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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/27141

Title: The Method of Fundamental Solutions for the solution of elliptic boundary value problems
Authors: Poullikkas, Andreas
Issue Date: 1997
Publisher: © Andreas Poullikkas
Abstract: We investigate the use of the Method of Fundamental Solutions (MFS) for the numerical solution of elliptic problems arising in engineering. In particular, we examine harmonic and biharmonic problems with boundary singularities, certain steady-state free boundary flow problems and inhomogeneous problems. The MFS can be viewed as an indirect boundary method with an auxiliary boundary. The solution is approximated by a linear combination of fundamental solutions of the governing equation which are expressed in terms of sources located outside the domain of the problem. The unknown coefficients in the linear combination of fundamental solutions and the location of the sources are determined so that the boundary conditions are satisfied in a least squares sense. The MFS shares the same advantages of the boundary methods over domain discretisation methods. Moreover, it is relatively easy to implement, it is adaptive in the sense that it takes into account sharp changes in the solution and/or in the geometry of the domain and it can easily incorporate complicated boundary conditions. [Continues.]
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.
URI: https://dspace.lboro.ac.uk/2134/27141
Appears in Collections:PhD Theses (Mechanical, Electrical and Manufacturing Engineering)

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