Canonical Problems in Scattering and Potential Theory Part 1: Canonical Structures in Potential Theory, 1st Edition (Hardback) book cover

Canonical Problems in Scattering and Potential Theory Part 1

Canonical Structures in Potential Theory, 1st Edition

By S.S. Vinogradov, P. D. Smith, E.D. Vinogradova

Chapman and Hall/CRC

392 pages

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Hardback: 9781584881629
pub: 2001-05-30
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Description

Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical scatterers with comprising edges and other complex cavity features. It is an authoritative account of mathematical developments over the last two decades that provides benchmarks against which solutions obtained by numerical methods can be verified.

The first volume, Canonical Structures in Potential Theory, develops the mathematics, solving mixed boundary potential problems for structures with cavities and edges. The second volume, Acoustic and Electromagnetic Diffraction by Canonical Structures, examines the diffraction of acoustic and electromagnetic waves from several classes of open structures with edges or cavities. Together these volumes present an authoritative and unified treatment of potential theory and diffraction-the first complete description quantifying the scattering mechanisms in complex structures.

Reviews

" … self-contained and well written… addressed to mathematicians, physicists, and electrical engineers."

- Mathematical Reviews

"It does…provide a very comprehensive reference work on a method of solution of a wide variety of potential problems involving bodies with edges, and anyone wishing to solve such a problem would be well advised to consult it either for the solution or for possible methods to approach it."

-Derek Collins, SIAM Review, Vol 44, No. 2, 2002

Table of Contents

PART I: CANONICAL STRUCTURES IN POTENTIAL THEORY

Mathematical Aspects of Potential Theory

Dual or Triple Series and Integral Equations

Electrostatic Potential Theory for Open Spherical Shells and Cavities

Open Spheroidal Conducting Shells and Cavities

Charged Toroidal Shells and Cavities

Potential Theory for Conical Structures with Edges

Two-Dimensional Potential Theory

Rigorous Solution Methods for more Complicated Structures

APPENDICES

PART II: ACOUSTIC AND ELECTROMAGNETIC DIFFRACTION BY CANONICAL STRUCTURES

Mathematical Aspects of Wave Scattering

Acoustic Diffraction from a Circular Hole in a Thin Spherical Shell

Acoustic Diffraction from a Spherical Shell with Two Holes or an Equatorial Slot

Electromagnetic Diffraction from a Circular Hole in a Perfectly Conducting Spherical Shell

Electromagnetic Diffraction from a Spherical Shell with Two Circular Holes or an Equatorial Slot

Spherical Cavities with Dielectric Inclusions of Spherical Shape

Diffraction from Spheroidal Cavities

Applications of the Abel Integral Transform to Diffraction by Other Classes of Canonical Scatterers

Conclusion.

About the Series

Monographs and Surveys in Pure and Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations