Do I still need to define u1, u2, u3 = Functions(V), where V is in original space? After the variational problem is solved I split w as

u1, u2, u3 = split(w)

and try to print u1, u2, u3 in files, but I get

AttributeError: 'Indexed' object has no attribute 'function_space'.

Also, I can't interpolate or assign. In the end, I want to pass u1, u2, u3 to some other functions u1_, u2_, u3_, which also appear in the residual expressions. But this produces a 'Mismatching function spaces' error.




On 26/11/14 11:12, David Ham wrote:
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@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

-- 
 
 Dr Anna Kalogirou
 Research Fellow
 School of Mathematics
 University of Leeds