[firedrake] Specify boundary conditions at a corner

Tue Aug 25 00:48:21 BST 2015

David,

I get the following error:

Traceback (most recent call last):
  File "Test_LSAug.py", line 41, in <module>
    class PointDirichletBC(DirichletBC):
  File "Test_LSAug.py", line 42, in PointDirichletBC
    @utils.cached_property
AttributeError: 'module' object has no attribute 'cached_property'

When I comment out that line, i get a long error. When I try to import
utils and all the other modules that bcs.py imports, i get errors
saying those modules don't exist. Know what's going on?

Thanks,
Justin

On Mon, Aug 24, 2015 at 3:14 AM, David Ham <David.Ham at imperial.ac.uk> wrote:
> 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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