### Abstract

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.

Language | English |
---|---|

Pages | 93-106 |

Number of pages | 22 |

Journal | Journal of Engineering Mathematics |

Volume | 104 |

Issue number | 1 |

Early online date | 9 Sep 2016 |

DOIs | |

Status | Published - Jun 2017 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Journal of Engineering Mathematics*, vol. 104, no. 1, pp. 93-106. DOI: 10.1007/s10665-016-9875-5

}

TY - JOUR

T1 - Exact integration of surface and volume potentials

AU - Carley,Michael

AU - Angioni,Stefano

PY - 2017/6

Y1 - 2017/6

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

UR - http://dx.doi.org/10.1007/s10665-016-9875-5

U2 - 10.1007/s10665-016-9875-5

DO - 10.1007/s10665-016-9875-5

M3 - Article

VL - 104

SP - 93

EP - 106

JO - Journal of Engineering Mathematics

T2 - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

SN - 0022-0833

IS - 1

ER -