| Issue |
ESAIM: M2AN
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
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|---|---|---|
| Page(s) | S65 - S102 | |
| DOI | https://doi.org/10.1051/m2an/2020030 | |
| Published online | 26 February 2021 | |
An integral equation formulation of the N-body dielectric spheres problem. Part I: numerical analysis
Center for Computational Engineering Science, Mathematics Department, RWTH Aachen University, Schinkelstrasse 2, Aachen 52062, Germany
* Corresponding author: hassan@mathcces.rwth-aachen.de
Received:
4
February
2019
Accepted:
25
April
2020
In this article, we analyse an integral equation of the second kind that represents the solution of N interacting dielectric spherical particles undergoing mutual polarisation. A traditional analysis can not quantify the scaling of the stability constants- and thus the approximation error- with respect to the number N of involved dielectric spheres. We develop a new a priori error analysis that demonstrates N-independent stability of the continuous and discrete formulations of the integral equation. Consequently, we obtain convergence rates that are independent of N.
Mathematics Subject Classification: 65N12 / 65N15 / 65N35 / 65R20
Key words: Boundary integral equations / numerical analysis / error analysis / N-body problem / polarisation
© EDP Sciences, SMAI 2021
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