# Boundary integral equation methods for high frequency scattering problems

**Stephen Langdon
**

Department of Mathematical Sciences

University of Reading

Whiteknights, United Kingdom

### Abstract:

Standard finite or boundary element approaches for the numerical solution of high frequency scattering problems, with piecewise polynomial approximation spaces, suffer from the limitation that the number of degrees of freedom required to maintain accuracy must increase at least linearly with respect to frequency in order to maintain accuracy. This can lead to excessively expensive computations at high frequencies. To reduce the computational cost, recent work has focused on the inclusion of oscillatory functions in the approximation space, so as to better represent the oscillatory solution. In this talk we review this approach as applied to some simple problems of scattering by convex obstacles, we discuss implementation issues, and we describe the extension of these ideas to more complicated scattering problems.