Periodicity and periodicity conditions on boundaries

Periodicity

When a device has repetitive patterns, it is possible to model a fraction of the device (the basic pattern), and to impose appropriate periodicity conditions on the periodicity planes.

From a physical point of view, periodicity boundary conditions are set via the state variable (potential).

Periodicity condition (or cyclic)	Anti-periodicity condition (or anti-cyclic)
Identical values of the variable on the homologous nodes	Opposite values of the variable on the homologous nodes

Example

Let's reconsider the preceding example.

The boundary conditions to impose on boundaries 1 and 2 are periodicity conditions:

• periodic type (or cyclic)

  in the 1^st case (study domain 1)

• anti-periodic type (or anti-cyclic)

  in the 2^nd case (study domain 2 and 2')