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A new method of fundamental solutions applied to nonhomogeneous elliptic problems. (English) Zbl 1070.65119
This paper is build on two previous papers of the authors [The MFS method adapted for a nonhomogeneous equation, in: Advances in Computational Engineering and Sciences, ed. S. N. Atluri (Tech. Science Press, Los Angeles, 2001) [in: Boundary Elements, Vol. XXIC, eds. C. Brebbia, A. Tadeu and V. Popov. WIT Press, 67–76 (2002; Zbl 1011.65086)]. In this paper they present theoretical results and numerical solutions for Poisson and non-homogeneous Helmholtz problems. They develop an approximation scheme in which a set of frequencies and point sources leads to an extended method of fundamental solutions (MFS), used to approximate a function in a bounded domain and to derive a straightforward approximation for a particular solution of the partial differential equation. They give numerical results to show that this extended MFS is a valuable simple method for solving certain nonhomogeneous elliptic problems.

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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