{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,9]],"date-time":"2025-03-09T05:02:48Z","timestamp":1741496568192,"version":"3.38.0"},"reference-count":72,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,12,13]],"date-time":"2024-12-13T00:00:00Z","timestamp":1734048000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,12,13]],"date-time":"2024-12-13T00:00:00Z","timestamp":1734048000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2025,3]]},"DOI":"10.1007\/s40314-024-03003-y","type":"journal-article","created":{"date-parts":[[2024,12,13]],"date-time":"2024-12-13T18:53:01Z","timestamp":1734115981000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fast linear solvers for incompressible CFD simulations with compatible discrete operator schemes"],"prefix":"10.1007","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2036-558X","authenticated-orcid":false,"given":"Yongseok","family":"Jang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8164-4646","authenticated-orcid":false,"given":"J\u00e9r\u00f4me","family":"Bonelle","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4142-7356","authenticated-orcid":false,"given":"Carola","family":"Kruse","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5736-4532","authenticated-orcid":false,"given":"Frank","family":"H\u00fclsemann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8796-8599","authenticated-orcid":false,"given":"Ulrich","family":"R\u00fcde","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,12,13]]},"reference":[{"key":"3003_CR1","doi-asserted-by":"publisher","first-page":"492","DOI":"10.1016\/j.cma.2017.12.004","volume":"331","author":"N Ahmed","year":"2018","unstructured":"Ahmed N, Bartsch C, John V, Wilbrandt U (2018) An assessment of some solvers for saddle point problems emerging from the incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng 331:492\u2013513. https:\/\/doi.org\/10.1016\/j.cma.2017.12.004","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"4","key":"3003_CR2","doi-asserted-by":"publisher","first-page":"886","DOI":"10.1137\/S0895479894278952","volume":"17","author":"PR Amestoy","year":"1996","unstructured":"Amestoy PR, Davis TA, Duff IS (1996) An approximate minimum degree ordering algorithm. SIAM J Matrix Anal Appl 17(4):886\u2013905. https:\/\/doi.org\/10.1137\/S0895479894278952","journal-title":"SIAM J Matrix Anal Appl"},{"issue":"1","key":"3003_CR3","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1137\/S0895479899358194","volume":"23","author":"P Amestoy","year":"2020","unstructured":"Amestoy P, Duff I, L\u2019Excellent J-Y (2020) A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J Matrix Anal Appl 23(1):15\u201341. https:\/\/doi.org\/10.1137\/S0895479899358194","journal-title":"SIAM J Matrix Anal Appl"},{"issue":"3","key":"3003_CR4","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1016\/j.aml.2011.08.015","volume":"25","author":"P Angot","year":"2012","unstructured":"Angot P, Caltagirone J-P, Fabrie P (2012) A new fast method to compute saddle-points in constrained optimization and applications. Appl Math Lett 25(3):245\u2013251. https:\/\/doi.org\/10.1016\/j.aml.2011.08.015","journal-title":"Appl Math Lett"},{"issue":"2","key":"3003_CR5","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1137\/120866543","volume":"34","author":"M Arioli","year":"2013","unstructured":"Arioli M (2013) Generalized Golub-Kahan bidiagonalization and stopping criteria. SIAM J Matrix Anal Appl 34(2):571\u2013592. https:\/\/doi.org\/10.1137\/120866543","journal-title":"SIAM J Matrix