Group-based Compression of an FMM for Smooth Kernels

The fast multipole method (FMM) representation of matrices obtained by sampling smooth translationally invariant kernels can be compressed using a level-dependent iterative procedure. Here 'level' is used to refer to a level of an underlying octree. In this presentation it is shown that additional compression is obtained if the level-based compression is subsequently applied to each octree group at each level. The additional compression is most significant for geometric configurations characterized by a non-uniform distribution of the underlying degrees of freedom (DOF). The compressed FMM representation retains translational invariance and there is no increase in the total number of translators.