论文标题
在多屏幕上进行声学散射的Calderón预处理
Calderón Preconditioning for Acoustic Scattering at Multi-Screens
论文作者
论文摘要
我们为多屏幕上的Helmholtz外部问题提出了一个预处理。为此，我们将商空间和操作员的预处理结合在一起。对于一类多屏幕（我们将其配置为\ emph {type a}多屏幕），我们表明这种方法会阻止对角线calderón预处理，并导致光谱条件编号，而在简单屏幕的情况下，与$ h $一样，仅以$ h $进行对数。由于所得的方案包含的DOF比严格要求的更多的DOF，因此我们还提出了删除几乎所有冗余的策略，而预先调节器的有效性很大。我们通过提供代表性的数值结果来验证这些发现。 进一步的数值实验表明，这些结果可以扩展到超出A型多屏幕，并且此处介绍的数值方法可以应用于从业者遇到的所有多屏幕上，从而导致模拟成本大大降低。
We propose a preconditioner for the Helmholtz exterior problems on multi-screens. For this, we combine quotient-space BEM and operator preconditioning. For a class of multi-screens (which we dub \emph{type A} multi-screens), we show that this approach leads to block diagonal Calderón preconditioners and results in a spectral condition number that grows only logarithmically with $h$, just as in the case of simple screens. Since the resulting scheme contains many more DoFs than strictly required, we also present strategies to remove almost all redundancy without significant loss of effectiveness of the preconditioner. We verify these findings by providing representative numerical results. Further numerical experiments suggest that these results can be extended beyond type A multi-screens and that the numerical method introduced here can be applied to essentially all multi-screens encountered by the practitioner, leading to a significantly reduced simulation cost.
