Galerkin's Method Using the Annular Patch Segments to Solve a Round Disk Capacitor

摘要

In this paper, a numerical method is presented to calculate the charge density distribution and capacitance of a round disk capacitor by using the annular patch segments to gain more benefits over the conventional triangular patches. The proposed annular patches successfully eliminate the discretizing errors often encountered in the triangular patches, thereby it leads us to get more accurate solutions. Furthermore, the Galerkin's method is utilized to accelerate the solution convergence and also to obtain more accuracy at the matrix formulation stage. By specializing the method of moments to an integral equation, the charge distribution and capacitance can be obtained. To examine the accuracy of the proposed method, numerically computed charge density and capacitance are compared to the corresponding exact solutions for a single circular disk. Based on these error comparisons, the Galerkin's method equipped with annular patches ensures the superiority to the triangular patches and to the point matching method. The proposed Galerkin's method is applied to the round disk capacitor to calculate the equipotential lines.