Mitic, Peter; (2004) A Generic Circular Source Distribution for solving potential problems using Meshless Methods. In: Mitic, Peter and Jacob, Christian J and Carne, Janet, (eds.) New Ideas in Symbolic Computation: Proceedings of the 6th International Mathematica Symposium. Positive Corporation: Alton, Hampshire, UK.

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Abstract

Approximate solutions to the potential equation “2U = 0 in a simply-connected 2-dimensional domain D are found using the Method of Fundamental Solutions (MFS) with sources placed on a circle. Previous research has shown that a few discrete points sources placed a large distance from D can give good numerical accuracy. The discrete source distribution can be random, and a circular source distribution is one which could be used for any domain. Several domains are considered, and an attempt is made to determine an optimal radius for the source distribution and number of sources required in order to give sufficient accuracy. Simple configurations for D give results whose accuracy depends in an ordered and predictable way on the source radius and the number of sources. With more complex domains the source radius and the number of sources have a crucial impact on accuracy.

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