Professor Monk has been an active researcher in finite elements for Maxwell's equations for over 10 years, and in inverse problems for much longer. He performed the first error analysis of edge finite element methods for Maxwell's equations both in the time and frequency domain. Most recently he has worked on coupling of integral equations and finite element methods.
In inverse problems, he was the author (with Professor David Colton) of the dual space method for inverse scattering in 1985 and obtained the first 3D reconstructions in acoustic inverse scattering in 1987. Most recently, he has been working on the Linear Sampling Method of Colton and Kirsch to extend it to realistic scattering problems and to obtain inverse electromagnetic scattering results.
Recently Dr Monk co-organized a GAMM workshop at Kiel University, Germany on electromagnetic scattering. He has been invited to deliver a short course on numerical methods for Maxwell's equations by the Chinese Academy of Science and to take part in a workshop in England on hyperbolic problems funded by the London Mathematical Society.
Professor Monk is an editor for SIAM Journal of Numerical Analysis and a principal editor for the the Journal of Computational and Applied Mathematics. His research has been funded by AFOSR for many years.
Professor Monk will give ten lectures as follows:
The lectures will combine ideas from functional analysis and numerical
analysis. They will be as self contained as possible so that those with a
knowledge of standard finite element methods but no knowledge of scattering
theory, or those with a knowledge of scattering theory but not finite
elements will benefit.