Inexact FETI‐DP methods
Inexact FETI‐DP methods
复制标题
不精确的 FETI-DP 方法
DOI：
10.1002/nme.1758
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发表时间：
2007
影响因子：
2.9
通讯作者：
O. Rheinbach
中科院分区：
文献类型：
--
作者：
A. Klawonn;O. Rheinbach
考虑了不精确的FETI - DP域分解方法。基于FETI - DP作为鞍点问题的公式的预调节器被使用，允许粗问题的不精确解。本文还考虑了预设鞍点问题的一个正定的重新表述，它也允许近似解。在原始FETI - DP鞍点系统上迭代的公式中，也可能不精确地解决局部诺伊曼子域问题。给出了局部问题和粗问题的良好近似解，得到了与标准FETI - DP方法相同质量的收敛界。数值实验比较了采用GMRES和CG作为Krylov空间方法的二维和三维弹性不精确方法与标准FETI - DP方法的收敛性。在并行计算的基础上，将一种不精确FETI - DP算法与标准FETI - DP方法进行了比较，获得了相似的并行性能。本文还演示了非精确变量的并行可扩展性。结果表明，对于非常多的子域和非常大的粗糙问题，非精确方法是优越的。版权所有©2006约翰威利父子有限公司
Inexact FETI‐DP domain decomposition methods are considered. Preconditioners based on formulations of FETI‐DP as a saddle point problem are used which allow for an inexact solution of the coarse problem. A positive definite reformulation of the preconditioned saddle point problem, which also allows for approximate solvers, is considered as well. In the formulation that iterates on the original FETI‐DP saddle point system, it is also possible to solve the local Neumann subdomain problems inexactly. Given good approximate solvers for the local and coarse problems, convergence bounds of the same quality as for the standard FETI‐DP methods are obtained. Numerical experiments which compare the convergence of the inexact methods with that of standard FETI‐DP are shown for 2D and 3D elasticity using GMRES and CG as Krylov space methods. Based on parallel computations, a comparison of one variant of the inexact FETI‐DP algorithms and the standard FETI‐DP method is carried out and similar parallel performance is achieved. Parallel scalability of the inexact variant is also demonstrated. It is shown that for a very large number of subdomains and a very large coarse problem, the inexact method can be superior. Copyright © 2006 John Wiley & Sons, Ltd.