Dear Prof. Bangerth,
I am also solving a similar problem. But I have a query from your last
reply.
Let us consider an 1D domain with periodic BC applied on both ends. Then
it is clear from your reply that the gradient terms have equal and opposite
contribution in the weak form and they just vanish. In homogeneous Neumann
BC also these terms do not participate. However, the difference is that
with periodic
BC they normal component of the gradients need not be zero. Hence my
question is
how this fact (i.e. non-zero value of normal component of gradient) is
being ensured
in the case when we are applying periodic BC.
Also, in the periodic BC implementation of dealii is this part of the BC,
i.e. equality
(with -ve sign ) of normal component of the gradients are taken care of?
I shall be thankful if you please clarify this point.
Thanks and regards,
Anup.
On Wed, Nov 30, 2016 at 4:06 PM, Wolfgang Bangerth <bange...@colostate.edu>
wrote:
> On 11/30/2016 10:38 AM, Hamed Babaei wrote:
>
>>
>> I am considering Periodic Boundary Condition for a problem which is very
>> simillar to step-25. Before applying periodic condition, I considered
>> homogeneous Newmann Boundary condition in external surfaces by simply
>> omitting
>> Neumann term in week formulation (v , n.grad(u) )=0. However, since
>> Neumann BC
>> has meaning when we have external surface and now I have periodicity
>> condition, It seems I can not have both periodic and neumann BC
>> simultaneously. Therefore I am going to eliminate Neumann condition by
>> keeping
>> the term (v, n.grad(u)) in my right hand side as a generalized force term.
>>
>
> If the solution is periodic, let's say across the left and right sides of
> the domain, then you have that
> u(left) = u(right)
> v(left) = v(right)
> n(left) = -n(right)
> and
> grad(u)|_left = grad(u)|_right
>
> In other words, you have that
> (v, n.grad(u))_{Gamma_left} = - (v, n.grad(u))_{Gamma_right}
> and consequently (if left/right are the only periodic parts of the
> boundary)
> (v, n.grad(u))_{Gamma_periodic)
> = (v, n.grad(u))_{Gamma_left} + (v, n.grad(u))_{Gamma_right}
> = 0.
>
> That means that the term you have should not appear in the bilinear form.
>
> Best
> W.
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: bange...@colostate.edu
> www: http://www.math.colostate.edu/~bangerth/
>
>
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