A directional equispaced interpolation-based fast multipole method for oscillatory kernels

Fast multipole methods (FMMs) based on the oscillatory Helmholtz kernel can reduce the cost of solving N-body problems arising from boundary integral equations (BIEs) in acoustics or electromagnetics. However, their cost strongly increases in the high-frequency regime. This paper introduces a new directional FMM for oscillatory kernels (defmm: directional equispaced interpolation-based fmm), whose precomputation and application are FFT-accelerated due to poly-nomial interpolations on equispaced grids. We demonstrate the consistency of our FFT approach and show how symmetries can be exploited in the Fourier domain. We also describe the algorithmic de-sign of defmm, well-suited for the BIE nonuniform particle distributions, and present performance optimizations on one CPU core. Finally, we exhibit important performance gains on all test cases for defmm over a state-of-the-art FMM library for oscillatory kernels.