中山大学学报（自然科学版）（中英文）2025，Vol.64Issue(5)：50-58,9.DOI:10.13471/j.cnki.acta.snus.ZR20240178
面向大规模并行计算的区域平衡PDE求解方法
Balancing domain decomposition method of solving PDE for massively parallel computing
摘要
Abstract
This study investigates the numerical solution efficiency and memory consumption of Poisson equation,heat conduction equation,and wave equation,using a non-overlapping domain decomposition method(DDM).To address the large-scale and singular nature of interface problems between subdomains generated by DDM,the balanced domain decomposition(BDD)method was employed.This method integrates conjugate gradient iteration with preconditioning techniques.The parallel algorithm is based on a symmetric multiprocessing(SMP)architecture,where all processor units are equal in status and share memory.First,the implementation of DDM and BDD based on the Poisson equation is introduced.Next,the finite element discretization processes and corresponding discrete matrix forms for the three PDEs are presented.Then,by increasing the total degrees of freedom while maintaining H/h ratio,the variation in iteration counts under different conditions is compared.Additionally,the iterative efficiency and memory consumption of DDM and BDD when solving these three PDEs are analyzed and contrasted under 1 000×1 000 and 2 000×2 000 mesh partitions.Finally,the diffusion-reaction equation is used to verify that BDD is more efficient than DDM in numerical solutions.关键词
区域平衡分解方法/数值效率/并行处理/数值可扩展性Key words
balancing domain decomposition/numerical efficiency/parallel processing/numerical scalability分类
数理科学引用本文复制引用
陈玉惠,黄诗杰,姚清河..面向大规模并行计算的区域平衡PDE求解方法[J].中山大学学报（自然科学版）（中英文）,2025,64(5):50-58,9.基金项目
广东省基础与应用基础研究基金(2021B1515310001,2022B1515120009) （2021B1515310001,2022B1515120009）
