I. David Abrahams
Dept. of Mathematics, Keele Univ., Keele ST5 5BG, UK
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.