摘要
代数多重网格(AMG)是一种高效的线性方程组求解预条件方法.半结构AMG利用结构化信息高效计算,且支持存在非结构信息,因此可以同时达到高性能和高灵活性,从而广泛应用于科学与工程计算的各个场景中.然而,目前主流半结构AMG求解器在绝对速度和可扩展性上仍然具有明显缺陷,为此我们研发了Semi-StructMG求解器.一方面,它利用多维粗化,降低了复杂度,提高了单步运行速度和可扩展性;另一方面,它在光滑器和插值算子中考虑块间连边,改善了在各种复杂问题中的收敛性.我们在基准测试和多个真实应用中对Semi-StructMG进行了测试,相比hypre中的SSAMG,Split和BoomerAMG达到了5.97x,15.2x和3.85x的加速比.
Algebraic multigrid(AMG)is an efficient method for solving linear equation systems as preconditioners.Semi-structured AMG utilizes structured information for efficient computation and supports the presence of unstructured information,thus achieving both high performance and high flexibility,making it widely used in various scenarios of scientific and engineering computing.However,the current mainstream semi-structured AMG solvers still have significant deficiencies in absolute speed and scalability.Therefore,we developed SemiStructMG.On the one hand,it utilizes multidimensional coarsening to reduce complexity,improving single step running speed and scalability;On the other hand,it considers interblock connections in the smoother and interpolation operators,improving convergence in various complex problems.We tested Semi-StructMG in benchmark tests and multiple realworld applications,and achieved speedup of 5.97x,15.2x,and 3.85x compared to SSAMG,Split and BoomerAMG in hypre.
作者
贾朝蓬
宗毅
张晨松
孙健
牟龙江
王建春
徐小文
王欣亮
于沛楠
薛巍
Jia Zhaopeng;Zong Yi;Zhang Chensong;Sun Jian;Mu Longjiang;Wang Jianchun;Xu Xiaowen;Wang Xinliang;Yu Peinan;Xue Wei(Tsinghua University,Beijing 100084,China;Academy of Mathematics and Systems Science,Beijing 100190,China;CMA Earth System Modeling and Prediction Center,Beijing 100081,China;Laoshan Laboratory,Qingdao 266100,China;China Ship Scientific Research Center,Wuxi 214082,China;Institute of Applied Physics and Computational Mathematics,Beijing 100094,China;Huawei Technologies Co.,Ltd,Beijing 100085,China)
出处
《数值计算与计算机应用》
2025年第4期283-295,共13页
Journal on Numerical Methods and Computer Applications
基金
国家重点研发计划项目(2023YFB3001703)
国家自然科学基金(U2242210)资助.
关键词
代数多重网格(AMG)
稀疏矩阵
结构化矩阵
预条件子.
algebraic multigrid(AMG)
sparse matrix
structured grid
preconditioner.2010 Mathematics Subject Classification:65F08,65N55.
