ABSTRACT

The weak variational formulation and the fundamental solutions are the two building blocks for the direct boundary element methods. The adage that one can formulate and develop a boundary element method for any boundary value problem if the fundamental solution for the governing equation is known is not without merit. This chapter presents some techniques to derive the fundamental solutions for the equations. It finds eigenfunctions for boundary value problems, and then represents the Dirac delta function as a sum of eigenfunctions. This will lead readers to certain methods of explicitly finding fundamental solutions of some boundary value problems that are considered in the sequel.