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

TL;DR

This paper introduces a parallel algebraic multigrid method for H(curl) and H(div) problems using the ParELAG library, demonstrating effective multilevel preconditioning and solver performance.

Contribution

It develops a novel element-based algebraic multigrid hierarchy that preserves the de Rham sequence for H(curl) and H(div) problems within the ParELAG library.

Findings

Effective parallel multigrid preconditioners for H(curl) and H(div) problems.

Numerical results show good parallel scalability.

Demonstrates capabilities and components of 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.