Classically transmission conditions between subdomains are optimized for a simplified two subdomain decomposition to obtain optimized Schwarz methods for many subdomains. We investigate here if such a simplified optimization suffices for the magnetotelluric approximation of Maxwell's equation which leads to a complex diffusion problem. We start with a direct analysis for 2 and 3 subdomains, and present asymptotically optimized transmission conditions in each case. We then optimize transmission conditions numerically for 4, 5 and 6 subdomains and observe the same asymptotic behavior of optimized transmission conditions. We finally use the technique of limiting spectra to optimize for a very large number of subdomains in a strip decomposition. Our analysis shows that the asymptotically best choice of transmission conditions is the same in all these situations, only the constants differ slightly. It is therefore enough for such diffusive type approximations of Maxwell's equations, which include the special case of the Laplace and screened Laplace equation, to optimize transmission parameters in the simplified two subdomain decomposition setting to obtain good transmission conditions for optimized Schwarz methods for more general decompositions.
翻译：子域之间的常规传输条件得到优化, 以简化两个子数据元分解, 以获得许多子数据元的优化 Schwarz 方法。 我们在此调查, 如果这种简化的优化方法足以解决马克斯韦尔等式的磁极极近似问题, 从而导致复杂的扩散问题 。 我们从直接分析 2 和 3 子数据开始, 并在每种情况下呈现非同步优化的传输条件 。 然后, 我们从数字上优化4 、 5 和 6 子数据元的传输条件, 并观察同样的优化传输条件的无症状行为 。 我们最终使用限制光谱的技术, 优化在条形分解状态下的大量子数据 。 我们的分析显示, 在所有这些情况下, 对传输条件的无症状最佳选择都是相同的, 只有常数略有不同 。 因此, 足够用于对 Maxwell 等同的 diffive 型近似性传输条件, 包括 Laplace 和 筛选 Laplace 等式的特殊情形, 以优化两种子数据传输参数, 优化在两个简化的子数据分层分解位置上, 以获得更好的最佳传输条件 。
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