  In this paper we present a spectral collocation method for the fast
evaluation of the Landau collision operator for plasma physics, which allows us
to obtain spectrally accurate numerical solutions. The method is inspired by
the seminal work [36], but it is specifically designed for Coulombian
interactions, taking into account the particular structure of the operator. It
allows us to reduce the number of discrete convolutions to provide an
approximation of the Landau operator. Then, we show that the method preserves
the total mass whereas momentum and energy are approximated with spectral
accuracy. Numerical results for the Landau equation in three dimensions in
velocity space are presented to illustrate the efficiency of the present
approach.
