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The rapid and accurate evaluation of convolutions with singular kernels playscrucial roles in a wide range of scientific and engineering applications.Building on the recently introduced Truncated Fourier Filtering method forsmooth kernels, this work presents a fast, high-order numerical methodologythat extends the approach to singular kernels and non-smooth domains. Themethod relies on truncated Fourier expansions of a prescribed order $F$ for thecharacteristic function of the integration domain, as well as expansions forthe products of characteristic functions and singular functions. This versionof the article is a preliminary draft, shared to facilitate earlydissemination. The complete version will be available shortly.

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