Bloch-Floquet and other periodic boundary conditions


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0
3 months ago by
Hi!

The Poisson example with periodic boundary conditions
https://fenicsproject.org/olddocs/dolfin/2016.2.0/python/demo/documented/periodic/python/documentation.html
seem not to be to easily changed to a more general form such as Bloch-Floquet. How does one apply more general periodic boundary conditions in fenics? Say

u(0)=u(L)*cos(k*L)


or

u(0)=u(L)+k

or

u1(0)+iu2(0)=(u1(L)+iu2(L))*exp(i*k*L)
(which can of cause be split into real and imaginary parts)

Best Regards,
Søren
Community: FEniCS Project

1 Answer


5
3 months ago by
How about reformulating the problem for a function \( v \) defined as
  • \( v(x) = \left[ \frac{\cos(k L) - 1}{L} x + 1 \right] u(x), \)
resp.
  • \( v(x) = u(x) + \frac{k x}{L}, \)
with the standard periodic BC?
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