This volume consists ofsurvey articles on current topics in computational wave prop­ agation and inverse problems, written by leading experts in their respective fields. The idea to compile such a volume arose in conjunction with the LMS Durham Symposium on Computational Methods for Wave Propagation in Direct Scattering held at the University of Durham from 15th-25th July 2002, which we jointly or­ ganised. The meeting, attended by 70 participants from the UK and overseas, was structured around a number of short, three lecture, survey courses on a range of top­ ics on computational wave propagation and inverse problems beginning at the level of a graduate student. We were delighted to secure the participation of distinguished international researchers to present these lectures. We felt that it would be valuable to record this material for the benefit of a wider audience, and the idea was hatched that the individual lecturers should be invited to contribute a survey article. Fortunately, many of the speakers not only agreed to undertake this arduous task, but produced what we hope you will agree are the high quality contributions found in this volume. Finally, it is a pleasure to thank the Engineering and Physical Sciences Research Council of Great Britain and the London Mathematical Society for providing the generous support that allowed the meeting to take place. Mark Ainsworth Glasgow, 2003 Penny Davies Dugald Duncan Paul Martin Bryan Rynne Contents New Results on Absorbing Layers and Radiation Boundary Conditions Thomas Hagstrom .

New Results on Absorbing Layers and Radiation Boundary Conditions.- Fast, High-Order, High-Frequency Integral Methods for Computational Acoustics and Electromagnetics.- Galerkin Boundary Element Methods for Electromagnetic Scattering.- Computation of resonance frequencies for Maxwell equations in non-smooth domains.- hp-Adaptive Finite Elements for Time-Harmonic Maxwell Equations.- Variational Methods for Time-Dependent Wave Propagation Problems.- Some Numerical Techniques for Maxwell's Equations in Different Types of Geometries.- On Retarded Potential Boundary Integral Equations and their Discretisation.- Inverse Scattering Theory for Time-Harmonic Waves.- Herglotz Wave Functions in Inverse Electromagnetic Scattering Theory.- Appendix: Colour Figures.