Computational Analysis of the Capacitance by the Boundary Element Method

Abstract

The boundary element method (BEM) has had an advantage of discretizing the boundary over the finite element method and the finite difference method for so long. The curved and straight elements are crucial for the discretization process. The BEM has been of fundamental importance in as far as solving a two -dimensional Laplace problem is concerned. The study aimed at using the BEM to compute the capacitance as compared to the ordinary physics methods. The BEM and its applications were reviewed in relation to curved and straight elements. The Dirac-Delta and the Green's functions were behind the use of the BEM. A model problem was tested for analysis of the BEM with curved elements in relation to the computation of the capacitance. The MATLAB programs ( . , . , 5. , . , . ,1. , 5. , 2. , and . ) and subprograms were used among others in solving the problem and also in the analysis. Findings involved the computation of the matrix terms for curved elements in relation to the cylinder curvatures. Findings also showed and compared three methods of computing the capacitance in a model problem from electrostatics. The concentric cylinder considered in this study had different shape plates where the BEM showed a fundamental advantageous stage of the BEM in calculating the capacitance for various curvature plate shapes than any other numerical method by simply increasing on the number of elements. The BEM avoids assumptions about the inner plate and treating the situation as a connected domain.The FEM and FDM [2] and [10] are less recent than the BEM in their application to the Laplace problem. The method has been developed into a robust technique for especially modeling elasticity and acoustics [9] and [10]. In this study, the method was applied to the Laplace's equation for the exterior problems involving the evaluation of the capacitance between the concentric cylinders. The term "element" was used to mean the geometry and type of approximation to a given variable. On the other hand, the term "node" was used to define the element geometry or the variables involved in the problem.In using the BEM on the interior Laplace problem, we noted that a different number of nodes is used for the variable approximations which may be linear, quadratic or otherwise. Some of these approximations