论文标题
定向稳定的基于插值的快速多极方法用于振荡核
A Directional Equispaced interpolation-based Fast Multipole Method for oscillatory kernels
论文作者
论文摘要
基于振荡性Helmholtz内核的快速多极方法（FMM）可以降低求解由声学或电磁学中边界积分方程（BIE）引起的N体问题的成本。但是，它们的成本在高频制度中大大增加。本文引入了用于振荡核的新定向FMM（DEFMM-定向稳态插值的FMM），该方向的预定和应用是由于在稳态的网格上的多项式插值而被FFT加速了。我们证明了我们的FFT方法的一致性，并展示了如何在傅立叶域中利用对称性。我们还描述了DEFMM的算法设计，非常适合BIE不均匀的粒子分布，并在一个CPU核心上进行了性能优化。最后，我们在振荡性内核的最先进的FMM库上对DEFMM的所有测试用例表现出重要的性能提高。
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 acoustic 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 polynomial 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 design of defmm, well-suited for the BIE non-uniform 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.
