Analysis of a two-level method for anisotropic diffusion equations on aligned and nonaligned grids

DOI10.1002/nla.1847zbMath1313.65324arXiv1105.1173OpenAlexW2593557483MaRDI QIDQ2931538

Guozhu Yu, Ludmil T. Zikatanov, Jin-Chao Xu

Publication date: 25 November 2014

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.1173

zbMATH Keywords

numerical testsiterative methodfinite element discretizationmultigrid convergencePoisson equationtwo-level methodanisotropic problemregular meshGauss-Seidel smootherquasi-uniform mesh

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (3)

Meta-mgnet: meta multigrid networks for solving parameterized partial differential equations ⋮ Algebraic multigrid methods ⋮ An efficient high-order numerical solver for diffusion equations with strong anisotropy

Cites Work

• Algebraic multilevel preconditioning methods. I
• Tensor product type subspace splittings and multilevel iterative methods for anisotropic problems
• Uniform convergence of the multigrid {V}-cycle for an anisotropic problem
• Algebraic Multilevel Preconditioning Methods, II
• Convergence Estimates for Multigrid Algorithms without Regularity Assumptions
• Multilevel Block Factorization Preconditioners
• On the multilevel preconditioning of Crouzeix–Raviart elliptic problems
• Two‐sided bounds on the convergence rate of two‐level methods
• Robust optimal multilevel preconditioners for non‐conforming finite element systems
• Iterative Methods by Space Decomposition and Subspace Correction
• V-cycle Convergence with Unsymmetric Smoothers and Application to an Anisotropic Model Problem
• On Multilevel Preconditioners which are Optimal with Respect to Both Problem and Discretization Parameters
• Convergence analysis of V-Cycle multigrid methods for anisotropic elliptic equations
• ROBUST SUBSPACE CORRECTION METHODS FOR NEARLY SINGULAR SYSTEMS

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