Helmholtz Equation

Abstract

As we begin this fourth chapter we do suppose that you have begun to observe a pattern with the formulation of the Green element equations. Here we shall follow the same procedure that we had employed in the two previous chapters, and that is to seek a Fredholm integral equation of the second kind with a singular kernel for the differential equation, discretize the integral equation over the computational domain, and then approximate the distributions of functional quantities (known and unknown) with appropriate element shape functions. The outcome of these steps is a system of discrete equations that completely describes the solution behavior of the system being modeled. Before embarking on developing the system of discrete equations for the Helmholtz equation, we choose a physical problem to which it applies. We do this so as to elicit a good engineering appreciation of the differential equation being addressed.