The boundary element method is described and investigated, especially in respect of its application to two-dimensional laplace problems. Both empirical and algebraic anaalyses (including the efects of the approximation of the boundary and boundary functions and the precision of the evaluation of the discrete forms) are developed.

Methods for the automatic evaluation of the discrete forms of the Laplace and Helmholtz integral operators are reviewed and extended. Boundary element methods for the solution of the exterior Helmholtz problems with general (but most importantly Neumann) boundary conditions are reviewed and some are explicitly stated using a new notation.

Boundary element methods based on the boundary integral equations introduced by Brakhage and Werner / Leis / Panich / Kussmaul (indirect) are given prime consideration and implemented for three-dimensional problems. The influence of the choice of weighting parameter on the performance of the methods is explored and further guidance is given.

The application of boundary element methods and methods based on the Rayleigh Integral to acoustic radiation problems are considered. Methods for speeding up their solution via the boundary element method are developed. Library subroutines for the solution of acoustic radiation and scattering problems are described and demonstrated.

Computational techniques for the problem of predicting the noise produced by a running engine are reviewed and appraised. The application of the boundary element method to low noise engine design and in the design of noise shields is considered. The boundary element method is applied to the Ricardo crankcase simularion rig, which is an engine-like structure. A comparison of predicted and measured sound power spectra is given.