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Sci. Comput."],"published-print":{"date-parts":[[2023,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>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 [Formula: see text] and [Formula: see text] 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.<\/jats:p>","DOI":"10.1137\/21m1433253","type":"journal-article","created":{"date-parts":[[2023,6,28]],"date-time":"2023-06-28T17:17:07Z","timestamp":1687972627000},"page":"S371-S400","source":"Crossref","is-referenced-by-count":3,"title":["Parallel Element-Based Algebraic Multigrid for   \\(\\boldsymbol{H}\\)  (c\n                    <u>ur<\/u>\n                    l) and   \\(\\boldsymbol{H}\\)  (div) Problems Using the ParELAG Library"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2251-1827","authenticated-orcid":true,"given":"Delyan Z.","family":"Kalchev","sequence":"first","affiliation":[{"name":"Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA 94551 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Panayot S.","family":"Vassilevski","sequence":"additional","affiliation":[{"name":"Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA 94551 USA."},{"name":"Department of Mathematics and Statistics, Portland State University, Portland, OR 97207 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5142-2559","authenticated-orcid":true,"given":"Umberto","family":"Villa","sequence":"additional","affiliation":[{"name":"Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX 78712 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,6,26]]},"reference":[{"key":"ref1","unstructured":"HYPRE: Scalable Linear Solvers and Multigrid Methods, http:\/\/computing.llnl.gov\/projects\/hypre-scalable-linear-solvers-multigrid-methods."},{"key":"ref2","unstructured":"METIS: Graph Partitioning and Fill-Reducing Matrix Ordering, http:\/\/glaros.dtc.umn.edu\/gkhome\/views\/metis."},{"key":"ref3","unstructured":"MFEM: Modular Finite Element Methods Library, https:\/\/doi.org\/10.11578\/dc.20171025.1248, http:\/\/mfem.org."},{"key":"ref4","unstructured":"ParELAG Mini Applications in MFEM, http:\/\/github.com\/mfem\/mfem\/tree\/master\/miniapps\/parelag."},{"key":"ref5","unstructured":"ParELAG: Parallel Element Agglomeration Algebraic Multigrid Upscaling and Solvers, http:\/\/github.com\/LLNL\/parelag."},{"key":"ref6","unstructured":"STRUMPACK: Structured Matrix Package, http:\/\/portal.nersc.gov\/project\/sparse\/strumpack."},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1137\/130943091"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-7172-1_1"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202512500248"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-97-00826-0"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1007\/PL00005386"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-10-01278-4"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1137\/100798806"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1002\/nla.577"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827502407706"},{"key":"ref16","first-page":"186","volume":"15","author":"Bochev P. 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