论文标题
封闭形式优化的传输条件，用于与许多子域的复杂扩散
Closed form optimized transmission conditions for complex diffusion with many subdomains
论文作者
论文摘要
在过去十年中，域分解方法中优化的传输条件一直是密集研究工作的重点。传统上，针对两种子域模型配置进行了优化的传输条件，然后用于许多子域中。我们首次在此直接针对许多子域进行优化的传输条件，以针对一类复杂的扩散问题进行优化。我们的渐近分析导致许多子域的封闭形式优化的传输条件，并表明网格尺寸中的渐近最佳选择与常数的两个子域最佳选择仅不同，为此，我们明确地得出了对子域数量的依赖性，包括无限型子域的限制案例，导致了新的Insights to New Insights to Speceights。我们的结果包括Robin和Ventcell的传输条件，我们还首次优化了两侧Ventcell条件。我们通过数值实验来说明我们的结果，这是针对我们的分析和超越情况所涵盖的情况。
Optimized transmission conditions in domain decomposition methods have been the focus of intensive research efforts over the past decade. Traditionally, transmission conditions are optimized for two subdomain model configurations, and then used in practice for many subdomains. We optimize here transmission conditions for the first time directly for many subdomains for a class of complex diffusion problems. Our asymptotic analysis leads to closed form optimized transmission conditions for many subdomains, and shows that the asymptotic best choice in the mesh size only differs from the two subdomain best choice in the constants, for which we derive the dependence on the number of subdomains explicitly, including the limiting case of an infinite number of subdomains, leading to new insight into scalability. Our results include both Robin and Ventcell transmission conditions, and we also optimize for the first time a two-sided Ventcell condition. We illustrate our results with numerical experiments, both for situations covered by our analysis and situations that go beyond.
