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 |
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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 journal › Article
}
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 -