Boundary element method in axially symmetric electric fields

Boundary element method in axially symmetric electric fields

This work deals with boundary element method for axisymmetric problems with ten examples. The main objective of the work is numerical computation of capacities in the axisymmetric electrostatic field using boundary element method. The first chapter begins with theoretical introduction in form of Green`s theorems. We introduce Dirac’s delta function and gradient theorem. Green’s theorem and Dirac’s delta function are then used, as one possibility, to derive basic integral equation for 3-D electrostatic field. Second chapter begins with solution of potential and field around charged circle. Next, we modify basic integral equation for static axisymmetric tasks. As one of the interesting possibilities, we consider the transformation of surface integral, which describes the influence of field source i.e. free charges, in a curvilinear integral. In third chapter, boundary element method is used to implement previously introduced equations. Integral parameters of axisymmetric field are found (capacities, forces). Two different methods for force calculation are given: Coulomb’s law and Maxwell’s stress tensor. We use analytical results, where they exist, in order to check the accuracy of numerical ones. The first six examples illustrate the application of the reduced form of integral equation. The seventh one illustrates the determination of partial capacities of test coils placed in the box of a conducting toroid. The last three examples illustrate the solution of the complete form of integral equation. Examples are, for better understanding of problems, brightened with pictures of equipotential lines.