An integral equation formulation of the N-body dielectric spheres problem. Part I: numerical analysis

Hassan, Muhammad; Stamm, Benjamin

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021), pp. S65-S102

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.

Classification : 65N12, 65N15, 65N35, 65R20
Keywords: Boundary integral equations, numerical analysis, error analysis, $$-body problem, polarisation

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