Mathematical Modeling in Diffraction Theory: Based on A Priori Information on the Analytical Properties of the Solution

Mathematical Modeling in Diffraction Theory: Based on A Priori Information on the Analytical Properties of the Solution provides the fundamental physical concepts behind the theory of wave diffraction and scattered wave fields as well as its application in radio physics, acoustics, optics, radio astronomy, biophysics, geophysics, and astrophysics.

This book provides a coherent discussion of several advanced topics that have the potential to push forward progress in this field. It begins with examples illustrating the importance of taking a priori information into account when developing algorithms for solving diffraction problems, with subsequent chapters discussing the basic analytical representations of wave fields, the auxiliary current and source methods for solving the problems of diffraction at compact scatterers, the null field and matrix methods that are widely used to solve problems in radio-physics, radio-astronomy, and biophysics, and the continued boundary condition and pattern equation method.

Provides ideas and techniques for obtaining a priori information on analytical properties of wave fields and provides methods for solving diffraction problemsIncludes numerous concrete examples of localization of singularities of analytical continuation of wave fieldsPresents a qualitative explanation of the formation of visions of objectsFormulates the concept of “invisible” objectsSupplies appropriate computer programs for all presented methods

Mathematical Modeling in Diffraction Theory, 1st Edition

• Introduction
• Chapter 1: Analytic Properties of Wave Fields
  • Abstract
  • 1.1 Derivation of Basic Analytic Representations of Wave Fields
  • 1.2 Analytic Properties of the Wave Field Pattern and the Domains of Existence of Analytic Representations
• Chapter 2: Methods of Auxiliary Currents and Method of Discrete Sources
  • Abstract
  • 2.1 Existence and Uniqueness Theorems
  • 2.2 Solution of the MAC Integral Equation and the MDS
  • 2.3 Rigorous Solution of the Diffraction Problem by MAC [9, 16]
  • 2.4 Modified MDS
• Chapter 3: Null Field and T-Matrix Methods
  • Abstract
  • 3.1 NFM for Scalar Diffraction Problems
  • 3.2 NFM for Vector Diffraction Problems
  • 3.3 Results of Numerical Studies
  • 3.4 T-Matrix Method
• Chapter 4: Method of Continued Boundary Conditions
  • Abstract
  • 4.1 Method of Continued Boundary Conditions for Scalar Diffraction Problems
  • 4.2 Method of Continued Boundary Conditions for Vector Problems of Diffraction
  • 4.3 Results of Numerical Investigations
  • 4.4 Modified Method of Continued Boundary Conditions
• Chapter 5: Pattern Equation Method
  • Abstract
  • 5.1 Solution of Two-Dimensional Problem of Diffraction at a Compact Scatterer Using the Pattern Equation Method
  • 5.2 Wave Diffraction at a Group of Bodies
  • 5.3 Wave Diffraction at Periodic Gratings
  • 5.4 Solution of the Three-Dimensional Acoustic Problem of Diffraction at a Compact Scatterer
  • 5.5 Plane Wave Scattering at a Periodic Interface Between Media
  • 5.6 Calculation of the Reflection and Transmission Coefficients in a Plane Dielectric Waveguide with Foreign Objects Near It
• References
• Index