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A spectral collocation method for the Landau equation in plasma physics
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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.
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Numerical analysis of the homogeneous Landau equation: approximation, error estimates and simulation
A Fourier spectral scheme for the Landau-Coulomb equation is proven to converge with explicit error bounds: larger truncated domains and more Fourier modes push the error below any prescribed tolerance on any fixed ti...
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