对限制Additive Schwarz的变式解释,加上Helmholtz问题的阻力传输条件 (A variational interpretation of Restricted Additive Schwarz with impedance transmission condition for the Helmholtz problem)

In this paper we revisit the Restricted Additive Schwarz method for solving discretized Helmholtz problems, using impedance boundary conditions on subdomains (sometimes called ORAS). We present this method in its variational form and show that it can be seen as a finite element discretization of a parallel overlapping domain decomposition method defined at the PDE level. In a fourthcoming paper, the authors have proved certain contractive properties of the error propagation operator for this method at the PDE level, under certain geometrical assumptions. We illustrate computationally that these properties are also enjoyed by its finite element approximation, i.e., the ORAS method.

翻译：在本文中,我们重新审视了利用分域(有时称为ORAS)的阻力边界条件解决分散散散散散散散散散散的Helmholtz 问题的方法(有时称为ORAS),我们以其变异形式提出这种方法,并表明这种方法可被视为PDE一级界定的平行重叠域分解方法的有限分解元素。在第四期论文中,作者根据某些几何假设,证明PDE一级错误传播操作员在这种方法上具有某些合同性。我们用计算方法说明,这些特性也是其定数元素近似值(即ORAS方法)所享受的。