Sponsor
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344 (LLNL-JRNL-824368). The work of the second author was partially supported by NSF under grant DMS-1619640.
Published In
Siam Journal on Scientific Computing
Document Type
Pre-Print
Publication Date
10-15-2023
Abstract
This paper presents the use of element-based algebraic multigrid (AMGe) hierarchies, implemented in the Parallel Element Agglomeration Algebraic Multigrid Upscaling and Solvers (ParELAG) 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 the Auxiliary-Space Maxwell Solver or the 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.
Locate the Document
DOI
10.1137/21M1433253
Persistent Identifier
https://archives.pdx.edu/ds/psu/40927
Publisher
Siam Journal on Scientific Computing
Citation Details
Kalchev, D. Z., Vassilevski, P. S., & Villa, U. (2021). Parallel Element-based Algebraic Multigrid for H (curl) and H (div) Problems Using the ParELAG Library. arXiv preprint arXiv:2107.05613.
Description
Pre-Print