{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:34:18Z","timestamp":1787337258865,"version":"build-2736575974"},"reference-count":65,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1620063"],"award-info":[{"award-number":["DMS-1620063"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,6]]},"abstract":"<jats:p>Advanced finite-element discretizations and preconditioners for models of poroelasticity have attracted significant attention in recent years. The equations of poroelasticity offer significant challenges in both areas, due to the potentially strong coupling between unknowns in the system, saddle-point structure, and the need to account for wide ranges of parameter values, including limiting behavior such as incompressible elasticity. This paper was motivated by an attempt to develop monolithic multigrid preconditioners for the discretization developed in [C. Rodrigo et al., Comput. Methods App. Mech. Engrg, 341 (2018), pp. 467--484]; we show here why this is a difficult task and, as a result, we modify the discretization in [Rodrigo et al.] through the use of a reduced-quadrature approximation, yielding a more \u201csolver-friendly\u201d discretization. Local Fourier analysis is used to optimize parameters in the resulting monolithic multigrid method, allowing a fair comparison between the performance and costs of methods based on Vanka and Braess--Sarazin relaxation. Numerical results are presented to validate the local Fourier analysis predictions and demonstrate efficiency of the algorithms. Finally, a comparison to existing block-factorization preconditioners is also given.<\/jats:p>","DOI":"10.1137\/21m1429072","type":"journal-article","created":{"date-parts":[[2022,6,24]],"date-time":"2022-06-24T11:24:14Z","timestamp":1656069854000},"page":"S54-S81","source":"Crossref","is-referenced-by-count":10,"title":["Monolithic Multigrid for a Reduced-Quadrature Discretization of Poroelasticity"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6603-8840","authenticated-orcid":true,"given":"James H.","family":"Adler","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3476-2487","authenticated-orcid":true,"given":"Yunhui","family":"He","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7533-0416","authenticated-orcid":true,"given":"Xiaozhe","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6364-0684","authenticated-orcid":true,"given":"Scott","family":"MacLachlan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Ohm","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2022,6,24]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2047"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/19M1261250"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-93873-8_1"},{"key":"atypb4","volume-title":"HAZmath: A Simple Finite Element, Graph, and Solver Library","author":"Adler J. 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Sch\u00f6berl,\n                      Robust Multigrid Methods for Parameter Dependent Problems\n                      , Ph.D. thesis, Johannes Kepler Universit\u00e4t Linz, Linz, Austria, 1999."},{"key":"atypb57","volume-title":"F. 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