Icosahedral Discretization of the Two-Sphere

Abstract

We present an almost uniform triangulation of the two-sphere, derived from the icosahedron, and describe a procedure for discretization of a partial differential equation using this triangular grid. The accuracy of our procedure is described by a strong theoretical estimate, and verified by large-scale numerical experiments. We also describe a data structure for this spherical discretization that allows fast computation on either a vector computer or an asynchronous parallel computer.