Unlike standard algebraic remeshing techniques, the Thompson transformation remeshing technique [34] is based on the resolution of a partial differential equation of the elliptic type, and remains robust for larger mesh deformations. One of the advantages of using the Thompson transformation is that the mesh can contain any type of element (quadrilaterals, triangles, bricks, wedges, tetrahedra). The other models are more limited due to their use of slicing; if tetrahedra or triangles are included in the mesh, slicing becomes impossible because the mesh is not logically organized.

The topology of the parent mesh is almost arbitrary. The drawback is the large CPU time and memory requirements. For most 2D problems, however, this cost increase remains quite acceptable.