标题： 快速奇异核卷积在一般非光滑域上的截断傅里叶滤波方法 显示英文标题

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

摘要： 具有奇异核的卷积的快速准确评估在广泛的科学和工程应用中起着至关重要的作用。基于最近引入的适用于光滑核的截断傅里叶滤波方法，本文提出了一种快速、高阶数值方法，将该方法扩展到奇异核和非光滑域。该方法依赖于对积分域的特征函数以及特征函数与奇异函数乘积的指定阶数（$F$）的截断傅里叶展开。本文版本为初步草稿，旨在促进早期传播。完整版本即将发布。 显示英文摘要

摘要： 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 $F$ for the characteristic function of the integration domain, as well as expansions for the products of characteristic functions and singular functions. This version of the article is a preliminary draft, shared to facilitate early dissemination. The complete version will be available shortly.