发表机构
Massachusetts Institute of Technology; University of Wisconsin-Madison; State University of New York Polytechnic Institute; Worcester Polytechnic Institute（麻省理工学院; 威斯康星大学麦迪逊分校; 纽约州立理工大学; 伍斯特理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对各向异性椭圆问题的内部罚间断伽辽金离散，设计非重叠加性 Schwarz 预条件子，使其与跳跃系数和子域大小无关，并通过辅助空间减小粗网格规模，数值实验验证了其鲁棒性。
AI 中文摘要
我们设计并分析了一种用于各向异性椭圆问题内部罚间断伽辽金离散的非重叠加性 Schwarz 预条件子。该预条件方法与 Krylov 子空间迭代相结合，被证明与高度间断（且各向异性）的跳跃系数以及子域大小无关。为提高效率，我们考虑了多种辅助空间以减小粗网格算子的规模。我们展示了如何修改加性 Schwarz 预条件子，使其适用于非对称的 IPDG 格式。多个数值实验验证了理论并确认了预条件子的鲁棒性。
英文摘要
We design and analyze a nonoverlapping additive Schwarz preconditioner for interior penalty discontinuous Galerkin discretizations of anisotropic elliptic problems. The preconditioned method coupled with a Krylov subspace iteration is shown to be independent of the highly discontinuous (and anisotropic) jump coefficients as well as the subdomain size. To increase efficacy, various auxiliary spaces are considered to reduce the size of the coarse grid operator. We demonstrate how to modify the additive Schwarz preconditioner such that it is applicable to the nonsymmetric IPDG schemes. Several numerical experiments verify the theory and validate the robustness of the preconditioner.
Comments29 pages, 6 figures
