Exact integration of surface and volume potentials

Michael Carley; Stefano Angioni

doi:10.1007/s10665-016-9875-5

Exact integration of surface and volume potentials

Michael Carley, Stefano Angioni

Department of Mechanical Engineering

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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.

Original language	English
Pages (from-to)	93-106
Number of pages	22
Journal	Journal of Engineering Mathematics
Volume	104
Issue number	1
Early online date	9 Sept 2016
DOIs	https://doi.org/10.1007/s10665-016-9875-5
Publication status	Published - Jun 2017

Keywords

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

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10.1007/s10665-016-9875-5

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Cite this

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title = "Exact integration of surface and volume potentials",

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.",

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N2 - 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.

AB - 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.

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

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JO - Journal of Engineering Mathematics

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Exact integration of surface and volume potentials

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Exact integration of surface and volume potentials

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