# Infinite box transformation

## Infinite box: definition

In the terminology of the software, using a transformation to model an infinite domain is called the infinite box technique or method.

The exterior domain (infinite) is linked to an image domain (called the infinite box ) through a space transformation.

The use of the infinite box implicitly assumes a null field at infinity.

## Infinite box, Flux 3D

The transformation used in Flux 3D, said to be in a parallelipipedic layer (not a skewed surface), is described by two superimposed parallelepipeds or cylinders. The faces of the exterior parallelepiped or cylinder are the image of the infinite, where the potential and field are equal to zero.

Interior domain Exterior image domain, i.e., infinite box Representation of the two domains by the software   ## Infinite box, Flux 2D

For Flux 2D, the infinite box is described by two superimposed discs (crown shaped). The external circle is the image of the infinite.

Interior domain External image domain, i.e. infinite box Representation of the two domains by the software   ## How to choose the dimensions ?

The dimensions of the infinite box are defined by the user. This requires a certain experience because there is no general rule.

We can, however, give some advice:

• the distance between the device and the interior surface of the infinite box is at least equal to the dimension of the device in this direction
• the dimensions of the infinite box are related to the mesh. In Flux 3D, the number of elements on the thickness of the box must be roughly equal (at least) to two (second-order elements) or to three (first-order elements).

The mesh and the size of the infinite box must take into account the phenomena studied, and the computations to be performed as follows:

• if one is interested in computing a global or a local quantity inside the device, it is unnecessary to refine the mesh of the infinite box;
• if on the contrary, one is interested in computing the field created outside the device, one should define a box of more significant size and refine the mesh inside.

It is recommended to parameterize the dimensions of the infinite box to adjust its size during the meshing.

## Boundary conditions

Flux automatically assigns boundary conditions on the infinite box.