Approximate Fundamental Solutions and Alternative Formulations

Abstract

The two main problem areas associated with the application of the Boundary Element Method to the solution of physical problems are:-

• 1. The determination of the form of the appropriate fundamental solution.

• 2. The evaluation of the integral of this singular function over the elements needed for the determination of the diagonal terms in the influence matrices.

In this paper the method of ‘reference points’ is described which avoids the second difficulty and a method for the construction of the fundamental solution for any linear partial differential equation is given. These methods are discussed with examples from two-dimensional potential and diffraction theory in order to demonstrate simply the principles involved. All the examples were solved using an Apple II microcomputer, demonstrating the efficiency and usefulness of the Boundary Element Method.