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

S. V. Dolgov; A. P. Smirnov; E. E. Tyrtyshnikov

doi:10.1016/j.jcp.2014.01.029

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

S. V. Dolgov, A. P. Smirnov, E. E. Tyrtyshnikov

Research output: Contribution to journal › Article › peer-review

13 Citations (SciVal)

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.

Original language	English
Pages (from-to)	268-282
Number of pages	15
Journal	Journal of Computational Physics
Volume	263
Early online date	22 Jan 2014
DOIs	https://doi.org/10.1016/j.jcp.2014.01.029
Publication status	Published - 15 Apr 2014

Bibliographical note

Funding Information:
This work was partially supported by RFBR Grants 13-01-12061 (ofi-m-2013) , 12-01-91333 (nnio-a) , 11-01-00549-a , 12-01-33013 (mol-a-ved) , 12-01-31056 , Government Contracts 16.740.12.0727, Π1112, 8500, support programmes of the RAS Presidium and RAS Department of Mathematical Sciences and the Stipend of President of Russia .

Keywords

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

ASJC Scopus subject areas

Numerical Analysis
Modelling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2014.01.029

Cite this

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title = "Low-rank approximation in the numerical modeling of the Farley-Buneman instability in ionospheric plasma",

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.",

keywords = "DMRG, High-dimensional problems, Hybrid methods, Ionospheric irregularities, MPS, Plasma waves and instabilities, Tensor train format, Vlasov equation",

author = "Dolgov, {S. V.} and Smirnov, {A. P.} and Tyrtyshnikov, {E. E.}",

note = "Funding Information: This work was partially supported by RFBR Grants 13-01-12061 (ofi-m-2013) , 12-01-91333 (nnio-a) , 11-01-00549-a , 12-01-33013 (mol-a-ved) , 12-01-31056 , Government Contracts 16.740.12.0727, Π1112, 8500, support programmes of the RAS Presidium and RAS Department of Mathematical Sciences and the Stipend of President of Russia . ",

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AU - Dolgov, S. V.

AU - Smirnov, A. P.

AU - Tyrtyshnikov, E. E.

N1 - Funding Information: This work was partially supported by RFBR Grants 13-01-12061 (ofi-m-2013) , 12-01-91333 (nnio-a) , 11-01-00549-a , 12-01-33013 (mol-a-ved) , 12-01-31056 , Government Contracts 16.740.12.0727, Π1112, 8500, support programmes of the RAS Presidium and RAS Department of Mathematical Sciences and the Stipend of President of Russia .

PY - 2014/4/15

Y1 - 2014/4/15

N2 - 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.

AB - 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.

KW - DMRG

KW - High-dimensional problems

KW - Hybrid methods

KW - Ionospheric irregularities

KW - MPS

KW - Plasma waves and instabilities

KW - Tensor train format

KW - Vlasov equation

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JF - Journal of Computational Physics

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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