Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning
Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning
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线性和非线性子结构受限加法 Schwarz 迭代和预处理
DOI：
10.1016/j.cam.2018.04.014
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
T. Vanzan
中科院分区：
文献类型：
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作者：
F. Chaouqui;Martin J. Gander;P. Kumbhar;T. Vanzan
子结构区域分解（DD）方法已被广泛研究，它们通常与非重叠分解。我们在这里介绍一个子结构版本的限制添加剂施瓦茨（RAS），我们称之为SRAS，我们讨论了它的优点相比，标准体积制定的施瓦茨方法时，他们都被用来作为迭代求解器和预条件的Krylov方法。为了将SRAS扩展到非线性问题，我们引入了SRASPEN（子结构限制加法施瓦茨预条件精确牛顿），其中SRAS被用作牛顿方法的预条件。我们仔细研究子结构的影响，这些方法的收敛性和性能，以及它们的实现。最后，我们介绍了两个层次的版本的非线性SRAS和SRASPEN。数值实验证实了制定一个施瓦茨方法在子结构水平的优势。
Substructured domain decomposition (DD) methods have been extensively studied, and they are usually associated with nonoverlapping decompositions. We introduce here a substructured version of Restricted Additive Schwarz (RAS) which we call SRAS, and we discuss its advantages compared to the standard volume formulation of the Schwarz method when they are used both as iterative solvers and preconditioners for a Krylov method. To extend SRAS to nonlinear problems, we introduce SRASPEN (Substructured Restricted Additive Schwarz Preconditioned Exact Newton), where SRAS is used as a preconditioner for Newton's method. We study carefully the impact of substructuring on the convergence and performance of these methods as well as their implementations. We finally introduce two-level versions of nonlinear SRAS and SRASPEN. Numerical experiments confirm the advantages of formulating a Schwarz method at the substructured level.
DOI：
10.1137/1.9780898718003
发表时间：
2003-05
期刊：
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影响因子：
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作者：
Y. Saad
通讯作者：
Y. Saad