Low-rank approximation in the numerical modeling of the Farley-Buneman instability in ionospheric plasma

Authors:
S. V. Dolgov;A. P. Smirnov;E. E. Tyrtyshnikov
Affiliations:
Max-Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig 04103, Germany and Institute of Numerical Mathematics of Russian Academy of Sciences, Gubkina 8, Moscow 119333, Russi ...;Lomonosov Moscow State University, Moscow, Russia;Institute of Numerical Mathematics of Russian Academy of Sciences, Gubkina 8, Moscow 119333, Russia and Lomonosov Moscow State University, Moscow, Russia and Moscow Institute of Physics and Techno ...
Venue:
Journal of Computational Physics
Year:
2014

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Abstract

We consider numerical modeling of the Farley-Buneman instability in the Earth's ionosphere plasma. The ion behavior is governed by the kinetic Vlasov equation with the BGK collisional term in the four-dimensional phase space, and since the finite difference discretization on a tensor product grid is used, this equation becomes the most computationally challenging part of the scheme. To relax the complexity and memory consumption, an adaptive model reduction using the low-rank separation of variables, namely the Tensor Train format, is employed. The approach was verified via a prototype MATLAB implementation. Numerical experiments demonstrate the possibility of efficient separation of space and velocity variables, resulting in the solution storage reduction by a factor of order tens.