still would like to know the answer to my original question. Or
perhaps, instead of a single corner, I would like to set (x=0,y<0.1)
and (x<0.1,y=0) to a specific value while everywhere else is set to a
different value.

Thanks,
Justin

On Sat, Aug 22, 2015 at 11:58 AM, Andrew McRae <a.mcrae12 at imperial.ac.uk> wrote:
> This doesn't answer your main question, but setting an appropriate nullspace
> might be more appropriate than pinning a single value; see
> http://www.firedrakeproject.org/solving-interface.html
>
> [If I'm wrong, I'll let the usual suspects correct my misinformation]
>
> On 22 August 2015 at 18:47, Justin Chang <jychang48 at gmail.com> wrote:
>>
>> David,
>>
>> How exactly do I use that class in my code? Say I have the following
>> function spaces/discretization based on the least-squares finite
>> element method:
>>
>> # Mesh
>> mesh = UnitSquareMesh(seed,seed)
>> V = VectorFunctionSpace(mesh,"CG",1)
>> Q = FunctionSpace(mesh,"CG",1)
>> W = V*Q
>> v,p = TrialFunctions(W)
>> w,q = TestFunctions(W)
>>
>> # Weak form
>> g = Function(V)
>>
>> g.interpolate(Expression(("cos(pi*x[0])*sin(pi*x[1])+2*pi*cos(2*pi*x[0])*sin(2*pi*x[1])","-sin(pi*x[0])*cos(pi*x[1])+2*pi*sin(2*pi*x[0])*cos(2*pi*x[1])")))
>> a = dot(v+grad(p),w+grad(q))*dx + div(v)*div(w)*dx
>> L = dot(w+grad(q),g)*dx
>>
>> # Boundary conditions
>> bc1 = DirichletBC(W.sub(0).sub(0),
>> Expression("cos(pi*x[0])*sin(pi*x[1])"), (1,2))
>> bc2 = DirichletBC(W.sub(0).sub(1),
>> Expression("-sin(pi*x[0])*cos(pi*x[1])"), (3,4))
>> bc_all = [bc1,bc2]
>>
>> # Solve
>> cg_parameters = {
>>     'ksp_type': 'cg',
>>     'pc_type': 'bjacobi'
>>     }
>> solution = Function(W)
>> A = assemble(a,bcs=bc_all)
>> b = assemble(L,bcs=bc_all)
>> solver =
>> LinearSolver(A,solver_parameters=cg_parameters,options_prefix="cg_")
>> solver.solve(solution,b)
>>
>> If I run the above code I get an error saying 'LinearSolver failed to
>> converge after %d iterations with reason: %s', 196,
>> 'DIVERGED_INDEFINITE_MAT'. Which I am guessing has to do with the lack
>> of a boundary condition for the Q space, thus I want to ensure a
>> unique solution by prescribing the bottom left constraint to a zero
>> value.
>>
>> Thanks,
>> Justin
>>
>>
>> On Fri, Aug 21, 2015 at 4:52 AM, David Ham <David.Ham at imperial.ac.uk>
>> wrote:
>> > Hi Justin,
>> >
>> > The nice way of doing this would require better subdomain support than
>> > we
>> > have right now. However there is a slightly hacky way of doing it which
>> > I
>> > think will cover your case nicely.
>> >
>> > If you take a look at the DirichletBC class (in bcs.py), you'll notice
>> > that
>> > the set of nodes at which the BC should be applied is calculated in
>> > DirichletBC.nodes . So you could simply subclass DirichletBC and replace
>> > nodes with a function which returns the index of the zero node. For
>> > example
>> > (and I confess this is a sketch code which I haven't tried to run):
>> >
>> > class PointDirichletBC(DirichletBC):
>> >     @utils.cached_property
>> >     def nodes(self):
>> >         # Find the array of coordinate values.
>> >         x = self.function_space().mesh().coordinates.dat.data_ro
>> >         # Find the location of the zero rows in that
>> >         return np.where(~x.any(axis=1))[0]
>> >
>> > Does that work for you?
>> >
>> > Cheers,
>> >
>> > David
>> >
>> > On Fri, 21 Aug 2015 at 03:32 Justin Chang <jychang48 at gmail.com> wrote:
>> >>
>> >> Hi all,
>> >>
>> >> If I create a mesh using UnitSquareMesh or UnitCubeMesh, is there a
>> >> way to subject a single point (as opposed to an entire edge/face) to a
>> >> DirichletBC? I want to subject the the location x=0,y=0 to some value.
>> >>
>> >> Thanks,
>> >> Justin
>> >>
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>> >
>> >
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