ABSTRACT
This chapter provides Laplace and Poisson equations which represent a wide range of problems in applied mathematics, physics and engineering. Some of the physical situations which have models involving these equations are: steady-state heat conduction problems, torsion problems in solid mechanics, diffusion flow in porous media, incompressible inviscid fluid flow, electrostatic potential problems, Newtonian potentials, and magnetostatics. The chapter introduces the boundary element method for two–and three#8211;dimensional steady#8211;state potential problems. In a very general form, this method starts by subdividing the boundary of the region into finitely many elements (hence the name boundary element method, or BEM). This method then becomes a particular case of the weighted residual technique, except that it usually produces a singularity when the equation using the fundamental solution is discretized on the boundary. A simple way to introduce this method is to integrate the fundamental solution of boundary value problems on the boundary.
