ufl team mailing list archive

["Martin Sandve Alnæs" <martinal@xxxxxxxxx>]

2008/6/23  <kent-and@xxxxxxxxx>:
>> If we should add notation for boundary conditions to UFL, then I think
>> it must also be supported through the UFC interface so that the
>> assembler may assemble the correct matrix/vector directly (without
>> zeroing out entries in a separate step).
>
> I don't understand what you mean with this. It has to be a separate step
> that is performed after the tabulate_tensor functions.

The assembler cannot use UFL directly, and UFL is supposed to pass
through a form compiler. Somebody must convert the UFL to something
the C++ assembler can eat, and UFC is the interface we hide equation
details behind. Unless you have a better option?


>> Regarding the notation, maybe it should be a constraint on the
>> function spaces. Take for example Poisson with u = g on the boundary:
>>
>>   Find u in H^1_g : a(v, u) = L(v) for all v in H^1_0
>>
>> The boundary conditions are part of the test and trial spaces
>> (subscripts g and 0 on H^1). We could do something like
>>
>>   V = FunctionSpace("Lagrange", "triangle", 1) # test space
>>   W = FunctionSpace("Lagrange", "triangle", 1) # trial space
>>   V.restrict(g)
>>   W.restrict(0)
>>
>>   a = dot(grad(v), grad(u))*dx
>>   L = v*f*dx
>>
>
> We could do that.
>
> Boundary conditions are usually part of the test and trial space, but this
> is just short-hand
> notation. Either you can say
>
> Find u in H^1_g : a(v, u) = L(v) for all v in H^1_0
>
> where H^1_g are the functions in H^1 with Tu=g on \partial \Omega
> (and similar with H^1_0)
>
> or you can say
>
> Find u in H^1 : a(v, u) = L(v) for all v in H^1 with Tu = g on \partial
> \Omega
> (and similar with v).
>
> It is just that H^1_0 is so established that we hardly think of traces.
>
> But I think
>
> T(i) * u == g
>
> looks good, it can also be done on the test or trial space

I think you've still not answered the question about how this is used.
The line above won't work alone, we'll have to do at least

  bc = T(i) * u == g

which looks a bit more strange than your line alone,
and then 'bc' must be attached to an equation somehow
if we are to pass around simple objects like we do with forms.


> V = FunctionSpace("Lagrange", "triangle", 1)
> T(i)* V == g
>
> But we can also do restrict (in both cases).

I don't think I like the V.restrict(g) option.
One reason is purely visual, it doesn't quite
"fit" with the rest of UFL. More importantly,
I'd like to use the same element object for
coefficient functions and basis functions.
Maybe we can do:

V = FiniteElement("Lagrange", "triangle", 1)
Vg = Restricted(V, g, i) # subspace of V with u=g on dS_i
u = TrialFunction(Vg)
f = Function(V)

--
Martin