Anal Appl"},{"key":"3003_CR6","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1090\/S0273-0979-10-01278-4","volume":"47","author":"DN Arnold","year":"2010","unstructured":"Arnold DN, Falk RS, Winther R (2010) Finite element exterior calculus: from Hodge theory to numerical stability. Bull Am Math Soc (NS) 47:281\u2013354. https:\/\/doi.org\/10.1090\/S0273-0979-10-01278-4","journal-title":"Bull Am Math Soc (NS)"},{"key":"3003_CR7","volume-title":"Studies in linear and nonlinear programming","author":"KJ Arrow","year":"1958","unstructured":"Arrow KJ, Hurwicz L, Uzawa H (1958) Studies in linear and nonlinear programming. Stanford University Press, Stanford"},{"key":"3003_CR8","doi-asserted-by":"publisher","DOI":"10.1137\/21M1429011","author":"P-L Bacq","year":"2022","unstructured":"Bacq P-L, Notay Y (2022) A new semialgebraic two-grid method for Oseen problems. SIAM J Sci Comput. https:\/\/doi.org\/10.1137\/21M1429011","journal-title":"SIAM J Sci Comput"},{"key":"3003_CR9","unstructured":"Balay S, Abhyankar S, Adams MF, Brown J, Brune P, Buschelman K, Dalcin L, Dener A, Eijkhout V, Gropp WD, Kaushik D, Knepley MG, May DA, McInnes LC, Mills RT, Munson T, Rupp K, Sanan P, Smith BF, Zampini S, Zhang H, Zhang H (2021) PETSc users manual. Technical Report ANL-95\/11 - Revision 3.15, Argonne National Laboratory"},{"key":"3003_CR10","unstructured":"Balay S, Abhyankar S, Adams MF, Benson S, Brown J, Brune P, Buschelman K, Constantinescu EM, Dalcin L, Dener A, Eijkhout V, Faibussowitsch J, Gropp WD, Hapla V, Isaac T, Jolivet P, Karpeev D, Kaushik D, Knepley MG, Kong F, Kruger S, May DA, McInnes LC, Mills RT, Mitchell L, Munson T, Roman JE, Rupp K, Sanan P, Sarich J, Smith BF, Zampini S, Zhang H, Zhang H, Zhang J (2022) PETSc Web page. https:\/\/petsc.org\/"},{"issue":"4","key":"3003_CR11","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1137\/0722038","volume":"22","author":"RE Bank","year":"1985","unstructured":"Bank RE, Douglas CC (1985) Sharp estimates for multigrid rates of convergence with general smoothing and acceleration. SIAM J Numer Anal 22(4):617\u2013633. https:\/\/doi.org\/10.1137\/0722038","journal-title":"SIAM J Numer Anal"},{"issue":"1","key":"3003_CR12","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1142\/S0218202512500492","volume":"23","author":"L Beir\u00e3o da Veiga","year":"2013","unstructured":"Beir\u00e3o da Veiga L, Brezzi F, Cangiani A, Manzini G, Marini LD, Russo A (2013) Basic principles of virtual element methods. Math Model Methods Appl Sci 23(1):199\u2013214. https:\/\/doi.org\/10.1142\/S0218202512500492","journal-title":"Math Model Methods Appl Sci"},{"key":"3003_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0962492904000212","volume":"14","author":"M Benzi","year":"2005","unstructured":"Benzi M, Golub GH, Liesen J (2005) Numerical solution of saddle point problems. Acta Numer 14:1\u2013137. https:\/\/doi.org\/10.1017\/S0962492904000212","journal-title":"Acta Numer"},{"issue":"4","key":"3003_CR14","doi-asserted-by":"publisher","first-page":"486","DOI":"10.1002\/fld.2267","volume":"66","author":"M Benzi","year":"2011","unstructured":"Benzi M, Olshanskii MA, Wang Z (2011) Modified augmented Lagrangian preconditioners for the incompressible Navier-Stokes equations. Int J Numer Methods Fluids 66(4):486\u2013508. https:\/\/doi.org\/10.1002\/fld.2267","journal-title":"Int J Numer Methods Fluids"},{"key":"3003_CR15","unstructured":"Bonelle J (2014) Compatible discrete operator schemes on polyhedral meshes for elliptic and Stokes equations. PhD thesis, Universit\u00e9 