[firedrake] Solve multiple variational problems at once

[David Ham]

Actually, assuming the original problems were written so that v is in the
same space as u1, which is how I read the spec, then this is ill-posed.
Instead you need to pull the test function from the mixed space too.

W = MixedFunctionSpace(...)

w = Function(W)
v = TestFunction(W)

u1, u2, u3 = split(w)
v1, v2, v3 = split(v)

F = fn(u1, u2, u3; v1)
etc...


solve(F + G + H == 0, w)

On 26 November 2014 at 10:28, Mitchell, Lawrence <
lawrence.mitchell at imperial.ac.uk> wrote:

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> On 26/11/14 10:19, Anna Kalogirou wrote:
> > Dear all,
> >
> > How would I solve multiple nonlinear variational problems
> > simultaneously? For example, say that I have three residuals
> >
> > F(u1,u2,u3;v) = 0 G(u1,u2,u3;v) = 0 H(u1,u2,u3;v) = 0,
> >
> > where v is the test function. I need to solve all three of them
> > together. Any suggestions?
>
> Assuming you have:
>
> W = MixedFunctionSpace(...)
>
> w = Function(W)
>
> u1, u2, u3 = split(w)
>
> F = fn(u1, u2, u3; v)
> etc...
>
> Since you're linear in v, can you not just write:
>
>
> solve(F + G + H == 0, w)
>
> ?
>
> Or am I missing something?
>
> Lawrence
>
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-- 
Dr David Ham
Departments of Mathematics and Computing
Imperial College London

http://www.imperial.ac.uk/people/david.ham
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