1 Introduction
In this paper the problem of computing
the properties of the acoustic field exterior to a panel
set in an infinite, reflecting baffle is considered.
Computational methods for solving this problem are based on the Rayleigh integral [1].
Such methods have been derived and applied
to the problem of computing the properties of the acoustic field
exterior to a flat or near-flat panel for some time.
These methods are generally derived through applying a direct numerical
integration method (see, for example Schenck [2])
to the Rayleigh integral. The resulting method is often termed the
simple source method.
However, the integrand of the Rayleigh integral can be singular
or near-singular and it becomes increasingly oscillatory as the
wavenumber increases. Hence the direct numerical integration
that underlies the simple source method is likely
to be a computationally inefficient means of obtaining the solution
in many cases.
The purpose of this paper is to formally introduce and demonstrate
a method that is derived through numerical product integration
of the Rayleigh integral and it is
termed the Rayleigh integral method. The method is superior
to the simple source method as its accuracy is virtually unaffected
by the nature of the integrand.
The structure of the Rayleigh integral method is similar to that of
the boundary element method and is more efficient and versatile
than the simple source method.
This paper is extracted from the author's thesis [3]
and intended as
a companion paper to Kirkup [4] and Kirkup and Henwood
[5], the
three papers together considering different models and hence different
methods of solution of acoustic radiation problems.