[firedrake] Specify boundary conditions at a corner

[David Ham]

Hi Justin,

Having subclassed DirichletBC, what you now have is a new type of Dirichlet
"boundary" object, so you just use it as a Dirichlet condition:

bc3 = PointDirichletBC(W.sub(1), 0, 0)

bc_all = [bc1, bc2, bc3]

However Andrew is right, removing the nullspace is almost certainly a
better solution in this case.

Cheers,

David

On Sun, 23 Aug 2015 at 05:23 Justin Chang <jychang48 at gmail.com> wrote:

> 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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