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 $N$.
翻译:在本篇文章中,我们分析了第二种类型的整体等式,它代表了在相互两极化中相互互动的电外球微粒的解决方案。传统分析无法量化稳定常数的大小,从而也无法量化近似差错。我们开发了一种新的先验错误分析,以表明整体等式连续和离散配方的稳定性是独立的。因此,我们获得了独立于美元之外的趋同率。