Peter Monk

Department of Mathematical Sciences

University of Delaware

Using the rough surface scattering problem as a model, I shall introduce forward and inverse acoustic scattering. For the forward problem we wish to compute the acoustic field scattered by a surface formed by perturbing a half space. This problem arises for example in predicting highway traffic noise, and in transverse electromagnetic scattering. The theoretical underpinnings of such models is still being investigated and I shall give some results of joint work with Simon Chandler-Wilde at the University of Reading, UK regarding variational methods for the Dirichlet problem. I shall also discuss the resulting finite element schemes. For the inverse problem, we seek to determine the shape of the rough surface from measurements of the scattered field. This problem is ill-posed and non-linear. I shall present some preliminary results for this problem also.