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Fast Multipole Methods (FMMs) based on the oscillatory Helmholtz kernel canreduce the cost of solving N-body problems arising from Boundary IntegralEquations (BIEs) in acoustic or electromagnetics. However, their cost stronglyincreases in the high-frequency regime. This paper introduces a new directionalFMM for oscillatory kernels (defmm - directional equispaced interpolation-basedfmm), whose precomputation and application are FFT-accelerated due topolynomial interpolations on equispaced grids. We demonstrate the consistencyof our FFT approach, and show how symmetries can be exploited in the Fourierdomain. We also describe the algorithmic design of defmm, well-suited for theBIE non-uniform particle distributions, and present performance optimizationson one CPU core. Finally, we exhibit important performance gains on all testcases for defmm over a state-of-the-art FMM library for oscillatory kernels.

A Directional Equispaced interpolation-based Fast Multipole Method for oscillatory kernels