Mitic, Peter; Rashed, Youssef F.; (2003) The method of meshless fundamental solutions with sources at infinity. In: Mitic, P and Carne, J and Ramsden, P, (eds.) Challenging the Boundaries of Symbolic Computation. (pp. pp. 89-96). World Scientific Publishing

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Abstract

The method of external source collocation is used to solve a discretised boundary value problem, ∇2U = 0, where U is the potential in a two-dimensional simply-connected region D, subject to a mixture of Neumann and Dirichlet boundary conditions. Numerical analysis has, to date, been hindered by an accumulation of round-off error, which has made it impossible to investigate accuracy of the Meshless Fundamental Solutions method unless sources are near the boundary. Symbolic analysis allows a full investigation of ill-conditioned systems in which sources can be placed "at infinity". This analysis provides an indication of how many sources must be used and where they should be placed.

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