Application of Singular Shape Functions for the Surface Charge Approximation in the Boundary Element Method

In this paper we consider application of singular functions for constructing finite element shapefunctions in problems of the electric field computation by the method of secondary sources. The main idea of this approach is based on the use of analytical solutions of the Laplace equation in the vicinity of special points of charged electrodes. Compared to traditional technologies of the charge density approximation on electrode surfaces, the considered approach allows to achieve high accuracy of calculation of electric field intensity in the vicinity of the charged object, including its angles and faces. The efficiency and high accuracy of the results obtained with such approximations is approved by comparison of the numerically derived field distributions with available analytical solutions.