Fast Spectral Methods for the Fokker-Planck-Landau Collision Operator

L. Pareschi; G. Russo; G. Toscani

doi:10.1006/jcph.2000.6612

Fast Spectral Methods for the Fokker-Planck-Landau Collision Operator

L. Pareschi
, G. Russo
, G. Toscani

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

87 Scopus citations

Abstract

In this paper we present a new spectral method for the fast evaluation of the Fokker-Planck-Landau (FPL) collision operator. The method allows us to obtain spectrally accurate numerical solutions with simply O(n log₂n) operations in contrast with the usual O(n²) cost of a deterministic scheme. We show that the method preserves the total mass whereas momentum and energy are approximated with spectral accuracy. Numerical results for the FPL equation for Maxwell molecules and for Coulomb interactions in two and three dimensions in velocity space are also given.

Original language	English
Pages (from-to)	216-236
Number of pages	21
Journal	Journal of Computational Physics
Volume	165
Issue number	1
DOIs	https://doi.org/10.1006/jcph.2000.6612
State	Published - 20 Nov 2000
Externally published	Yes

Keywords

Fast Fourier transform
Fokker-Planck-Landau equation
Spectral methods

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10.1006/jcph.2000.6612

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title = "Fast Spectral Methods for the Fokker-Planck-Landau Collision Operator",

abstract = "In this paper we present a new spectral method for the fast evaluation of the Fokker-Planck-Landau (FPL) collision operator. The method allows us to obtain spectrally accurate numerical solutions with simply O(n log2n) operations in contrast with the usual O(n2) cost of a deterministic scheme. We show that the method preserves the total mass whereas momentum and energy are approximated with spectral accuracy. Numerical results for the FPL equation for Maxwell molecules and for Coulomb interactions in two and three dimensions in velocity space are also given.",

keywords = "Fast Fourier transform, Fokker-Planck-Landau equation, Spectral methods",

author = "L. Pareschi and G. Russo and G. Toscani",

note = "Funding Information: 1 This work was partially supported by TMR project “Asymptotic Methods in Kinetic Theory,” Contract Number ERB FMRX CT97 0157.",

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AU - Pareschi, L.

AU - Russo, G.

AU - Toscani, G.

N1 - Funding Information: 1 This work was partially supported by TMR project “Asymptotic Methods in Kinetic Theory,” Contract Number ERB FMRX CT97 0157.

PY - 2000/11/20

Y1 - 2000/11/20

N2 - In this paper we present a new spectral method for the fast evaluation of the Fokker-Planck-Landau (FPL) collision operator. The method allows us to obtain spectrally accurate numerical solutions with simply O(n log2n) operations in contrast with the usual O(n2) cost of a deterministic scheme. We show that the method preserves the total mass whereas momentum and energy are approximated with spectral accuracy. Numerical results for the FPL equation for Maxwell molecules and for Coulomb interactions in two and three dimensions in velocity space are also given.

AB - In this paper we present a new spectral method for the fast evaluation of the Fokker-Planck-Landau (FPL) collision operator. The method allows us to obtain spectrally accurate numerical solutions with simply O(n log2n) operations in contrast with the usual O(n2) cost of a deterministic scheme. We show that the method preserves the total mass whereas momentum and energy are approximated with spectral accuracy. Numerical results for the FPL equation for Maxwell molecules and for Coulomb interactions in two and three dimensions in velocity space are also given.

KW - Fast Fourier transform

KW - Fokker-Planck-Landau equation

KW - Spectral methods

UR - https://www.scopus.com/pages/publications/0009597026

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DO - 10.1006/jcph.2000.6612

M3 - Article

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VL - 165

SP - 216

EP - 236

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 1

ER -

Fast Spectral Methods for the Fokker-Planck-Landau Collision Operator

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Keywords

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