Effective numerical methods for simulating diffusion on a spherical surface in three dimensions

In order to construct an algorithm for homogeneous diffusive motion that lives on a sphere, we consider the equivalent process of a randomly rotating spin vector of constant length. By introducing appropriate sets of random variables based on cross products, we construct families of methods with increasing efficacy that exactly preserve the spin modulus for every realisation. This is done by exponentiating an antisymmetric matrix whose entries are these random variables that are Gaussian in the simplest case.

Automated summary

This paper presents an algorithm for homogeneous diffusive motion on a sphere by considering the equivalent process of a randomly rotating spin vector. By introducing appropriate sets of random variables, families of methods are constructed that effectively preserve the spin modulus for every realization, achieved by exponentiating an antisymmetric matrix.