WIT Press


A Generalised Helmholtz Equation Fundamental Solution Using A Conformal Mapping And Dependent Variable Transformation

Price

Free (open access)

Paper DOI

10.2495/BE980471

Volume

21

Pages

6

Published

1998

Size

325 kb

Author(s)

Richard Paul Shaw and George D. Manolis

Abstract

Fundamental solutions to a generalized Helmholtz equation are determined through dependent variable transforms using the material properties and independent variable transforms based on conformal mapping. This allows variable wave speed media to be examined under some fairly broad material property constraints. Introduction While the usual Helmholtz equation suffices for many time harmonic wave problems, some heterogeneous media require a modification to be made, e.g. for underwater acoustics with heterogeneous density and compressibility properties, Brekhovskikh and Godin\ Consider then the 2D "generalized" heterogeneous Helmholtz equation V # {K(x, y )VU(x, y)} + N(x, y)U(x, y) = -Q(x, y) (1) which may be solved by several methods for several

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