Parallel implementation of efficient preconditioned linear solver for grid-based applications in chemical physics. II: QMR linear solver
Parallel implementation of efficient preconditioned linear solver for grid-based applications in chemical physics. II: QMR linear solver
复制标题
DOI：
10.1016/j.jcp.2006.03.031
复制
发表时间：
2006-11-20
影响因子：
4.1
通讯作者：
Poirier, Bill
中科院分区：
文献类型：
--
作者：
Chen, Wenwu;Poirier, Bill
化学物理中的线性系统经常涉及矩阵。具有一定的稀疏块结构。这些通常可以非常有效地解决使用迭代方法（矩阵向量乘积序列）结合块雅可比预条件[B。普瓦里尔，努默。Linear Algebra Appl.7（2000）715]。在一个由两部分组成的系列中，我们提出了一个高效的并行实现，并结合了几个额外的改进。本研究（论文II）表明，基本的并行稀疏矩阵向量乘积操作本身是整体的可扩展性瓶颈，表现得更差比专门的，块雅可比例程在同伴论文（论文I）中考虑。然而，一个简单的尺寸组合方案被发现，以减轻这一困难。(c)2006年爱思唯尔公司All rights reserved.
Linear systems in chemical physics often involve matrices. with a certain sparse block structure. These can often be solved very effectively using iterative methods (sequence of matrix-vector products) in conjunction with a block Jacobi preconditioner [B. Poirier, Numer. Linear Algebra Appl. 7 (2000) 715]. In a two-part series, we present an efficient parallel implementation, incorporating several additional refinements. The present study (paper II) indicates that the basic parallel sparse matrix-vector product operation itself is the overall scalability bottleneck, faring much more poorly than the specialized, block Jacobi routines considered in a companion paper (paper I). However, a simple dimensional combination scheme is found to alleviate this difficulty. (c) 2006 Elsevier Inc. All rights reserved.