Boundary Element Method - Chakraverty, Snehashish; Mahato, Nisha; Karunakar, Perumandla; Dilleswar Rao, Tharasi (Advanced Numerical and Semi-Analytical Methods for Differential Equations, 2019)
This chapter presents a brief introduction of the boundary element method (BEM) along with a simple example problem for easy understanding of the method. To use the BEM for solving boundary value problems, one must transform the problem into an equivalent boundary integral equation problem. In this regard, the fundamental solution and Green's integral theorems are very useful tools. Accordingly, the chapter discusses the fundamental solution, Green's function, and integral theorems. Before discussing the fundamental solution, a brief review of the Heaviside function and Dirac delta function in R 2 is needed. Green's function is described as integral kernel that can be used to solve differential equations. In the chapter, the Green's function may be considered as a fundamental solution for the differential equation. Green's integral formula is a very useful tool for finding the derivation of integral equations formed in the BEM.