论文标题
在存在反射的情况下，扫除分层介质的预处理
Sweeping preconditioners for stratified media in the presence of reflections
论文作者
论文摘要
在本文中，我们考虑在分层培养基中扫描时间谐波传播的预处理，尤其是在反射的存在下。在最著名的一类扫描前提下，通过吸收边界条件来近似于半空间问题。在存在反射的情况下，吸收边界条件并不能准确，从而导致这些扫描的预处理的性能不令人满意。我们探索在扫描中使用更准确的Dirichlet到Neumann运算符的潜力。为此，我们利用方程式为背景模型的可分离性。尽管这提高了Dirichlet到Neumann操作员的准确性，但我们从数值测试和分析论证中都发现，在存在反射的情况下，它对扰动非常敏感。这意味着，即使可以针对分层的介质设计准确地近似于Dirichlet到Neumann运算符，扫描的预处理也仅限于非常小的扰动。
In this paper we consider sweeping preconditioners for time harmonic wave propagation in stratified media, especially in the presence of reflections. In the most famous class of sweeping preconditioners Dirichlet-to-Neumann operators for half-space problems are approximated through absorbing boundary conditions. In the presence of reflections absorbing boundary conditions are not accurate resulting in an unsatisfactory performance of these sweeping preconditioners. We explore the potential of using more accurate Dirichlet-to-Neumann operators within the sweep. To this end, we make use of the separability of the equation for the background model. While this improves the accuracy of the Dirichlet-to-Neumann operator, we find both from numerical tests and analytical arguments that it is very sensitive to perturbations in the presence of reflections. This implies that even if accurate approximations to Dirichlet-to-Neumann operators can be devised for a stratified medium, sweeping preconditioners are limited to very small perturbations.