Paris-Est \u2013 \u00c9cole des Ponts"},{"issue":"2","key":"3003_CR16","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1051\/m2an\/2013104","volume":"48","author":"J Bonelle","year":"2014","unstructured":"Bonelle J, Ern A (2014) Analysis of compatible discrete operator schemes for elliptic problems on polyhedral meshes. ESAIM Math Model Numer Anal 48(2):553\u2013581. https:\/\/doi.org\/10.1051\/m2an\/2013104","journal-title":"ESAIM Math Model Numer Anal"},{"issue":"4","key":"3003_CR17","doi-asserted-by":"publisher","first-page":"1672","DOI":"10.1093\/imanum\/dru051","volume":"35","author":"J Bonelle","year":"2015","unstructured":"Bonelle J, Ern A (2015) Analysis of compatible discrete operator schemes for the Stokes equations on polyhedral meshes. IMA J Numer Anal 35(4):1672\u20131697. https:\/\/doi.org\/10.1093\/imanum\/dru051","journal-title":"IMA J Numer Anal"},{"key":"3003_CR18","doi-asserted-by":"publisher","unstructured":"Bonelle J, Ern A, Milani R (2020) Compatible discrete operator schemes for the steady incompressible Stokes and Navier\u2013Stokes equations. In: Kl\u00f6fkorn R, Keilegavlen E, Radu FA, Fuhrmann J (eds) International conference on finite volumes for complex applications. Springer, Berlin, pp 93\u2013101. https:\/\/doi.org\/10.1007\/978-3-030-43651-3_6","DOI":"10.1007\/978-3-030-43651-3_6"},{"key":"3003_CR19","first-page":"17","volume":"6","author":"A Bossavit","year":"1998","unstructured":"Bossavit A (1998) On the geometry of electromagnetism. J Japan Soc Appl Electromagn Mech 6:17\u2013281","journal-title":"J Japan Soc Appl Electromagn Mech"},{"issue":"1\u20134","key":"3003_CR20","first-page":"23","volume":"19","author":"A Brandt","year":"1986","unstructured":"Brandt A (1986) Algebraic multigrid theory: the symmetric case. Appl Math Comput 19(1\u20134):23\u201356","journal-title":"Appl Math Comput"},{"key":"3003_CR21","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970753","author":"A Brandt","year":"2011","unstructured":"Brandt A, Livne OE (2011) Multigrid techniques: 1984 guide with applications to fluid dynamics. SIAM, Philadelphia, Revised. https:\/\/doi.org\/10.1137\/1.9781611970753","journal-title":"SIAM, Philadelphia, Revised."},{"key":"3003_CR22","unstructured":"Brandt A, McCormick S, Huge J (1985) Algebraic multigrid (AMG) for sparse matrix equations. Sparsity Appl 257"},{"key":"3003_CR23","doi-asserted-by":"publisher","unstructured":"Brezzi F, Fortin M (1991) Mixed and hybrid finite element methods. Springer series in computational mathematics. Springer, New York. https:\/\/doi.org\/10.1007\/978-1-4612-3172-1","DOI":"10.1007\/978-1-4612-3172-1"},{"issue":"5","key":"3003_CR24","doi-asserted-by":"publisher","first-page":"1872","DOI":"10.1137\/040613950","volume":"43","author":"F Brezzi","year":"2005","unstructured":"Brezzi F, Lipnikov K, Shashkov M (2005) Convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes. SIAM J Numer Anal 43(5):1872\u20131896. https:\/\/doi.org\/10.1137\/040613950","journal-title":"SIAM J Numer Anal"},{"key":"3003_CR25","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719505","author":"WL Briggs","year":"2000","unstructured":"Briggs WL, Henson VE, McCormick SF (2000) A multigrid tutorial. SIAM, Philadelphia. https:\/\/doi.org\/10.1137\/1.9780898719505","journal-title":"SIAM, Philadelphia."