A hybrid geometric + algebraic multigrid method with semi‐iterative smoothers

DOI10.1002/nla.1925zbMath1340.65301OpenAlexW1954725639MaRDI QIDQ5502411

Xiangmin Jiao, Cao Lu, Nikolaos M. Missirlis

Publication date: 26 August 2015

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

Full work available at URL: https://doi.org/10.1002/nla.1925

zbMATH Keywords

numerical resultsmultigrid methodFEMfinite-elementKrylov subspace methodmesh refinementgeneralized finite differencefinite-volumeChebyshev-Jacobi methodmultistep Jacobi-like relaxation scheme

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Finite difference methods for boundary value problems involving PDEs (65N06) Preconditioners for iterative methods (65F08) Finite volume methods for boundary value problems involving PDEs (65N08)

Related Items (8)

NonInvasive Multigrid For SemiStructured Grids ⋮ A class of new stable, explicit methods to solve the non‐stationary heat equation ⋮ Algebraic Multigrid Using a Stencil–CSR Hybrid Format on GPUs ⋮ Hybrid multigrid methods for high-order discontinuous Galerkin discretizations ⋮ On multigrid methods for solving two-dimensional boundary-value problems ⋮ A comparison of the extrapolated successive overrelaxation and the preconditioned simultaneous displacement methods for augmented linear systems ⋮ Optimal and Low-Memory Near-Optimal Preconditioning of Fully Implicit Runge--Kutta Schemes for Parabolic PDEs ⋮ Multigrid methods 2013

Uses Software

• Matlab
• PETSc
• TetGen
• Triangle
• ML

Cites Work

• Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods. I, II
• Parallel multigrid smoothing: Polynomial versus Gauss--Seidel
• The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids
• Algebraic Multigrid Based on Element Interpolation (AMGe)
• Numerical Methods for Large Eigenvalue Problems
• A Parallel Geometric Multigrid Method for Finite Elements on Octree Meshes
• The Analysis of Smoothers for Multigrid Algorithms
• A Multigrid Tutorial, Second Edition
• An assessment of linear versus nonlinear multigrid methods for unstructured mesh solvers
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