Electrostatic problems for arbitrary rotationally symmetric double-connected conductors and complementary structures

This thesis considers potential theory problems for rotationally symmetric conductors. The profile of structures is arbitrary and it allows one to model a variety of screens important in applications. Mathematically, the problem is described by the boundary value problem for the Laplace equation subject to the Dirichlet boundary conditions. We consider two types of conductors: double-connected conductors with the apertures of equal angular size and complementary structures to them. The problem is solved by the semi-analytical Method of Regularization (MoR) that provides a mathematically rigorous solution. The MoR, based on Abel’s integral transform and theory of triple series equations with the Jacobi polynomials, allows us to transform the ill-posed initial system of series equations arising from the standard formulation of the problem to a well-conditioned second kind Fredholm matrix equation. Numerical algorithms based upon the solution of the matrix equation, after truncation to a finite system of equations, converge with guaranteed and predictable accuracy. In this thesis the generalization of the solution algorithm for arbitrarily shaped double-connected screens is developed in the case of rotationally symmetric prescribed potential and the solution for the complementary structures in general case (for arbitrarily preassigned potential) is obtained.