Some Aspects of the Method of Fundamental Solutions for Certain Harmonic Problems
Journal of Scientific Computing
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 6th Japan--China joint seminar on numerical mathematics, university of Tsukuba, Japan, 5-9 August 2002
A matrix decomposition RBF algorithm: Approximation of functions and their derivatives
Applied Numerical Mathematics
Meshfree Approximation Methods with MATLAB
Meshfree Approximation Methods with MATLAB
Matrix decomposition algorithms for elliptic boundary value problems: a survey
Numerical Algorithms
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In this work we develop an efficient algorithm for the application of the method of fundamental solutions to inhomogeneous polyharmonic problems, that is problems governed by equations of the form Δ 驴 u=f, 驴驴驴, in circular geometries. Following the ideas of Alves and Chen (Adv. Comput. Math. 23:125---142, 2005), the right hand side of the equation in question is approximated by a linear combination of fundamental solutions of the Helmholtz equation. A particular solution of the inhomogeneous equation is then easily obtained from this approximation and the resulting homogeneous problem in the method of particular solutions is subsequently solved using the method of fundamental solutions. The fact that both the problem of approximating the right hand side and the homogeneous boundary value problem are performed in a circular geometry, makes it possible to develop efficient matrix decomposition algorithms with fast Fourier transforms for their solution. The efficacy of the method is demonstrated on several test problems.