Convergence of both synchronous and asynchronous optimized Schwarz algorithms for the shifted Laplacian operator on a bounded rectangular domain, in a one‐way subdivision of the computational domain, with overlap, is shown. Convergence results are obtained under very mild conditions on the size of the subdomains and on the amount of overlap. A couple of results are also given, relating the convergence rate of the asynchronous method to changes in the size of the domain. Numerical experiments illustrate the theoretical results.

中文翻译：

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用于有界域的单向细分的同步和异步优化Schwarz方法

图中显示了在有界矩形域上的位移Laplacian算子的同步和异步优化Schwarz算法的收敛性，在计算域的单向细分中有重叠。在非常温和的条件下，可以在子域的大小和重叠量上获得收敛结果。还给出了一些结果，这些结果将异步方法的收敛速度与域大小的变化相关。数值实验说明了理论结果。