Generation of orthogonal curvilinear meshes in three dimensions

In this article a method of curvilinear orthogonal mesh generation in three dimensions is described. This technique is based on the solution of elliptic equations in two and three dimensions. Frequently, the generated meshes are not quite orthogonal; hence a modified Davies' algorithm is used to solve this problem. The effectiveness of the method is demonstrated using examples based on electromagnetic field problems. These curvilinear meshes have the ability to correctly represent non-uniform geometry, as well as regions containing singularities or high gradient fields