},{"issue":"1","key":"3003_CR26","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1017\/S0022112066000545","volume":"24","author":"OR Burggraf","year":"1966","unstructured":"Burggraf OR (1966) Analytical and numerical studies of the structure of steady separated flows. J Fluid Mech 24(1):113\u2013151. https:\/\/doi.org\/10.1017\/S0022112066000545","journal-title":"J Fluid Mech"},{"issue":"19","key":"3003_CR27","doi-asserted-by":"publisher","first-page":"7401","DOI":"10.1016\/j.jcp.2010.06.023","volume":"229","author":"L Codecasa","year":"2010","unstructured":"Codecasa L, Specogna R, Trevisan F (2010) A new set of basis functions for the discrete geometric approach. J Comput Phys 229(19):7401\u20137410. https:\/\/doi.org\/10.1016\/j.jcp.2010.06.023","journal-title":"J Comput Phys"},{"issue":"4","key":"3003_CR28","doi-asserted-by":"publisher","first-page":"1019","DOI":"10.1137\/040615729","volume":"27","author":"H De Sterck","year":"2006","unstructured":"De Sterck H, Yang UM, Heys JJ (2006) Reducing complexity in parallel algebraic multigrid preconditioners. SIAM J Matrix Anal Appl 27(4):1019\u20131039. https:\/\/doi.org\/10.1137\/040615729","journal-title":"SIAM J Matrix Anal Appl"},{"key":"3003_CR29","unstructured":"Desbrun M, Hirani AN, Leok M, Marsden JE (2005) Discrete exterior calculus. arXiv: http:\/\/arxiv.org\/abs\/math\/0508341"},{"issue":"1","key":"3003_CR30","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1007\/s10208-021-09542-8","volume":"23","author":"DA Di Pietro","year":"2023","unstructured":"Di Pietro DA, Droniou J (2023) An arbitrary-order discrete de Rham complex on polyhedral meshes: exactness, poincar\u00e9 inequalities, and consistency. Found Comput Math 23(1):85\u2013164. https:\/\/doi.org\/10.1007\/s10208-021-09542-8","journal-title":"Found Comput Math"},{"issue":"291","key":"3003_CR31","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1090\/S0025-5718-2014-02861-5","volume":"84","author":"DA Di Pietro","year":"2015","unstructured":"Di Pietro DA, Lemaire S (2015) An extension of the Crouzeix-Raviart space to general meshes with application to quasi-incompressible linear elasticity and Stokes flow. Math Comput 84(291):1\u201331. https:\/\/doi.org\/10.1090\/S0025-5718-2014-02861-5","journal-title":"Math Comput"},{"issue":"4","key":"3003_CR32","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1515\/cmam-2014-0018","volume":"14","author":"DA Di Pietro","year":"2014","unstructured":"Di Pietro DA, Ern A, Lemaire S (2014) An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators. Comput Methods Appl Math 14(4):461\u2013472. https:\/\/doi.org\/10.1515\/cmam-2014-0018","journal-title":"Comput Methods Appl Math"},{"issue":"2","key":"3003_CR33","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1142\/S0218202510004222","volume":"20","author":"J Droniou","year":"2010","unstructured":"Droniou J, Eymard R, Gallou\u00ebt T, Herbin R (2010) A unified approach to mimetic finite difference, hybrid finite volume and mixed finite volume methods. Math Model Methods Appl Sci 20(2):265\u2013295. https:\/\/doi.org\/10.1142\/S0218202510004222","journal-title":"Math Model Methods Appl Sci"},{"key":"3003_CR34","doi-asserted-by":"publisher","unstructured":"Dumitrasc A, Kruse C, Ruede U (2023) Generalized Golub\u2013Kahan bidiagonalization for nonsymmetric saddle point systems. https:\/\/doi.org\/10.48550\/arXiv.2310.06952","DOI":"10.48550\/arXiv.2310.06952"},{"issue":"2","key":"3003_CR35","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1137\/0720023","volume":"20","author":"SC Eisenstat","year":"1983","unstructured":"Eisenstat SC, Elman HC, Schultz MH (1983) Variational iterative methods for nonsymmetric systems of linear equations. SIAM J Numer Anal 20(2):345\u2013357. https:\/\/doi.org\/10.1137\/0720023","journal-title":"SIAM