On 11/30/2016 03:26 PM, Anup Basak wrote:
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.
It's because in the periodic case, the periodicity is part of the function
space and is enforced via constraints through the ConstraintMatrix object.
This does not happen for homogenous Neumann conditions.
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?
It isn't. You only enforce that the *values* of the solution are equal. The
equality of the gradients (and consequently the negative equality of the
normal component) happens as a result.
Best
W.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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