GenEO coarse spaces for heterogeneous indefinite elliptic problems
Niall Bootland, Victorita Dolean, Ivan G. Graham, Chupeng Ma, Robert Scheichl
备注：
26th International Domain Decomposition Conference (DD26) proceedings
发表信息：
Brenner, S.C., Chung, E., Klawonn, A., Kwok, F., Xu, J., Zou, J. (Eds.) Domain Decomposition Methods in Science and Engineering XXVI. Lecture Notes in Computational Science and Engineering, Vol. 145. Springer, Cham, pp. 117-125 (2022)
Motivated by recent work on coarse spaces for Helmholtz problems, we provide in this paper a comparative study on the use of spectral coarse spaces of GenEO type for heterogeneous indefinite elliptic problems within an additive overlapping Schwarz method. In particular, we focus here on two different but related formulations of local generalised eigenvalue problems and compare their performance numerically. Even though their behaviour seems to be very similar for several well-known heterogeneous test cases that are mildly indefinite, only one of the coarse spaces has so far been analysed theoretically, while the other one leads to a significantly more robust domain decomposition method when the indefiniteness is increased. We present a summary of upcoming results developing such a theory and describe how the numerical experiments illustrate it.
Spectral coarse spaces based on indefinite operators: the $H_k$-GenEO method
Inria（法国国家信息与自动化研究所）；Univ. Lille（里尔大学）；Laboratoire Paul Painlevé（保罗·潘勒韦实验室）；Eindhoven University of Technology（埃因霍温理工大学）；University of Strathclyde（斯特拉斯克莱德大学）；University of Bath（巴斯大学）
A robust and adaptive GenEO-type domain decomposition preconditioner for $\mathbf{H}(\mathbf{curl})$ problems in three-dimensional general topologies
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A correction adaptive two-grid finite element method for nonselfadjoint or indefinite elliptic problems
Lingnan Normal University（岭南师范学院）；Missouri University of Science and Technology（密苏里科技大学）；Guangzhou University（广州大学）；South China Normal University（华南师范大学）
A two-grid preconditioner with an adaptive coarse space for flow simulations in highly heterogeneous media
School of Mathematics and Information Science, Guangzhou University（广州大学数学与信息科学学院）；Department of Mathematics, The Chinese University of Hong Kong（香港中文大学数学系）
McMg: A Learned Phase-Space Multi-channel Multigrid Preconditioner for Helmholtz Equation
School of Mathematics, Jilin University（吉林大学数学学院）；Ocean University of China（中国海洋大学）；Shenzhen Loop Area Institute（深圳河套学院）；King Abdullah University of Science and Technology（卡布斯科学技术大学）
