BOUNDARY ELEMENT SOLUTION OF A BODY'S EXTERIOR ACOUSTIC FIELD NEAR ITS INTERNAL EIGENVALUES

A relatively straightforward Boundary Element Method (BEM) for the numerical solution of the exterior Helmholtz problem is specified in a tutorial fashion. The algorithm employs the Combined Helmholtz Integral Equation Formulation (CHIEF) and then Singular Value Decomposition (SVD) to solve the resulting system. Its accuracy and convergence characteristics are examined, and compared to the simplest boundary element method for exterior acoustics, the Helmholtz Integral Equation Formulation or HIEF. Boundary element and auxiliary (CHIEF) point requirements to obtain BEM solutions of a desired accuracy are described. This particular CHIEF algorithm is found to largely avoid the numerical difficulties of the HIEF technique while retaining theoretical and practical implementation simplicity.