J Numer Anal"},{"key":"3003_CR36","doi-asserted-by":"publisher","unstructured":"Elman H, Silvester D, Wathen A (2014) Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics, 2nd edn. Oxford University Press, Oxford, New York. https:\/\/doi.org\/10.1093\/acprof:oso\/9780199678792.001.0001","DOI":"10.1093\/acprof:oso\/9780199678792.001.0001"},{"key":"3003_CR37","doi-asserted-by":"publisher","unstructured":"Falgout RD, Yang UM (2002) hypre: A library of high performance preconditioners. In: Sloot PMA, Hoekstra AG, Tan CJK, Dongarra JJ (eds) Computational science \u2014 ICCS 2002, lecture notes in computer science. Springer, Berlin. https:\/\/doi.org\/10.1007\/3-540-47789-6_66","DOI":"10.1007\/3-540-47789-6_66"},{"key":"3003_CR38","doi-asserted-by":"publisher","unstructured":"Falgout RD, Jones JE, Yang UM (2006) The design and implementation of hypre, a library of parallel high performance preconditioners. In: Bruaset AM, Tveito A (eds) Numerical solution of partial differential equations on parallel computers. Springer, Berlin, pp 267\u2013294https:\/\/doi.org\/10.1007\/3-540-31619-1_8","DOI":"10.1007\/3-540-31619-1_8"},{"key":"3003_CR39","doi-asserted-by":"publisher","DOI":"10.1002\/9781119618737","author":"I Farahbakhsh","year":"2020","unstructured":"Farahbakhsh I (2020) Krylov subspace methods with application in incompressible fluid flow solvers. Wiley, Hoboken. https:\/\/doi.org\/10.1002\/9781119618737","journal-title":"Wiley, Hoboken."},{"issue":"5","key":"3003_CR40","doi-asserted-by":"publisher","first-page":"3073","DOI":"10.1137\/18M1219370","volume":"41","author":"PE Farrell","year":"2019","unstructured":"Farrell PE, Mitchell L, Wechsung F (2019) An augmented Lagrangian preconditioner for the 3D stationary incompressible Navier-Stokes equations at high Reynolds number. SIAM J Sci Comput 41(5):3073\u20133096. https:\/\/doi.org\/10.1137\/18M1219370","journal-title":"SIAM J Sci Comput"},{"key":"3003_CR41","unstructured":"Fortin M, Glowinski R (1983) Augmented Lagrangian methods: applications to the numerical solution of boundary-value problems vol. 15 in studies in mathematics and its applications. North-Holland Publishing Co., Amsterdam"},{"issue":"3","key":"3003_CR42","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1016\/0021-9991(82)90058-4","volume":"48","author":"U Ghia","year":"1982","unstructured":"Ghia U, Ghia KN, Shin CT (1982) High-re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. J Comput Phys 48(3):387\u2013411. https:\/\/doi.org\/10.1016\/0021-9991(82)90058-4","journal-title":"J Comput Phys"},{"key":"3003_CR43","doi-asserted-by":"publisher","first-page":"276","DOI":"10.4208\/nmtma.2010.33.2","volume":"3","author":"L Giraud","year":"2010","unstructured":"Giraud L, Haidar A, Saad Y (2010) Sparse approximations of the Schur complement for parallel algebraic hybrid linear solvers in 3D. Numer Math Theor Meth Appl 3:276\u2013294. https:\/\/doi.org\/10.4208\/nmtma.2010.33.2","journal-title":"Numer Math Theor Meth Appl"},{"issue":"6","key":"3003_CR44","doi-asserted-by":"publisher","first-page":"2076","DOI":"10.1137\/S1064827500375096","volume":"24","author":"GH Golub","year":"2003","unstructured":"Golub GH, Greif C (2003) On solving block-structured indefinite linear systems. SIAM J Sci Comput 24(6):2076\u20132092. https:\/\/doi.org\/10.1137\/S1064827500375096","journal-title":"SIAM J Sci Comput"},{"key":"3003_CR45","doi-asserted-by":"publisher","first-page":"409","DOI":"10.6028\/jres.049.044","volume":"49","author":"MR