In this article we consider the implementation of a version of the fast multipole method for scattering by large objects. We put particular emphasis on error and execution time. In contrast to the traditional moment method, the fast multipole method (FMM) has an O(N1.5) CPU requirement per incidence angle. This substantially reduced CPU time is achieved by subdividing the far-zone elements into groups whose weighted contribution is then interacted with the test element. The size of the groups and the various approximations used in the interaction of the groups play an important role in the solution accuracy, but so far the effect of these parameters on the solution accuracy has not been considered. Guidelines are given for choosing the various parameters affecting the speed and solution accuracy of the method, such as the near-group distance and sampling rate based on an error criterion. Our study is carried out with reference to a version of the FMM referred to as the fast far-field approximation.
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Bindiganavale et al. (1996) studied this question.