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The equal spacing of N points on a sphere with application to partition-of-unity wave diffraction problems.

Peake, M.J. and Trevelyan, J. and Coates, G. (2014) 'The equal spacing of N points on a sphere with application to partition-of-unity wave diffraction problems.', Engineering analysis with boundary elements., 40 . pp. 114-122.


This paper addresses applications involving the selection of a set of points on a sphere, in which the uniformity of spacing can be of importance in enhancing the computational performance and/or the accuracy of some simulation. For the authors, the motivation for this work arises from the need to specify wave directions in a partition-of-unity approach for numerical analysis of wave diffraction problems. A new spacing method is presented, based on a physical analogy in which an arbitrary number of charged particles are held in static equilibrium on a spherical surface. The new method, referred to in this paper as the Coulomb force method, offers an improvement over simpler methods, e.g., latitude/longitude and discretised cube methods, in terms of both the uniformity of spacing and the arbitrary nature of the number of points N that can be considered. A simple extension to the algorithm allows points to be biased towards a direction of choice. Numerical results of a wave scattering problem solved with a partition-of-unity boundary element method demonstrate the benefits of the algorithm.

Item Type:Article
Keywords:Uniform distribution, Sphere, Helmholtz, Acoustics, Boundary element method, Partition of unity.
Full text:(AM) Accepted Manuscript
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Publisher statement:NOTICE: this is the author’s version of a work that was accepted for publication in Engineering analysis with boundary elements. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Engineering analysis with boundary elements., 40, 2014, 10.1016/j.enganabound.2013.11.020
Date accepted:No date available
Date deposited:10 January 2014
Date of first online publication:2014
Date first made open access:No date available

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