Optimized Schwarz methods
Optimized Schwarz methods
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DOI：
10.1137/s0036142903425409
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发表时间：
2006-01-01
影响因子：
2.9
通讯作者：
Gander, Martin J.
中科院分区：
文献类型：
--
作者：
Gander, Martin J.
优化的施瓦茨方法是一类新的施瓦茨方法，具有很强的收敛性.它们比经典的施瓦茨方法收敛得更快，并且当重叠量为网格参数的数量级时，它们的收敛速度比经典的施瓦茨方法的收敛速度更快，这在实际应用中是经常发生的.他们实现这一性能，通过使用新的子域之间的传输条件，极大地提高了子域之间的信息交换，并受到物理的基本问题。我们在本文中分析这些新的对称正定问题的方法，并显示其与其他现代区域分解方法，如新的有限元撕裂和互连（FETI）的变种。
Optimized Schwarz methods are a new class of Schwarz methods with greatly enhanced convergence properties. They converge uniformly faster than classical Schwarz methods and their convergence rates dare asymptotically much better than the convergence rates of classical Schwarz methods if the overlap is of the order of the mesh parameter, which is often the case in practical applications. They achieve this performance by using new transmission conditions between subdomains which greatly enhance the information exchange between subdomains and are motivated by the physics of the underlying problem. We analyze in this paper these new methods for symmetric positive definite problems and show their relation to other modern domain decomposition methods like the new Finite Element Tearing and Interconnect (FETI) variants.