Periodicity - 2D Magnetic Solutions

Introduction

Periodic boundary conditions are used when the physical geometry of interest is periodically repeating in nature. By applying the periodic boundary condition, we can reduce the model size, thereby reducing the computation time.

If your device is periodic, you can define a Periodicity.

It can be linear (by translation) or circular (by rotation).

The Periodicity allows you to create a periodicity (geometrical and physical aspects).

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).

Even periodicity

(or cyclic or periodic)

Odd periodicity

(or anti-cyclic or anti-periodic)
Identical values of the variable on the homologous nodes Opposite values of the variable on the homologous nodes
Note: The boundary conditions are defined in the same way for linear Periodicity.

Periodicity and infinite box

It is possible to combine infinite box and circular periodicity. In this case, the geometry of the infinite box (points and lines) automatically follows the periodicity attached to the study domain.

2D domain
No Periodicity Periodicity
Full infinite box of disc type A portion of infinite box of disc type following the circular Periodicity

Dialog box

Two types of periodicities exist :
  • Linear:

    The periodic part is repeated by translation along an axis.

    A typical example is a linear motor.

  • Rotational:

    The periodic part is repeated by rotation around an axis.

    A typical example is a rotating motor.

Table 1. Linear and Rotation Periodicity dialog boxes:
Linear Periodicity Rotational Periodicity
  • Geometrical Aspects:
    • Axis
      • For Circular Periodicity, the periodic axis will be always Z axis.
      • For Linear Periodicity, the periodic axis can be either X or Y axis. The periodic portion is repeated linearly on the selected axis.
    Note: It is mandatory to have identical geometry and mesh between these two boundaries. For more details on the boundary mesh, please refer to Motor Mesh.

  • Physical Aspects

    This option is necessary to define the physical definition in the non-represented portions.

    There are 2 possibilities:
    • Even i.e. cyclic
    • Odd i.e. anticyclic
    Table 2.
    Odd (anticyclic) Even (cyclic)

    For more information please refer to Periodicity conditions on boundaries.