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Volume 29, Issue 2
A Linear Scaling in Accuracy Numerical Method for Computing the Electrostatic Forces in the $N$-Body Dielectric Spheres Problem

Muhammad Hassan & Benjamin Stamm

DOI: 10.4208/cicp.OA-2020-0090

Commun. Comput. Phys., 29 (2021), pp. 319-356.

Published online: 2020-12

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  • Abstract

This article deals with the efficient and accurate computation of the electrostatic forces between charged, spherical dielectric particles undergoing mutual polarisation. We use the spectral Galerkin boundary integral equation framework developed by Lindgren et al. (J. Comput. Phys. 371 (2018): 712-731) and subsequently analysed in two earlier contributions of the authors to propose a linear scaling in cost algorithm for the computation of the approximate forces. We establish exponential convergence of the method and derive error estimates for the approximate forces that do not explicitly depend on the number of dielectric particles $N$. Consequently, the proposed method requires only $\mathcal{O}(N) $ operations to compute the electrostatic forces acting on $N$ dielectric particles up to any given and fixed relative error.

  • Keywords

Boundary integral equations, error analysis, $N$-body problem, linear scaling, polarisation, forces.

  • AMS Subject Headings

65N12, 65N15, 65N35, 65R20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-29-319, author = {Hassan , Muhammad and Stamm , Benjamin}, title = {A Linear Scaling in Accuracy Numerical Method for Computing the Electrostatic Forces in the $N$-Body Dielectric Spheres Problem}, journal = {Communications in Computational Physics}, year = {2020}, volume = {29}, number = {2}, pages = {319--356}, abstract = {

This article deals with the efficient and accurate computation of the electrostatic forces between charged, spherical dielectric particles undergoing mutual polarisation. We use the spectral Galerkin boundary integral equation framework developed by Lindgren et al. (J. Comput. Phys. 371 (2018): 712-731) and subsequently analysed in two earlier contributions of the authors to propose a linear scaling in cost algorithm for the computation of the approximate forces. We establish exponential convergence of the method and derive error estimates for the approximate forces that do not explicitly depend on the number of dielectric particles $N$. Consequently, the proposed method requires only $\mathcal{O}(N) $ operations to compute the electrostatic forces acting on $N$ dielectric particles up to any given and fixed relative error.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0090}, url = {http://global-sci.org/intro/article_detail/cicp/18468.html} }
TY - JOUR T1 - A Linear Scaling in Accuracy Numerical Method for Computing the Electrostatic Forces in the $N$-Body Dielectric Spheres Problem AU - Hassan , Muhammad AU - Stamm , Benjamin JO - Communications in Computational Physics VL - 2 SP - 319 EP - 356 PY - 2020 DA - 2020/12 SN - 29 DO - http://doi.org/10.4208/cicp.OA-2020-0090 UR - https://global-sci.org/intro/article_detail/cicp/18468.html KW - Boundary integral equations, error analysis, $N$-body problem, linear scaling, polarisation, forces. AB -

This article deals with the efficient and accurate computation of the electrostatic forces between charged, spherical dielectric particles undergoing mutual polarisation. We use the spectral Galerkin boundary integral equation framework developed by Lindgren et al. (J. Comput. Phys. 371 (2018): 712-731) and subsequently analysed in two earlier contributions of the authors to propose a linear scaling in cost algorithm for the computation of the approximate forces. We establish exponential convergence of the method and derive error estimates for the approximate forces that do not explicitly depend on the number of dielectric particles $N$. Consequently, the proposed method requires only $\mathcal{O}(N) $ operations to compute the electrostatic forces acting on $N$ dielectric particles up to any given and fixed relative error.

Hassan , Muhammad and Stamm , Benjamin. (2020). A Linear Scaling in Accuracy Numerical Method for Computing the Electrostatic Forces in the $N$-Body Dielectric Spheres Problem. Communications in Computational Physics. 29 (2). 319-356. doi:10.4208/cicp.OA-2020-0090
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