发表机构
University of Manitoba（曼尼托巴大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
为有界双连通域开发一种基于变换的新技术来数值求解全纯函数和拉普拉斯方程解的边值问题，基于已有方法，利用环域的塞戈核等推导新方法并通过修正施瓦茨问题验证有效性。
AI 中文摘要
我们为有界双连通域开发了一种新的基于变换的技术，该技术推广了统一变换方法，是数值求解全纯函数边值问题和拉普拉斯方程解的新途径。此工作基于Crowdy（2015）为多连通圆形域开发的变换方法以及H., Lanzani, Llewellyn Smith和Luca（2025）为单连通有界域开发的方法。环域的塞戈核和相应的变换定律在新技术的推导中起着关键作用。通过实现两个域的修正施瓦茨问题来证明这种新方法的有效性。
英文摘要
A new transform-based technique that generalizes the unified transform method is developed for bounded doubly connected domains as a novel way to numerically solve boundary value problems for holomorphic functions and solutions to the Laplacian. This work builds on the transform methods for multiply connected circular domains developed by Crowdy (2015, IMA J., 80) and the methods for simply connected bounded domains developed by H., Lanzani, Llewellyn Smith, and Luca (2025, Proc. A, 481). The Szegö kernel of the annulus and a corresponding transformation law is pivotal in the derivation of this new technique. The modified Schwarz problem for two domains is implemented to demonstrate the effectiveness of this new method.
