为提高代数多重网格(algebraic multigrid,AMG)并行算法的可扩展性能,提出一种基于聚集粗化和最大独立集算法的混合并行粗化算法。在每个进程内部独立实现聚集粗化,在此基础上,进程间采用PMIS(parallel maximum independent set)算法对...为提高代数多重网格(algebraic multigrid,AMG)并行算法的可扩展性能,提出一种基于聚集粗化和最大独立集算法的混合并行粗化算法。在每个进程内部独立实现聚集粗化,在此基础上,进程间采用PMIS(parallel maximum independent set)算法对边界点进行修正。针对现代多核处理器,结合细粒度的并行编程模型,实现MPI+OpenMP混合编程并行算法。数值实验结果验证了该算法的有效性,对于求解二维五点Laplace方程在集群"元"上并行规模达到256核,相对于AGMG软件包求解总时间提高了74%,测试结果优于hypre软件包,可扩展到128核心。展开更多
近年来,随着日常生活等实际应用领域中大规模稀疏矩阵求解问题的推动,代数多重网格(AMG)算法及其并行化的研究成为了数值计算领域的热点。本文在原始AMG算法和MPRS算法的基础上,对现有的并行AMG算法提出了一种优化的动态阈值算法(DVRS)...近年来,随着日常生活等实际应用领域中大规模稀疏矩阵求解问题的推动,代数多重网格(AMG)算法及其并行化的研究成为了数值计算领域的热点。本文在原始AMG算法和MPRS算法的基础上,对现有的并行AMG算法提出了一种优化的动态阈值算法(DVRS)。在Visual Studio 2008环境下,数值计算实验结果表明,新算法适用于更广泛的领域,与原有的并行AMG算法相比,改善了AMG并行计算的可扩展性。展开更多
To speed up three-dimensional （3D） DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method （AGMG）. We first discretize the differential equation of the secondar...To speed up three-dimensional （3D） DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method （AGMG）. We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner （AGMG-CG） to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling （3DDCXH）. In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.展开更多
文摘为提高代数多重网格(algebraic multigrid,AMG)并行算法的可扩展性能,提出一种基于聚集粗化和最大独立集算法的混合并行粗化算法。在每个进程内部独立实现聚集粗化,在此基础上,进程间采用PMIS(parallel maximum independent set)算法对边界点进行修正。针对现代多核处理器,结合细粒度的并行编程模型,实现MPI+OpenMP混合编程并行算法。数值实验结果验证了该算法的有效性,对于求解二维五点Laplace方程在集群"元"上并行规模达到256核,相对于AGMG软件包求解总时间提高了74%,测试结果优于hypre软件包,可扩展到128核心。
文摘近年来,随着日常生活等实际应用领域中大规模稀疏矩阵求解问题的推动,代数多重网格(AMG)算法及其并行化的研究成为了数值计算领域的热点。本文在原始AMG算法和MPRS算法的基础上,对现有的并行AMG算法提出了一种优化的动态阈值算法(DVRS)。在Visual Studio 2008环境下,数值计算实验结果表明,新算法适用于更广泛的领域,与原有的并行AMG算法相比,改善了AMG并行计算的可扩展性。
基金supported by the Natural Science Foundation of China(Nos.41404057,41674077 and 411640034)the Nuclear Energy Development Project of China,and the‘555’Project of Gan Po Excellent People
文摘To speed up three-dimensional （3D） DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method （AGMG）. We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner （AGMG-CG） to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling （3DDCXH）. In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.
