An Inexact Balancing Preconditioner for Large-Scale Structural Analysis
An Inexact Balancing Preconditioner for Large-Scale Structural Analysis
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DOI：
10.1299/jcst.2.150
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发表时间：
2008-05
期刊：
影响因子：
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通讯作者：
M. Ogino;R. Shioya;H. Kanayama
中科院分区：
文献类型：
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作者：
M. Ogino;R. Shioya;H. Kanayama
平衡区域分解（BDD）方法是一种著名的预条件子，由于其良好的收敛速度。BDD方法包括Neumann-Neumann预处理器和粗网格校正。一些研究已经考虑了BDD方法的各种现象和改进其收敛速度的应用。然而，在将BDD方法应用于大规模问题时，难以解决粗网格校正的粗问题，因为粗问题的大小与子域的数量成比例地增加（即，原问题的大小）。其他带有粗网格校正的预处理器也有同样的问题。为了克服这个问题，使用一个新的预处理，即不完全平衡区域分解与对角尺度（IBDD-DIAG）方法，在这项研究中提出。该方法基于BDD方法，由不完全平衡预条件子和简化的对角尺度预条件子构成。此外，它是并行的分层区域分解方法。为了评估这种新的方法，一些大规模问题的计算实例进行了演示。
The balancing domain decomposition (BDD) method is a well-known preconditioner due to its excellent convergence rate. The BDD method includes the Neumann-Neumann preconditioner and a coarse grid correction. Several studies have considered applications of the BDD method to various phenomena and improvement of its convergence rate. However, in applying the BDD method to large-scale problems, it is difficult to solve the coarse problem of a coarse grid correction since the size of the coarse problem increases in proportion to the number of subdomains (i.e., the size of the original problem). Other preconditioners with a coarse grid correction have the same problem. To overcome this problem, use of a new preconditioner, namely, incomplete balancing domain decomposition with a diagonal-scaling (IBDD-DIAG) method is proposed in this study. The method is based on the BDD method, and constructed by an incomplete balancing preconditioner and a simplified diagonal-scaling preconditioner. Moreover, it is parallelized by the hierarchical domain decomposition method. To evaluate this new approach, some computational examples of large-scale problems are demonstrated.