Symmetry: about

Symmetries attached to the study domain

If the model device is characterized by possible symmetries, those can be attached to the study domain.

The boundary conditions on the corresponding boundaries are imposed in the Physical module.

Symmetry axes: 2D domain

The symmetry axes can be:

  • either axes parallel (X, Y) to the main axes (OX, OY)
  • or an tilted axis that forms an angle with the main axis OX and passing by the origin of the coordinate system of the study domain

Symmetry axis

  • is an axis parallel with the OX axis (or passing by the OX axis)
  • passes through the OY axis at the y coordinate

Symmetry axis

  • is an tilted axis from the OX axis
  • forms θz angle with OX axis

Symmetry planes: 3D domain

The symmetry planes can be:

  • either planes parallel to the main planes (XOY, YOZ, XOZ)
  • or tilted planes passing through one of the main axis (OX, OY, OZ)

Symmetry plane

  • is the plane parallel to the XOY plane
  • passes through the OZ axis at the z coordinate

Symmetry plane

  • is the plane obtained by pivoting the XOY plane with an angle θ x around the OX axis

Symmetry and infinite box

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

The rules to be respected are presented in the table below.

Domain Rule
2D the axes of symmetry have to correspond to the main axes of the coordinate system of the study domain (X and Y)
3D the planes of symmetry have to correspond to the main planes of the coordinate system of the study domain (XOY, YOZ and ZOX)

Example: 2D domain

The examples of the infinite box geometry for the study domain with no symmetry and with the symmetries are presented in the table below.

no symmetry symmetries
Complete infinite box of disk type A quarter of the infinite box of disk type for symmetries versus X and Y axis

Example: 3D domain

The examples of the infinite box geometry for the study domain with no symmetry and with the symmetries are presented in the table below.

no symmetry symmetries
Complete infinite box of parallelepiped type A quarter of the infinite box of parallelepiped type for symmetries versus XY plane, YZ plane and ZX plane