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This article is the second in a series of two papers concerning themathematical study of a boundary integral equation of the second kind thatdescribes the interaction of $N$ dielectric spherical particles undergoingmutual polarisation. The first article presented the numerical analysis of theGalerkin method used to solve this boundary integral equation and derived$N$-independent convergence rates for the induced surface charges and totalelectrostatic energy. The current article will focus on computational aspectsof the algorithm. We provide a convergence analysis of the iterative methodused to solve the underlying linear system and show that the number of linersolver iterations required to obtain a solution is independent of $N$.Additionally, we present two linear scaling solution strategies for thecomputation of the approximate induced surface charges. Finally, we consider aseries of numerical experiments designed to validate our theoretical resultsand explore the dependence of the numerical errors and computational cost ofsolving the underlying linear system on different system parameters.

An Integral Equation Formulation of the $N$-body Dielectric Spheres Problem. Part II: Complexity Analysis