**By R. Belmans**

**Geometric transformations map** real geometrical shapes to arbitrary ones. Depending on the type of differential equation and on the transformation functions, the differential equation can change.

**Fig. 9.7. Half-symmetry of the model of a magnetic contactor.**

**Fig. 9.8. Binary boundary condition applied to reduce the model size to ‘/< of the entire cross-section.**

**Three common reasons for transforming the geometry are:**

**• to avoid difficulties with the automated mesh generation or refinement,**

**• to consider anisotropic materials and**

**• to compute the field of an infinite geometry.**

### Geometry

**When a model causes difficulties** during automated mesh generation, the shape of the model can be mapped into a simpler one (Fig. 9.9). The back transformation is done immediately after meshing or after solving the problem. If the problem is solved using the arbitrary shapes rather than the real geometry, the system of differential equations of the model undergoes the same transformation.

**Fig. 9.9. Transformation of the mesh of a discretised geometry.**