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.
翻译:本文件介绍利用ParELAG(Parallel Element Eglomeration Algebric MultiGridge Application and Solveers)库中实施的基于元素的代数多格(AMGe)等级,为H(curl)和H(div)配方制作多级先决条件和解答器。ParELAG为相容的巢穴空间构建了等级,在每一级别上形成精确的Rham序列。这样可以将混合平滑器应用于所有级别,在粗略水平上应用AMS(辅助-空间Maxwell解答器)或ADS(辅助-空间分解器)或ADS(辅助-空间分解器),获得完整的多格周期。提供了数字结果,显示了拟议方法的平行性能。作为介绍的一部分,本文件展示了ParELAG的一些能力,并概述了图书馆的一些组成部分和程序。