A multilevel kernel-split dual-space framework for fast transforms

In this talk, we present a multilevel kernel-split dual-space (MKDS) framework for fast transforms. The MKDS framework applies “kernel splitting” to avoid the well-separateness condition in the fast multipole method, needed to obtain low-rank approximation of far field interactions. Instead, it uses a hierarchy of Fourier transforms and separation of variables to accelerate the far-field calculation. The framework is dimension-independent and applicable to a broad class of translation invariant kernels. Its preliminary performance is illustrated by comparison with the state-of-art FMM3D and PVFMM libraries for the Laplace kernel in three dimensions. This is ongoing joint work with Leslie Greengard.