In this paper we motivate, discuss the implementation and present the resulting numerics for a new definition of strength of connection which is based on the notion of algebraic distance. This algebraic distance measure, combined with compatible relaxation, is used to choose suitable coarse grids and accurate interpolation operators for algebraic multigrid algorithms. The main tool of the proposed measure is the least squares functional defined using a set of relaxed test vectors. The motivating application is the anisotropic diffusion problem, in particular problems with non-grid aligned anisotropy. We demonstrate numerically that the measure yields a robust technique for determining strength of connectivity among variables, for both two-grid and multigrid solvers. %We illustrate the use of the measure to construct, in addition, an adaptive aggregation form of interpolation for the targeted anisotropic problems. %Our approach is not a two-level approach -- we provide preliminary results that show its extendability to multigrid. The proposed algebraic distance measure can also be used in any other coarsening procedure, assuming a rich enough set of the near-kernel components of the matrix for the targeted system is known or computed.
Local Multilevel Preconditioned Jacobi-Davidson Method for Elliptic Eigenvalue Problems on Adaptive Meshes
School of Mathematical Science, Tongji University（同济大学数学科学学院）；Key Laboratory of Intelligent Computing and Applications, Tongji University, Ministry of Education（同济大学教育部智能计算与应用重点实验室）
A hybrid recursive multilevel incomplete factorization preconditioner for solving general linear systems
Johann Bernoulli Institute for Mathematics and Computer Science - University of Groningen（格罗宁根大学）；School of Mathematical Sciences, University of Electronic Science and Technology of China（电子科技大学）
Neutron transport criticality calculations using a parallel monolithic multilevel Schwarz preconditioner together with a nonlinear diffusion acceleration method
Multilevel convergence analysis of multigrid-reduction-in-time
University of Stuttgart（斯图加特大学）；University of Colorado at Boulder（科罗拉多大学博尔德分校）；King’s College London（伦敦国王学院）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；University of New Mexico（新墨西哥大学）
On the approximation of the solution of partial differential equations by artificial neural networks trained by a multilevel Levenberg-Marquardt method
INPT-IRIT, University of Toulouse and ENSEEIHT（INPT-IRIT，图卢兹大学和ENSEEIHT）；ISAE-SUPAERO, University of Toulouse（ISAE-SUPAERO，图卢兹大学）
Nodal Coarsening and Approximate Ideal Interpolation for H(curl) in Algebraic Multigrid
The Pennsylvania State University（宾夕法尼亚州立大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Bergische Universität Wuppertal（伍珀塔尔大学）；University of New Mexico（新墨西哥大学）
Multilevel Preconditioning of Discontinuous-Galerkin Spectral Element Methods, Part I: Geometrically Conforming Meshes
RWTH Aachen（亚琛工业大学）；CNRS, UMR 7598, Laboratoire Jacques-Louis Lions（法国国家科学研究中心，联合研究单位7598，雅克-路易·利翁斯实验室）；UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions（巴黎第六大学，联合研究单位7598，雅克-路易·利翁斯实验室）；Politecnico di Torino（都灵理工大学）
A-posteriori-steered $p$-robust multigrid and domain decomposition methods with optimal step-sizes for mixed finite element discretizations of elliptic problems
TU Wien（维也纳工业大学）；Institute of Mathematics, Czech Academy of Sciences（捷克科学院数学研究所）；Inria（法国国家数字科学与多领域研究所）；Ecole nationale des ponts et chaussées（国立路桥学校）；University of Pittsburgh（匹兹堡大学）
Block preconditioning methods for asymptotic preserving scheme arising in anisotropic elliptic problems
强各向异性椭圆型方程的高效、鲁棒迭代求解是一个极具挑战性的问题。本文提出了一种块预处理方法来求解一类微宏保渐近（MMAP）格式的线性代数系统。MMAP方法由Degond { \it et al.}其中离散矩阵具有$2\times2$块结构。利用近似Schur补构造了一系列块预条件子。我们首先分析一个自然的近似舒尔补，它是原始非AP离散化的系数矩阵。然而，它往往是奇异的非常小的各向异性参数。然后，我们改进它通过使用更合适的近似边界行的确切舒尔补。利用这些块预条件子，建立了求解离散方程组的预条件GMRES迭代法。一些数值试验表明，块预处理方法可以是一个强大的战略方面的网格细化和各向异性的强度。
Two-level convergence of Algebraic Multigrid with Overlapping Smoothers and Spectral Coarse Grids
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Science and Technology Facilities Council, Scientific Computing Department, Rutherford Appleton Laboratory（英国科学与技术设施委员会，科学计算部，卢瑟福阿普尔顿实验室）
University of Colorado at Boulder（科罗拉多大学博尔德分校）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
A Unified Transmissibility-Based Interior Penalty DG Method for Heterogeneous and Anisotropic Diffusion
Observatoire volcanologique du Piton de la Fournaise（富尔内斯火山观测站）；PIMENT, University of La Réunion, ESIROI（留尼汪大学）；ITES, University of Strasbourg, CNRS（斯特拉斯堡大学）
