### Bloch-Floquet and other periodic boundary conditions

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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

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

How about reformulating the problem for a function \( v \) defined as

- \( v(x) = \left[ \frac{\cos(k L) - 1}{L} x + 1 \right] u(x), \)

- \( v(x) = u(x) + \frac{k x}{L}, \)

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