[firedrake] Specify boundary conditions at a corner

[Andrew McRae]

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
> >>
> >> _______________________________________________
> >> firedrake mailing list
> >> firedrake at imperial.ac.uk
> >> https://mailman.ic.ac.uk/mailman/listinfo/firedrake
> >
> >
> > _______________________________________________
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> > firedrake at imperial.ac.uk
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> >
>
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