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. In this study, the BEM has been of fundamental importance in as far as solving a two –dimensional Laplace problem is concerned.
The BEM, finite element method (FEM), and the finite difference method (FDM) and their applications were reviewed, with the BEM taking advantage of the other two in relation to curved and straight elements. The Laplace equation with its boundary integral formulation was done and the BEM applied. The Dirac-Delta and the Green’s functions were behind the use of the BEM. Finally, three model problems were tested for analysis of the BEM and curved elements in relation to solving the Laplace problem. The MATLAB programs and subprograms were used among others to solve the Laplace’s equation in the exterior of the Ellipse, interior of a unit circle, calculating the element data for a Dirichlet type problem. The same programs were used in computing the capacitance between the concentric cylinders and eventually in the analysis.
Findings showed the fundamental advantageous stage of the curved to straight elements, the suitability of the former to the latter when finding the potential and capacitance uniquely using the BEM. However the method is not applicable to partial differential equations (PDEs) whose fundamental solutions cannot be expressed in the explicit form.

Index Terms—Boundary, curved, capacitance, potential.

The author is with College of Engineering Design, Art and Technology, Makerere University, P. O. Box 7062, Kampala, Uganda (email: semwogereretwaibu@yahoo.co.uk).

Cite: Twaibu Semwogerere, "Application Analysis of the Curved Elements to a Two-Dimensional Laplace Problem Using the Boundary Element Method," International Journal of Applied Physics and Mathematics vol. 5, no. 3, pp. 167-176, 2015.