### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 2pSA5. On the approximate factorization of scalar and matrix Wiener--Hopf
kernels with applications in structural acoustics.

**I. David Abrahams
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*Dept. of Mathematics, Keele Univ., Keele ST5 5BG, UK
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The Wiener--Hopf technique has proved to be an extremely powerful aid to
solving problems in diffraction theory, and in particular for acoustic wave
scattering. The key step in the procedure is the factorization of the
Wiener--Hopf kernel into a product of two functions with (overlapping)
semi-infinite regions of analyticity. However, for complex problems, such as
those concerned with the interaction between fluids and structures, the
representation of the scalar factors can have technical difficulties which make
their computation both slow and delicate. Further, many important models of this
type give rise to matrix kernels, for which no exact factorization technique has
yet been devised. In this paper, a new procedure is presented to obtain
approximate but explicit factorizations of both scalar and matrix kernels. As
well as being simple to employ both analytically and numerically, the accuracy
of the component factors can be increased almost indefinitely with little
increase in numerical effort. Further, rigorous bounds on the error of these
approximations are easy to find. The method is demonstrated by way of example,
and the particular relevance of the new scheme to fluid/structure interaction
problems is discussed.