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.
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
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
Vinogradov\, S.S.; Smith\, P. D.; Vinogradova\, E.D.
" … 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