Fast Singular-Kernel Convolution on General Non-Smooth Domains via Truncated Fourier Filtering

Abstract

The rapid and accurate evaluation of convolutions with singular kernels plays crucial roles in a wide range of scientific and engineering applications. Building on the recently introduced Truncated Fourier Filtering method for smooth kernels, this work presents a fast, high-order numerical methodology that extends the approach to singular kernels and non-smooth domains. The method relies on truncated Fourier expansions of a prescribed order for the characteristic function of the integration domain, as well as expansions for the products of characteristic functions and singular functions.