Canonical Problems in Scattering and Potential Theory - Two volume set Acoustic and Electromagnetic Diffraction by Canonical Structures

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.

PART I: CANONICAL STRUCTURES IN POTENTIAL THEORYMathematical Aspects of Potential TheoryDual or Triple Series and Integral EquationsElectrostatic Potential Theory for Open Spherical Shells and CavitiesOpen Spheroidal Conducting Shells and CavitiesCharged Toroidal Shells and CavitiesPotential Theory for Conical Structures with EdgesTwo-Dimensional Potential TheoryRigorous Solution Methods for more Complicated StructuresAPPENDICESPART II: ACOUSTIC AND ELECTROMAGNETIC DIFFRACTION BY CANONICAL STRUCTURESMathematical Aspects of Wave ScatteringAcoustic Diffraction from a Circular Hole in a Thin Spherical ShellAcoustic Diffraction from a Spherical Shell with Two Holes or an Equatorial SlotElectromagnetic Diffraction from a Circular Hole in a Perfectly Conducting Spherical ShellElectromagnetic Diffraction from a Spherical Shell with Two Circular Holes or an Equatorial SlotSpherical Cavities with Dielectric Inclusions of Spherical ShapeDiffraction from Spheroidal CavitiesApplications of the Abel Integral Transform to Diffraction by Other Classes of Canonical ScatterersConclusion.