Parallel multilevel iterative linear solvers with unstructured adaptive grids for simulations in earth science
Parallel multilevel iterative linear solvers with unstructured adaptive grids for simulations in earth science
复制标题
用于地球科学模拟的具有非结构化自适应网格的并行多级迭代线性求解器
DOI：
10.1002/cpe.627
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
K. Nakajima
中科院分区：
文献类型：
--
作者：
K. Nakajima
提出了一种新的多网格预条件共轭梯度（MGCG）迭代算法。不完全Cholesky或不完全LU分解方法等具有预置条件的迭代求解器是大规模科学计算中最强大的工具。然而，这些方法收敛所需的迭代次数随着问题的规模而增加。在多网格求解器中，收敛速度与问题大小无关，并且迭代次数保持相当恒定。多重网格也是克雷洛夫迭代求解的一种很好的预处理算法。在本研究中，MGCG方法应用于半非结构化、自适应生成的棱柱网格上两个球面之间区域的泊松方程，以及局部细化的网格。在多达128个处理器的日立SR2201上使用该方法进行的计算显示出良好的可扩展性。版权所有©2002约翰威利父子有限公司
A new multigrid‐preconditioned conjugate gradient (MGCG) iterative method for parallel computers is presented. Iterative solvers with preconditioning, such as the incomplete Cholesky or incomplete LU factorization methods, represent some of the most powerful tools for large‐scale scientific computation. However, the number of iterations required for convergence by these methods increases with the size of the problem. In multigrid solvers, the rate of convergence is independent of problem size, and the number of iterations remains fairly constant. Multigrid is also a good preconditioning algorithm for Krylov iterative solvers. In this study, the MGCG method is applied to Poisson equations in the region between two spherical surfaces on semi‐unstructured, adaptively generated prismatic grids, and to grids with local refinement. Computations using this method on a Hitachi SR2201 with up to 128 processors demonstrated good scalability. Copyright © 2002 John Wiley & Sons, Ltd.