Hestenes","year":"1952","unstructured":"Hestenes MR, Stiefel E (1952) Methods of conjugate gradients for solving linear systems. J Res Natl Bur Stand 49:409\u2013435. https:\/\/doi.org\/10.6028\/jres.049.044","journal-title":"J Res Natl Bur Stand"},{"key":"3003_CR46","volume-title":"Deriving mimetic difference approximations to differential operators using algebraic topology","author":"J Hyman","year":"1988","unstructured":"Hyman J, Scovel J (1988) Deriving mimetic difference approximations to differential operators using algebraic topology. Los Alamos National Laboratory, Los Alamos"},{"key":"3003_CR47","unstructured":"hypre: High Performance Preconditioners. https:\/\/llnl.gov\/casc\/hypre, https:\/\/github.com\/hypre-space\/hypre"},{"issue":"5","key":"3003_CR48","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1137\/19M1249060","volume":"42","author":"F Kong","year":"2020","unstructured":"Kong F, Wang Y, Gaston DR, Permann CJ, Slaughter AE, Lindsay AD, DeHart MD, Martineau RC (2020) A highly parallel multilevel Newton-Krylov-Schwarz method with subspace-based coarsening and partition-based balancing for the multigroup neutron transport equation on three-dimensional unstructured meshes. SIAM J Sci Comput 42(5):193\u2013220. https:\/\/doi.org\/10.1137\/19M1249060","journal-title":"SIAM J Sci Comput"},{"issue":"1","key":"3003_CR49","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1186\/s40323-020-00181-2","volume":"7","author":"C Kruse","year":"2020","unstructured":"Kruse C, Darrigrand V, Tardieu N, Arioli M, R\u00fcde U (2020) Application of an iterative Golub-Kahan algorithm to structural mechanics problems with multi-point constraints. Adv Model Simul Eng Sci 7(1):45. https:\/\/doi.org\/10.1186\/s40323-020-00181-2","journal-title":"Adv Model Simul Eng Sci"},{"key":"3003_CR50","doi-asserted-by":"publisher","unstructured":"Kruse C, Sosonkina M, Arioli M, Tardieu N, R\u00fcde U (2020b) Parallel performance of an iterative solver based on the Golub\u2013Kahan bidiagonalization. In: Wyrzykowski R, Deelman E, Dongarra J, Karczewski K (eds) Parallel processing and applied mathematics. Lecture notes in computer science. Springer International Publishing, Cham, pp 104\u2013116. https:\/\/doi.org\/10.1007\/978-3-030-43229-4_10","DOI":"10.1007\/978-3-030-43229-4_10"},{"issue":"11","key":"3003_CR51","doi-asserted-by":"publisher","first-page":"5914","DOI":"10.1002\/cpe.5914","volume":"33","author":"C Kruse","year":"2021","unstructured":"Kruse C, Sosonkina M, Arioli M, Tardieu N, R\u00fcde U (2021) Parallel solution of saddle point systems with nested iterative solvers based on the Golub-Kahan bidiagonalization. Concur Comp Pract Exp 33(11):5914. https:\/\/doi.org\/10.1002\/cpe.5914","journal-title":"Concur Comp Pract Exp"},{"issue":"2","key":"3003_CR52","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1515\/cmam-2014-0004","volume":"14","author":"IV Lashuk","year":"2014","unstructured":"Lashuk IV, Vassilevski PS (2014) The construction of the coarse de Rham complexes with improved approximation properties. Comput Methods Appl Math 14(2):257\u2013303. https:\/\/doi.org\/10.1515\/cmam-2014-0004","journal-title":"Comput Methods Appl Math"},{"key":"3003_CR53","doi-asserted-by":"publisher","unstructured":"Lin PT, Shadid JN, Tsuji PH (2020). In: Brummelen H, Corsini A, Perotto S, Rozza G (eds) Krylov smoothing for fully-coupled AMG preconditioners for VMS resistive MHD. Springer, Cham, pp 277\u2013286. https:\/\/doi.org\/10.1007\/978-3-030-30705-9_24","DOI":"10.1007\/978-3-030-30705-9_24"},{"key":"3003_CR54","doi-asserted-by":"publisher","unstructured":"Meurant