Exact integration of surface and volume potentials

Michael Carley, Stefano Angioni

Research output: Contribution to journalArticle

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.
LanguageEnglish
Pages93-106
Number of pages22
JournalJournal of Engineering Mathematics
Volume104
Issue number1
Early online date9 Sep 2016
DOIs
StatusPublished - Jun 2017

Fingerprint

Surface integral
Analytical Integration
Elliptic integral
Coordinate Transformation
Recursion
Explicit Formula
Closed-form
Polynomials
Polynomial
Evaluation
Arbitrary

Keywords

  • Laplace equation; potential theory; boundary element method; integral equations; quadrature; elliptic integrals

Cite this

Exact integration of surface and volume potentials. / Carley, Michael; Angioni, Stefano.

In: Journal of Engineering Mathematics, Vol. 104, No. 1, 06.2017, p. 93-106.

Research output: Contribution to journalArticle

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