Fundamental solutions to Helmholtz's equation for inhomogeneous media by a first-order differential equation system |
| |
Authors: | George D. Manolis Richard P. Shaw |
| |
Affiliation: | Department of Civil Engineering, Aristotle University, Thessaloniki 54006, Greece;Department of Civil Engineering, State University of New York, Buffalo, NY 14260, USA |
| |
Abstract: | Helmholtz's equation with a variable wavenumber is solved for a point force through use of a first-order differential equation system approach. Since the system matrix in this formulation is non-constant, an eigensolution is no longer valid and recourse has to be made to approximate techniques such as series expansions and Picard iterations. These techniques can accommodate in principle any variation of the wavenumber with position and are applicable to scalar wave propagation in one, two and three dimensions, with the latter two cases requiring radial symmetry. As shown in the examples, good solution accuracy can be achieved in the near field region, irrespective of frequency, for the particular case examined, namely a wavenumber which increases (or decreases) as the square root of the radial distance from source to receiver. Finally, the resulting Green's functions can be used as kernels within the context of boundary element type solutions to study scalar wave scattering in inhomogeneous media. |
| |
Keywords: | first-order differential equation systems Green's functions Helmholtz's equation inhomogeneous media scalar wave equation wave propagation |
本文献已被 ScienceDirect 等数据库收录! |
|