Volume 38, Issue 1
Numerical Approximation of the Smoluchowski Equation Using Radial Basis Functions

Christiane Helzel & Maximilian Schneiders

J. Comp. Math., 38 (2020), pp. 176-194.

Published online: 2020-02

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  • Abstract

The goal of this paper is to present a numerical method for the Smoluchowski equation, a drift-diffusion equation on the sphere, arising in the modelling of particle dynamics. The numerical method uses radial basis functions (RBF). This is a relatively new approach, which has recently mainly been used for geophysical applications. For a simplified model problem we compare the RBF approach with a spectral method, i.e. the standard approach used in related physical applications. This comparison as well as our other accuracy studies show that RBF methods are an attractive alternative for these kind of models.

  • Keywords

Smoluchowski equation, Spectral method, Radial basis function method.

  • AMS Subject Headings

65M20, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

christiane.helzel@hhu.de (Christiane Helzel)

Maximilian.Schneiders@hhu.de (Maximilian Schneiders)

  • BibTex
  • RIS
  • TXT
@Article{JCM-38-176, author = {Helzel , Christiane and Schneiders , Maximilian }, title = {Numerical Approximation of the Smoluchowski Equation Using Radial Basis Functions}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {1}, pages = {176--194}, abstract = {

The goal of this paper is to present a numerical method for the Smoluchowski equation, a drift-diffusion equation on the sphere, arising in the modelling of particle dynamics. The numerical method uses radial basis functions (RBF). This is a relatively new approach, which has recently mainly been used for geophysical applications. For a simplified model problem we compare the RBF approach with a spectral method, i.e. the standard approach used in related physical applications. This comparison as well as our other accuracy studies show that RBF methods are an attractive alternative for these kind of models.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1908-m2018-0211}, url = {http://global-sci.org/intro/article_detail/jcm/13690.html} }
TY - JOUR T1 - Numerical Approximation of the Smoluchowski Equation Using Radial Basis Functions AU - Helzel , Christiane AU - Schneiders , Maximilian JO - Journal of Computational Mathematics VL - 1 SP - 176 EP - 194 PY - 2020 DA - 2020/02 SN - 38 DO - http://doi.org/10.4208/jcm.1908-m2018-0211 UR - https://global-sci.org/intro/article_detail/jcm/13690.html KW - Smoluchowski equation, Spectral method, Radial basis function method. AB -

The goal of this paper is to present a numerical method for the Smoluchowski equation, a drift-diffusion equation on the sphere, arising in the modelling of particle dynamics. The numerical method uses radial basis functions (RBF). This is a relatively new approach, which has recently mainly been used for geophysical applications. For a simplified model problem we compare the RBF approach with a spectral method, i.e. the standard approach used in related physical applications. This comparison as well as our other accuracy studies show that RBF methods are an attractive alternative for these kind of models.

Christiane Helzel & Maximilian Schneiders. (2020). Numerical Approximation of the Smoluchowski Equation Using Radial Basis Functions. Journal of Computational Mathematics. 38 (1). 176-194. doi:10.4208/jcm.1908-m2018-0211
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