G, Tebbens JD (2020) Krylov methods for nonsymmetric linear systems: from theory to computations. S. Comp. Math. Springer International Publishing, Cham, Spr.https:\/\/doi.org\/10.1007\/978-3-030-55251-0","DOI":"10.1007\/978-3-030-55251-0"},{"key":"3003_CR55","unstructured":"Milani R (2020) Compatible Discrete Operator schemes for the unsteady, incompressible Navier\u2013Stokes equations. PhD Thesis, Universit\u00e9 Paris Est"},{"issue":"4","key":"3003_CR56","doi-asserted-by":"publisher","first-page":"1444","DOI":"10.1137\/S1064827599362314","volume":"22","author":"Y Notay","year":"2000","unstructured":"Notay Y (2000) Flexible conjugate gradients. SIAM J Sci Comput 22(4):1444\u20131460. https:\/\/doi.org\/10.1137\/S1064827599362314","journal-title":"SIAM J Sci Comput"},{"issue":"6","key":"3003_CR57","first-page":"123","volume":"37","author":"Y Notay","year":"2010","unstructured":"Notay Y (2010) An aggregation-based algebraic multigrid method. Electron Trans Numer Anal 37(6):123\u2013146","journal-title":"Electron Trans Numer Anal"},{"issue":"4","key":"3003_CR58","doi-asserted-by":"publisher","first-page":"2288","DOI":"10.1137\/110835347","volume":"34","author":"Y Notay","year":"2012","unstructured":"Notay Y (2012) Aggregation-based algebraic multigrid for convection-diffusion equations. SIAM J Sci Comput 34(4):2288\u20132316. https:\/\/doi.org\/10.1137\/110835347","journal-title":"SIAM J Sci Comput"},{"key":"3003_CR59","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1007\/s00211-015-0710-0","volume":"132","author":"Y Notay","year":"2016","unstructured":"Notay Y (2016) A new multigrid approach for Stokes problems. Numer Math 132:51\u201384. https:\/\/doi.org\/10.1007\/s00211-015-0710-0","journal-title":"Numer Math"},{"issue":"5","key":"3003_CR60","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1137\/16M1071419","volume":"39","author":"Y Notay","year":"2017","unstructured":"Notay Y (2017) Algebraic multigrid for Stokes equations. SIAM J Sci Comput 39(5):88\u2013111. https:\/\/doi.org\/10.1137\/16M1071419","journal-title":"SIAM J Sci Comput"},{"issue":"5","key":"3003_CR61","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1002\/nla.542","volume":"15","author":"Y Notay","year":"2008","unstructured":"Notay Y, Vassilevski PS (2008) Recursive Krylov-based multigrid cycles. Numer Linear Algebra Appl 15(5):473\u2013487. https:\/\/doi.org\/10.1002\/nla.542","journal-title":"Numer Linear Algebra Appl"},{"key":"3003_CR62","doi-asserted-by":"publisher","first-page":"1394","DOI":"10.1016\/j.jcp.2013.08.005","volume":"257","author":"A Palha","year":"2014","unstructured":"Palha A, Pinto Rebelo P, Hiemstra R, Kreeft J, Gerritsma M (2014) Physics-compatible discretization techniques on single and dual grids, with application to the Poisson equation of volume forms. J Comput Phys 257:1394\u20131422. https:\/\/doi.org\/10.1016\/j.jcp.2013.08.005","journal-title":"J Comput Phys"},{"key":"3003_CR63","doi-asserted-by":"publisher","unstructured":"Ruge JW, St\u00fcben K (1987) Algebraic multigrid. pp 73\u2013130. https:\/\/doi.org\/10.1137\/1.9781611971057.ch4","DOI":"10.1137\/1.9781611971057.ch4"},{"issue":"2","key":"3003_CR64","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1137\/0914028","volume":"14","author":"Y Saad","year":"1993","unstructured":"Saad Y (1993) A flexible inner-outer preconditioned GMRES algorithm. SIAM J Sci Comput 14(2):461\u2013469. https:\/\/doi.org\/10.1137\/0914028","journal-title":"SIAM J Sci Comput"},{"key":"3003_CR65","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718003","author":"Y Saad","year":"2003","unstructured":"Saad Y (2003) Iterative methods for sparse linear systems. SIAM, Philadelphia. https:\/\/doi.org\/10.1137\/1.9780898718003","journal-title":"SIAM, Philadelphia."