The method of fundamental solutions for Helmholtz-type equations in composite materials

Authors:
B. Bin-Mohsin;D. Lesnic
Affiliations:
-;-
Venue:
Computers & Mathematics with Applications
Year:
2011

Citing 4
Cited 0

Error estimates for a fundamental solution method applied to reduced wave problems in a domain exterior to a disc

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
Stability and convergence of the method of fundamental solutions for Helmholtz problems on analytic domains

Journal of Computational Physics
The under-determined version of the MFS: Taking more sources than collocation points

Applied Numerical Mathematics
The method of fundamental solutions for linear diffusion-reaction equations

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	0.09

Visualization

Abstract

In this paper, we introduce and develop the method of fundamental solutions (MFS) for solving Helmholtz-type elliptic partial differential equations in composite materials. This study builds upon the previous developments and applications of the MFS to linear and nonlinear heat conduction, elasticity, and functionally graded composite layered materials. Numerical results are presented and discussed for four examples involving both the modified Helmholtz and the Helmholtz equations in two-dimensional or three-dimensional, bounded or unbounded, smooth or non-smooth composite domains. It was found that the method produces numerical results which are in good agreement with the analytical solutions, where available.