Gaussian radial basis functions for plasma physics: Numerical aspects

Paper in proceeding, 2015

A magnetized plasma is described by the Vlasov equation and the non-linear Fokker-Planck collision operator [1]. The Vlasov part describes phase-space advection and the collision operator adds dissipation due to collisional energy and momentum exchange. Numerical discretization of the collision operator, however, is far from trivial. Recently, we have developed a new approach [2] to address this issue. The new approach is based on an expansion in Gaussian Radial Basis Functions (RBFs), a method widely used in neural network calculations [3]. In this paper, we discusss useful details regarding the numerical implementation of the RBF method.