Canonical Problems in Scattering and Potential Theory Part II: Acoustic and Electromagnetic Diffraction by Canonical Structures (Monographs and Surveys in Pure and Applied Mathematics)

Annotation 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 This two-volume set describes a breakthrough in analytical techniques or accurately determining diffraction from classes of canonical scatterers. It is an authoritative account of mathematical developments over the last two decades, delivered in an accessible, concrete style rather than in abstract, formal one.Part 2: Acoustic and Electromagnetic Diffraction by Canonical Structures examines the diffraction of acoustic and electromagnetic waves from several classes of open structure with edges or cavities. Together these volumes present an authoritative and unified treatment of potential theory and diffraction. This second volume in a two-part set develops the approach given in the first volume to analyze the diffraction of acoustic and electromagnetic waves from several classes of open structures with edges or cavities. The approach is based on transformations connected with Abel's integral equation to invert a singular part of the operator defining the pt. 1. Canonical structures in potential theory pt. 2. Acoustic and electromagnetic diffraction by canonical structures.