},{"issue":"3","key":"3003_CR66","doi-asserted-by":"publisher","first-page":"856","DOI":"10.1137\/0907058","volume":"7","author":"Y Saad","year":"1986","unstructured":"Saad Y, Schultz MH (1986) GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7(3):856\u2013869. https:\/\/doi.org\/10.1137\/0907058","journal-title":"SIAM J Sci Stat Comput"},{"issue":"3","key":"3003_CR67","doi-asserted-by":"publisher","first-page":"245","DOI":"10.4208\/nmtma.2010.33.1","volume":"3","author":"A Segal","year":"2010","unstructured":"Segal A, Ur Rehman M, Vuik C (2010) Preconditioners for incompressible Navier-Stokes solvers. Numer Math Theor Meth Appl 3(3):245\u2013275. https:\/\/doi.org\/10.4208\/nmtma.2010.33.1","journal-title":"Numer Math Theor Meth Appl"},{"key":"3003_CR68","doi-asserted-by":"publisher","unstructured":"St\u00fcben K (2001) A review of algebraic multigrid. J Comput Appl Math 128(1):281\u2013309. https:\/\/doi.org\/10.1016\/S0377-0427(00)00516-1. (Numerical Analysis 2000. Vol. VII: Partial Differential Equations)","DOI":"10.1016\/S0377-0427(00)00516-1"},{"key":"3003_CR69","volume-title":"Multigrid","author":"U Trottenberg","year":"2000","unstructured":"Trottenberg U, Oosterlee CW, Sch\u00fcller A (2000) Multigrid. Elsevier, San Diego"},{"issue":"10","key":"3003_CR70","doi-asserted-by":"publisher","first-page":"1180","DOI":"10.1002\/FLD.2235","volume":"65","author":"M Ur Rehman","year":"2011","unstructured":"Ur Rehman M, Geenen T, Vuik C, Segal G, MacLachlan S (2011) On iterative methods for the incompressible Stokes problem. Int J Numer Methods Fluids 65(10):1180\u20131200. https:\/\/doi.org\/10.1002\/FLD.2235","journal-title":"Int J Numer Methods Fluids"},{"issue":"3","key":"3003_CR71","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1007\/BF02238511","volume":"56","author":"P Van\u011bk","year":"1996","unstructured":"Van\u011bk P, Mandel J, Brezina M (1996) Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. Computing 56(3):179\u2013196. https:\/\/doi.org\/10.1007\/BF02238511","journal-title":"Computing"},{"key":"3003_CR72","doi-asserted-by":"publisher","first-page":"591","DOI":"10.1017\/S0962492917000083","volume":"26","author":"J Xu","year":"2017","unstructured":"Xu J, Zikatanov L (2017) Algebraic multigrid methods. Acta Numer 26:591. https:\/\/doi.org\/10.1017\/S0962492917000083","journal-title":"Acta Numer"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-03003-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-024-03003-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-03003-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,8]],"date-time":"2025-03-08T07:58:40Z","timestamp":1741420720000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-024-03003-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,13]]},"references-count":72,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,3]]}},"alternative-id":["3003"],"URL":"https:\/\/doi.org\/10.1007\/s40314-024-03003-y","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2024,12,13]]},"assertion":[{"value":"16 April 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 September 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 November 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 December 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"79"}}