Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation

DOI10.1137/19M1286815zbMath1448.65235arXiv1910.06986OpenAlexW3035040295MaRDI QIDQ3300854

Delyan Z. Kalchev, Panayot S. Vassilevski

Publication date: 30 July 2020

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.06986

zbMATH Keywords

finite element methodpreconditioningalgebraic multigridstatic condensationinterior penaltyauxiliary spacesecond order elliptic 2D and 3D

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Second-order elliptic equations (35J15) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Preconditioners for iterative methods (65F08)

Related Items (2)

Parallel Element-Based Algebraic Multigrid for \(\boldsymbol{H}\) (curl) and \(\boldsymbol{H}\) (div) Problems Using the ParELAG Library ⋮ A Condensed Constrained Nonconforming Mortar-Based Approach for Preconditioning Finite Element Discretization Problems

Uses Software

• GitHub

Cites Work

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• The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids
• Almost optimal interior penalty discontinuous approximations of symmetric elliptic problems on nonmatching grids
• Smoothed Aggregation Spectral Element Agglomeration AMG: SA-ρAMGe
• Multigrid Smoothers for Ultraparallel Computing
• Multilevel Block Factorization Preconditioners
• On some versions of the element agglomeration AMGe method
• An Interior Penalty Finite Element Method with Discontinuous Elements
• An Elliptic Collocation-Finite Element Method with Interior Penalties
• Spectral AMGe ($\rho$AMGe)
• Two-grid Method for Linear Elasticity on Unstructured Meshes
• Mixed Finite Element Methods and Applications
• An improved convergence analysis of smoothed aggregation algebraic multigrid
• Sparse matrix element topology with application to AMG(e) and preconditioning
• Polynomial of Best Uniform Approximation to and Smoothing in Two-level Methods
• The Mathematical Theory of Finite Element Methods

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