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The Method of Meshless Fundamental Solutions with Sources at Infinity

Peter Mitic
Organization: Positive Corporation Limited
Youssef F. Rashed
Organization: Wessex Institute of Technology

2003 International Mathematica Symposium
Conference location

Imperial College, London

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.

*Mathematics > Algebra > Linear Algebra

external source collocation, Neumann and Dirichlet boundary conditions, numerical analysis, Meshless Fundamental Solutions, symbolic analysis
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