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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.

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