Effective three-dimensional electric field analysis by surface charge simulation method

In chapter 2, the three-dimensional electric field analysis by means of the Fourier-type surface charge is investigated and the following techniques which lead to high speed calculations are proposed: The effective improper integral calculation techniques which yield the direct computation of the potential and electric field coefficients when a field point is located on its own surface charge element. Precise and effective techniques of calculating Cauchy's integral which appears in the tangential field calculation when a field point is also located on its own surface charge element. The high speed integral techniques which are applicable to compu¬ tations of the potential and electric field coefficients when the surface charge densities are developed even by orthogonal polynomials such as the Tchebycheff polynomials as well as a power series. The fast computation techniques of the toroidal function, O^i/o^*)* and the associated toroidal function, S i ^(x) which is introduced to simplify field formulae and their executions in a computer. The co-ordinate transformation which can directly provide the normal and tangential field components on a surface charge is also proposed. The technique is used to simulate tilted bodies. The selection of the contour points. By allocating them with respect to the zero-points of the Tchebycheff polynomials, highly accurate results have been obtained. Constant, linear, and quadratic charge distributions on a polygon charge are investigated and their potential and field formulae are proposed in chapter 3. Also proposed are a variety of techniques which effectively execute the proposed formulae in a computer. Effectiveness of the higher order approximation of the polygon formulae as well as the usage of the null point as a contour point is also examined in the same chapter. Using proposed formulae, capacitance of an isolated square metal plate and electric field distribution between two square metal plates are calculated and compared with conventional values.