北京大学学报（自然科学版）2026，Vol.62Issue(3)：459-473,中插1-中插3,18.DOI:10.13209/j.0479-8023.2026.005
适用于周期性问题的Poisson模块库求解器的开发及验证
Development and Validation of a Poisson Solver Library for Periodic Boundary Problems
摘要
Abstract
For Poisson problems with periodic boundary conditions,the use of the traditional SOR solution algorithm does not permit the rapid convergence of the Poisson solver.To address this limitation,a novel multigrid iterative Poisson solver(Poisson-SOR-MG)based on finite difference methods was developed,leveraging multigrid acceleration techniques to overcome the drawbacks of SOR.Additionally,a 3D Fourier spectral transform algorithm was designed by coupling 1D Fast Fourier Transform(FFT)with 3D parallel communication algorithms,eliminating cumbersome transpose techniques.Building on this,a standard 2π-periodic Poisson-Fourier solver was developed and validated,achieving spectral accuracy.However,the standard 2π-periodic Poisson-Fourier solver cannot be directly applied to general engineering problems.To resolve this,theoretical analysis based on coordinate stretching transformations was conducted,leading to the further development and validation of a generalized arbitrary-periodic Poisson-Fourier solver.关键词
多重网格技术/3D傅里叶谱变换/Poisson求解器/SOR迭代法/坐标拉伸变换Key words
multigrid methods/3D Fourier spectral transformation/Poisson solvers/SOR iterative methods/coordinate mapping transformation引用本文复制引用
王雯,赵佳敏,李想,李青..适用于周期性问题的Poisson模块库求解器的开发及验证[J].北京大学学报（自然科学版）,2026,62(3):459-473,中插1-中插3,18.基金项目
国家重点研发计划(2022YFF1300803)和天目山实验室自主科研项目(TK-2024-D-004)资助 （2022YFF1300803）
