In this paper, we propose a two-level additive Schwarz domain decomposition preconditioner for the symmetric interior penalty Galerkin method for a second-order elliptic boundary value problem with highly heterogeneous coefficients. A specific feature of this preconditioner is that it is based on adaptively enriching its coarse space with functions created by solving generalized eigenvalue problems on thin patches covering the subdomain interfaces. It is shown that the condition number of the underlined preconditioned system is independent of the contrast if an adequate number of functions are used to enrich the coarse space. Numerical results are provided to confirm this claim.

中文翻译：

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P ₁间断的Galerkin多尺度有限元问题的Schwarz预处理器的自适应富集粗糙空间

在本文中，我们针对具有高异构系数的二阶椭圆边值问题，针对对称内部惩罚Galerkin方法提出了两级加法Schwarz域分解预处理器。该预处理器的一个特殊功能是，它基于通过解决覆盖子域接口的细小块上的广义特征值问题而创建的函数，来自适应地丰富其粗略空间。结果表明，如果使用足够数量的函数来丰富粗糙空间，则带下划线的预处理系统的条件数与对比度无关。提供了数值结果以证实这一主张。