Periodicity and periodicity conditions on boundaries


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


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 1st case (study domain 1)

  • anti-periodic type (or anti-cyclic)

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