Parallel Solver for $$\boldsymbol{H}$$ (div) Problems Using Hybridization and AMG

DOI10.1007/978-3-319-52389-7_6zbMath1367.65172OpenAlexW2596931072MaRDI QIDQ5282895

Panayot S. Vassilevski, Chak Shing Lee

Publication date: 17 July 2017

Published in: Lecture Notes in Computational Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-52389-7_6

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) Iterative numerical methods for linear systems (65F10)

Related Items

Preconditioning of a hybridized discontinuous Galerkin finite element method for the Stokes equations, An observation on the uniform preconditioners for the mixed Darcy problem, Multilevel Hierarchical Decomposition of Finite Element White Noise with Application to Multilevel Markov Chain Monte Carlo, Nonlinear multigrid based on local spectral coarsening for heterogeneous diffusion problems, Algebraic Hybridization and Static Condensation with Application to Scalable $H$(div) Preconditioning, Multilevel Hierarchical Decomposition of Finite Element White Noise with Application to Multilevel Markov Chain Monte Carlo, Multilevel Spectral Coarsening for Graph Laplacian Problems with Application to Reservoir Simulation

Uses Software

• BoomerAMG
• PCBDDC

Cites Work

• \textit{BoomerAMG}: A parallel algebraic multigrid solver and preconditioner
• Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method
• PCBDDC: A Class of Robust Dual-Primal Methods in PETSc
• A Block-Diagonal Algebraic Multigrid Preconditioner for the Brinkman Problem
• Mixed and Hybrid Finite Element Methods
• First-Order System Least Squares for Second-Order Partial Differential Equations: Part I
• Preconditioning discrete approximations of the Reissner-Mindlin plate model
• A Preconditioner for Substructuring Based on Constrained Energy Minimization
• A Characterization of Hybridized Mixed Methods for Second Order Elliptic Problems
• Parallel Auxiliary Space AMG Solver for $H(div)$ Problems
• Mixed Generalized Multiscale Finite Element Methods and Applications
• Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces
• Error analysis of variable degree mixed methods for elliptic problems via hybridization
• QuadrilateralH(div) Finite Elements