一种基于探测的优化传输条件的数值算法
A numerical algorithm based on probing to find optimized transmission conditions
摘要：
优化Schwarz方法（OSM）基于沿着子域之间的接口的优化传输条件。优化的传输条件是在理论水平上推导出来的，使用在过去几十年中开发的技术。这些分析背后的假设是相当强的，所以OSM的适用性仍然是有限的。在这篇手稿中，我们提出了一个数值算法，以获得优化的传输条件，为任何给定的问题。该算法需要在离线阶段执行很少的子域求解。这种额外的成本通常可以忽略不计，因为即使在单查询上下文中，收敛速度也会更快。
英文摘要：
Optimized Schwarz Methods (OSMs) are based on optimized transmission conditions along the interfaces between the subdomains. Optimized transmission conditions are derived at the theoretical level, using techniques developed in the last decades. The hypothesis behind these analyses are quite strong, so that the applicability of OSMs is still limited. In this manuscript, we present a numerical algorithm to obtain optimized transmission conditions for any given problem at hand. This algorithm requires few subdomain solves to be performed in an offline phase. This additional cost is usually negligible due to the resulting faster convergence, even in a single-query context.
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