Parallel Element-based Algebraic Multigrid for H(curl) and H(div) Problems Using the ParELAG Library

Abstract

This paper presents the use of element-based algebraic multigrid (AMGe) hierarchies, implemented in the ParELAG (Parallel Element Agglomeration Algebraic Multigrid Upscaling and Solvers) library, to produce multilevel preconditioners and solvers for H(curl) and H(div) formulations. ParELAG constructs hierarchies of compatible nested spaces, forming an exact de Rham sequence on each level. This allows the application of hybrid smoothers on all levels and AMS (Auxiliary-space Maxwell Solver) or ADS (Auxiliary-space Divergence Solver) on the coarsest levels, obtaining complete multigrid cycles. Numerical results are presented, showing the parallel performance of the proposed methods. As a part of the exposition, this paper demonstrates some of the capabilities of ParELAG and outlines some of the components and procedures within the library.

References in corpus (4)

• Finite element exterior calculus: from Hodge theory to numerical stability
• Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions
• Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation
• A Condensed Constrained Nonconforming Mortar-based Approach for Preconditioning Finite Element Discretization Problems

Cited by in corpus (1)

• Scalable Multilevel Monte Carlo Methods Exploiting Parallel Redistribution on Coarse Levels