Speaker
Ludvig af Klinteberg, Mälardalen University
Abstract
Kernel splitting expresses a singular kernel as a superposition of a
localized near field and a smooth far field. This enables fast
summation methods such as FFT-based Ewald schemes and the recent
adaptive DMK method. For spectral accuracy the kernel split is
commonly derived using a Gaussian mollifier, which decays rapidly in
both real and Fourier space.
We show that a more efficient split for the kernels of Stokes flow can
be obtained by replacing the Gaussian with a prolate spheroidal wave
function (PSWF). PSWFs have optimal space-frequency concentration,
leading to splits that require significantly fewer Fourier modes,
compared to a Gaussian split with the same accuracy and
localization. This can be directly integrated into existing fast Ewald
frameworks, and we show results for a new DMK implementation for
Stokes flow.