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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:263

Article

Dolgov, S. V.^1,2  Smirnov, A. P.³  Tyrtyshnikov, E. E.^2,3,4,5 

[1] Max Planck Inst Math Sci, D-04103 Leipzig, Germany

[2] Russian Acad Sci, Inst Numer Math, Moscow 119333, Russia

[3] Moscow MV Lomonosov State Univ, Moscow, Russia

[4] Moscow Inst Phys & Technol, Moscow, Russia

[5] Univ Podlasie, Siedlce, Poland

关键词: High-dimensional problems;    DMRG;    MPS;    Tensor train format;    Ionospheric irregularities;    Plasma waves and instabilities;    Vlasov equation;    Hybrid methods;   

DOI  :  10.1016/j.jcp.2014.01.029

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free