Analytical and Computational Methods in Scattering and Applied Mathematics

Professor Ralph Kleinman was director of the Center for the Mathematics of Waves and held the UNIDEL Professorship of the University of Delaware. Before his death in 1998, he made major scientific contributions in the areas of electromagnetic scattering, wave propagation, and inverse problems. He was instrumental in bringing together the mathematical and engineering communities working in these fields, and actively collaborated with a number of colleagues from both communities. It was in Professor Kleinman's memory that leading researchers in the fields of wave propagation, scattering, and applied mathematics gathered for an international conference at the University of Delaware in November 1998. This Research Note comprises papers on these topics presented at the conference along with other contributions by Ralph's colleagues. The papers consist of authoritative overviews by experts in their fields and new results from leading researchers. With many of the contributions multidisciplinary in nature and presentation of recent advances, Analytical and Computational Methods in Scattering and Applied Mathematics will prove of interest to engineers working in electromagnetics and wave propagation and to applied mathematicians working in partial differential equations and inverse problems

Table of Contents:
Preface, Optimization of Radiating Fields and the Example of Null-Placement, Modified Gradient and Contrast Source Inversion, Identification of Acoustically Soft Solids of Revolution in a Waveguide Using the ICBA Method, Recollections of Ralph Kleinman, An Asymptotic Wave Interpretation of Sonar Reflections from a Rough Surface, Critical Values in Inverse Scattering Theory, The Finite Element Approximation of Scattering in a Layered Medium, The Far-Field Expansion Theorem in Thermoelastic Scattering, Theoretical Notes on Scattering from One-Dimensional Penetrable Rough Surfaces, Higher-Order Slender Body Theory, Acoustic Scattering in Dispersions, Applied Analysis in Ship Hydrodynamics, Mathematical Foundations for the Boundary-Field Equation Methods in Acoustic and Electromagnetic Scattering, Obstacle Scattering as Seen by R.K. and R.K. On Nonlinearized Wavefield Inversion Methods and the Identification of Buried Objects, Scattering in a 2-D Optical Waveguide, Scattering by Inclusions, Pointwise Interpolation Inequalities for Riesz and Bessel Potentials, Spectrum of Multidimensional Schrödinger Operators with Sparse Potentials, On Inverse Problems for the Wave Equation with Time Dependent Potentials, Photo Album.