On the numerical simulation of particle dynamics in the radiation belt: 2. Procedure based on the diagonalization of the diffusion tensor

In this paper, we conclude the survey and comparison of different numerical methods used to solve the diffusion equation for particle dynamics in the Earth's radiation belt, initiated in Camporeale et al. (2013). Here we focus on the diagonalization procedure introduced by Albert and Young (2005) that, by performing a change of coordinates, solves the diffusion equation in a space where the mixed diffusion terms are null. We describe the diagonalization procedure and its numerical implementation, which is not as straightforward as the implementation of a traditional solver in a rectangular domain. We compare the computing times with and without the diagonalization procedure, and we conclude that this procedure is generally not advantageous from the point of view of computational efficiency.