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Journal of Engineering Mathematics

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09-09-2016

Exact integration of surface and volume potentials

Authors: Michael Carley, Stefano Angioni

Published in: Journal of Engineering Mathematics | Issue 1/2017

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Abstract

A method for exact analytical integration of potentials from sources distributed on planar and volume elements is presented. The method is based on reduction of the surface integrals to a function similar to an incomplete elliptic integral, giving the integrals in closed form as functions of geometric properties of the surface or volume element. Explicit formulae and recursions are given for the integrals, allowing the evaluation of the potential for arbitrary polynomial sources. Volume integrals are derived from the surface integrals using a simple coordinate transformation which gives the volume integral with little more effort than that required for the surface calculation.

previous article Interplay of quantum size effect, anisotropy and surface stress shapes the instability of thin metal films

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Title: Exact integration of surface and volume potentials
Authors: Michael Carley
Stefano Angioni
Publication date: 09-09-2016
Publisher: Springer Netherlands
Published in: Journal of Engineering Mathematics / Issue 1/2017
Print ISSN: 0022-0833
Electronic ISSN: 1573-2703
DOI: https://doi.org/10.1007/s10665-016-9875-5

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