Compressed Fast Multipole Representations for Homogeneous 3-D Kernels

For homogeneous kernels, the memory requirements associated with H² representations of integral equation matrices can be reduced by incorporating translational invariance. Starting with a non-translationally invariant H² representation, this can be accomplished using a left/right iterative algorithm. In this paper, it is shown that a similar algorithm can also be used to compress an existing fast multipole method (FMM). It is observed that the iterative compression converges faster when used to compress an FMM than when it is applied to an H² representation. Resulting savings in floating-point operations are indicated, and extensions of the reported method are discussed.