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Method-of-Moments (MoM) based 3-D electromagnetic analysis programs typically generate dense systems of equations which are extremely expensive to solve. In the last several years, very fast MoM solvers have been developed by sparsifying the dense system using a hierarchy of multipole expansions or grid projection plus the fast Fourier transform. The hierarchical multipole algorithms represented clusters of source distributions with an expansion in the center of the cluster, where as grid projection algorithms represent clusters using grid-locked point sources. In this paper we consider how to improve the efficiency of either algorithm by using grid-locked multipole expansions to represent clusters of sources.