{
  "id": "1902.01315",
  "version": "v1",
  "published": "2019-02-04T17:12:57.000Z",
  "updated": "2019-02-04T17:12:57.000Z",
  "title": "An Integral Equation Formulation of the $N$-Body Dielectric Spheres Problem. Part I: Numerical Analysis",
  "authors": [
    "Muhammad Hassan",
    "Benjamin Stamm"
  ],
  "comment": "29 page article (45 including Appendix)",
  "categories": [
    "math.NA"
  ],
  "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 $N$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-04T17:12:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N12",
      "65N15",
      "65N35",
      "65R20"
    ],
    "keywords": [
      "body dielectric spheres problem",
      "integral equation formulation",
      "numerical analysis",
      "particles undergoing mutual polarisation",
      "spherical particles undergoing mutual"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}