Finite element methods in scalar scattering problems

Numerical methods for the scalar scattering problem are necessary because exact analytic solutions can only be found for scattering bodies of simple shape. Moreover, any such analytic solutions are often given as infinite series of slow convergence and contain special functions which are not well suited for straightforward calculation. The problem is particularly acute when the dimensions of the scatterer are comparable to the wavelength of the incident field. An integral equation formulation of the problem is presented which is also amenable to solution by finite element techniques. Two such methods are reviewed - the well known CHIEF method due to Schenck and the newly implemented CONDOR method which is basically the method of Burton and Miller made numerically feasible by the results of Terai. At any wavenumber, the CONDOR method produces a unique solution which satisfies the radiation conditions; it avoids the difficulties of the CHIEF method in the selection of interior collocation points at higher frequencies.