ufl team mailing list archive

[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.

>
> 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

V = FunctionSpace("Lagrange", "triangle", 1)
T(i)* V == g

But we can also do restrict (in both cases).


Kent