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arXiv · 1902.01315

An Integral Equation Formulation of the $N$-Body Dielectric Spheres Problem. Part I: Numerical Analysis

Muhammad Hassan·Benjamin Stamm
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Abstract

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 $N$.

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Muhammad Hassan, Benjamin Stamm. 2019-02-04. An Integral Equation Formulation of the $N$-Body Dielectric Spheres Problem. Part I: Numerical Analysis. https://arxiv.org/abs/1902.01315

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