Iterative Methods for Calculating Static Fields and Wave Scattering by Small Bodies

1. Basic Problems.- §1. Statement of the Electrostatic Problems for Perfect Conductors.- §2. Statement of the Basic Problem for Dielectric Bodies.- §3. Reduction of the Basic Problems to Fredholm’s Integral Equations of the Second Kind.- §4. Reduction of the Static Problems to Fredholm’s Integral Equations of the First Kind.- 2. Iterative Processes6 for Solving Fredholm’s Integral Equations for the Static Problems.- §1. An Iterative Process for Solving the Problem of Equilibrium Charge Distribution and Charge Distribution on a Conductor Placed in an Exterior Static Field.- §2. An Iterative Process for Solving the Problem of Dielectric Bodies in an Exterior Static Field.- §3. A Stable Iterative Process for Finding the Equilibrium Charge Distribution.- §4. An Iterative Process for Calculating the Equilibrium Charge Distribution on the Surface of a Screen.- 3. Calculating Electric Capacitance.- §1. Capacitance of Solid Conductors and Screens.- §2. Variational Principles and Two-Sided Estimates of Capacitance.- §3. Capacitance of Conductors in an Anisotropic and Nonhomogeneous Medium.- §4. Physical Analogues of Capacitance.- §5. Calculating the Potential Coefficients.- 4. Numerical Examples.- §1. Introduction.- §2. Capacitance of a Circular Cylinder.- §3. Capacitance of a Parallelepiped of Arbitrary Shape.- §4. Interaction Between Conductors.- 5. Calculating the Polarizability Tensor.- §1. Calculating the Polarizability Tensor of a Solid body.- §2. The Polarizability Tensor of a Thin Metallic Screen.- §3. The Polarizability Tensors of a Flaky-Homogeneous Body or a System of Bodies.- §4. Variational Principles for Polarizability.- 6. Iterative Methods of Solving some Integral Equations Basic in the Theory of Static Fields: Mathematical Results.-§1. Iterative Methods of Solving the Fredholm Equations of the Second Kind at a Characteristic Value.- §2. Iterative Processes for Solving Some Operator Equations.- §3. Iterative Processes for Solving the Exterior and Interior Boundary Value Problems.- §4. An Iterative Process for Solving the Fredholm Integral Equations of the First Kind with Pointwise Positive Kernel.- 7. Wave Scattering by Small Bodies.- §1. Introduction.- §2. Scalar Wave Scattering: The Single-Body Problem.- §3. Scalar Wave Scattering: The Many-Body Problem.- §4. Electromagnetic Wave Scattering.- §5. Radiation from Small Apertures and the Skin Effect for Thin Wires.- §6. The Inverse Problem of Radiation Theory.- Problems.- Bibliographical Notes.- List of Symbols.