Wave Scattering by Small Bodies of Arbitrary Shapes

The following sections are included:

• Preface

• Contents

• Introduction

The following sections are included:

• Statement of Electrostatic Problems for Perfect Conductors

• Statement of the Basic Problem for Dielectric Bodies

• Reduction of the Basic Problems to Fredholm's Integral Equations of the Second Kind

• Reduction of the Static Problems to Fredholm's Integral Equations of the First Kind

The following sections are included:

• An Iterative Process for Solving the Problem of Equilibrium Charge Distribution and Charge Distribution on a Conductor Placed in an Exterior Static Field

• An Iterative Process for Solving the Problem for Dielectric Bodies in an Exterior Static Field

• A Stable Iterative Process for Finding the Equilibrium Charge Distribution

• An Iterative Process for Calculating the Equilibrium Charge Distribution on the Surface of a Screen

The following sections are included:

• Capacitance of Solid Conductors and Screens

• Variational Principles and Two-Sided Estimates of Capacitance

• Capacitance of Conductors in an Anisotropic and Non-homogeneous Medium

• Physical Analogues of Capacitance

• Calculating the Potential Coefficients

The following sections are included:

• Introduction

• Capacitance of a Circular Cylinder

• Capacitances of Parallelepipeds

• Interaction Between Conductors

The following sections are included:

• Calculating the Polarizability Tensor of a Solid Body

• Polarizability Tensors of Thin Metallic Screens

• Polarizability Tensors of Flaky-Homogeneous Bodies or a System of Bodies

• Variational Principles for Polarizability Tensors

The following sections are included:

• Iterative Methods of Solving the Fredholm Equations of the Second Kind at a Characteristic Value

• Iterative Processes for Solving Some Operator Equations

• Iterative Processes for Solving the Exterior and Interior Boundary Value Problems

• An Iterative Process for Solving the Predholm Integral Equations of the First Kind with Pointwise Positive Kernel

The following sections are included:

• Introduction

• Scalar Wave Scattering: The Single-Body Problem

• Scalar Wave Scattering: The Many-Body Problem

• Electromagnetic Wave Scattering

• Radiation from Small Apertures and the Skin Effect for Thin Wires

• An Inverse Problem of Radiation Theory

The following sections are included:

• Fredholm Alternative and a Characterization of the Fredholm Operators
  • Introduction
  • Proofs

• A Characterization of Unbounded Fredholm Operators
  • Statement of the result
  • Proof

• Fredholm Alternative for Analytic Operators

The following sections are included:

• Introduction

• Proofs

• Exterior Boundary-Value Problems

• Quasiisometrical Mappings
  • Definitions and main properties
  • Interior metric and boundary metrics
  • Boundary behavior of quasiisometrical homeomorphisms

• Quasiisometrical Homeomorphisms and Embedding Operators
  • Compact embedding operators for rough domains
  • Examples

• Conclusions

The following sections are included:

• Introduction

• Integral Equation Method for the Dirichlet Problem

• Integral Equation Method for the Neumann Problem

• Integral Equation Method for the Robin Problem

• The Method based on the Fredholm Property

• The Method based on the Maximum Principle

• Continuity of Solutions to Operator Equations with Respect to a Parameter
  • Introduction
  • Proofs

The following sections are included:

• Introduction

• Basic Equations

• Justification of the Proposed Method

The following sections are included:

• Modified Rayleigh Conjecture and Applications
  • Introduction
  • Direct scattering problem and MRC
  • Inverse scattering problem and MRC
  • Proofs

• Modified Rayleigh Conjecture Method for Multidimensional Obstacle Scattering Problems
  • Introduction
  • Numerical Experiments
  • Conclusions

• Modified Rayleigh Conjecture for Static Fields
  • Solving boundary-value problems by MRC
  • Proofs

The following sections are included:

• Appendix A: Optimal with Respect to Accuracy Algorithms for Calculation of Multidimensional Weakly Singular Integrals and Applications to Calculation of Capacitances of Conductors of Arbitrary Shapes
  • Introduction
  • Definitions of Optimality
  • Classes of Functions
  • Auxiliary Statements
  • Optimal Methods for Calculating Integrals of the Form (A.1)
    • Lower bounds for the functionals ζ_nm and ζ_N
    • Optimal cubature formulas for calculating integrals (A.1)
  • Optimal Methods for Calculating Integrals of the Form Tf
    • Lower bounds for the functionals ζ_mn and ζ_N
    • Cubature formulas
  • Calculation of Weakly Singular Integrals on Non-Smooth Surfaces
  • Calculation of Weights of Cubature Formulas
  • Iterative Methods for Calculating Electrical Capacitancies of Conductors of Arbitrary Shapes
  • Numerical Examples

• Problems

• Bibliographical Notes

• Bibliography

• List of Symbols

• Index