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

• Published in: Journal of computational physics 2014-04, Vol.263, p.268-282
• Main Authors: Dolgov, S.V., Smirnov, A.P., Tyrtyshnikov, E.E.
• Format: Article
• Language: English
• Subjects: Computation; DMRG; High-dimensional problems; Hybrid methods; Instability; Ionospheric irregularities; Mathematical analysis; Mathematical models; Matlab; MPS; Plasma (physics); Plasma waves and instabilities; Separation; Tensor train format; Tensors; Vlasov equation
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2014.01.029

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.