Analytical and Computational Methods in Scattering and Applied Mathematics

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Fadil Santosa, Ivar Stakgold
CRC Press, Mar 15, 2000 - Mathematics - 288 pages
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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
 

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Contents

Optimization of Radiating Fields and the Example of NullPlacement
1
Modified Gradient and Contrast Source Inversion
13
Identification of Acoustically Soft Solids of Revolution in a Waveguide using the ICBA Method
27
Recollections of Ralph Kleinman
37
An Asymptotic Wave Interpretation of Sonar Reflections from a Rough Surface
41
Critical Values in Inverse Scattering Theory
57
The Finite Element Approximation of Scattering in a Layered Medium
67
The FarField Expansion Theorem in Thermoelastic Scattering
85
Applied Analysis in Ship Hydrodynamics
135
Mathematical Foundations for the BoundaryField Equation Methods in Acoustic and Electromagnetic Scattering
149
Obstacle Scattering as Seen by RK and RK
165
On Nonlinearized Wavefield Inversion Methods and the Identification of Buried Objects
177
Scattering in a 2D Optical Waveguide
195
Scattering by Inclusions
209
Pointwise Interpolation Inequalities for Riesz and Bessel Potentials
217
Spectrum of Multidimensional Schrodinger Operators with Sparse Potentials
231

Theoretical Notes on Scattering from OneDimensional Penetrable Rough Surfaces
97
HigherOrder Slender Body Theory
111
Acoustic Scattering in Dispersions
123
On Inverse Problems for the Wave Equation with Time Dependent Potentials
255
Photo Album
262
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