An efficient explicit numerical scheme for diffusion-type equations with a highly inhomogeneous and highly anisotropic diffusion tensor

Abstract A locally split-step explicit (LSSE) algorithm was developed for efficiently solving a multi-dimensional advection-diffusion type equation involving a highly inhomogeneous and highly anisotropic diffusion tensor, which makes the problem very ill-conditioned for standard implicit methods involving the iterative solution of large linear systems. The need for such an optimized algorithm arises, in particular, in the frame of thermonuclear fusion applications, for the purpose of simulating fast charged-particle slowing-down with an ion Fokker–Planck code. The LSSE algorithm is presented in this paper along with the results of a model slowing-down problem to which it has been applied.