Volume 55, 2021Regular 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
|Page(s)||S65 - S102|
|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: email@example.com
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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