{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T23:29:39Z","timestamp":1779924579664,"version":"3.53.1"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,7,3]],"date-time":"2020-07-03T00:00:00Z","timestamp":1593734400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,7,3]],"date-time":"2020-07-03T00:00:00Z","timestamp":1593734400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2021,5]]},"DOI":"10.1007\/s11075-020-00961-2","type":"journal-article","created":{"date-parts":[[2020,7,3]],"date-time":"2020-07-03T06:14:55Z","timestamp":1593756895000},"page":"137-160","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A central-line coarse preconditioner for Stokes flows in artery-like domains"],"prefix":"10.1007","volume":"87","author":[{"given":"Yingzhi","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0296-8640","authenticated-orcid":false,"given":"Xiao-Chuan","family":"Cai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2020,7,3]]},"reference":[{"issue":"1","key":"961_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1093\/imanum\/drl017","volume":"27","author":"ZZ Bai","year":"2007","unstructured":"Bai, Z. Z., Golub, G. H.: Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems. IMA J. Numer. Anal. 27 (1), 1\u201323 (2007)","journal-title":"IMA J. Numer. Anal."},{"issue":"5","key":"961_CR2","doi-asserted-by":"publisher","first-page":"881","DOI":"10.1023\/B:BITN.0000014548.26616.65","volume":"43","author":"M Benzi","year":"2003","unstructured":"Benzi, M., Gander, M. J., Golub, G. H.: Optimization of the Hermitian and skew-Hermitian splitting iteration for saddle-point problems. BIT Numer. Math. 43(5), 881\u2013900 (2003)","journal-title":"BIT Numer. Math."},{"issue":"1","key":"961_CR3","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1137\/S0895479802417106","volume":"26","author":"M Benzi","year":"2004","unstructured":"Benzi, M., Golub, G. H.: A preconditioner for generalized saddle point problems. SIAM J. Matrix Anal. Appl. 26(1), 20\u201341 (2004)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"961_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0962492904000212","volume":"14","author":"M Benzi","year":"2005","unstructured":"Benzi, M., Golub, G. H., Liesen, J.: Numerical solution of saddle point problems. Acta Numer. 14, 1\u2013137 (2005)","journal-title":"Acta Numer."},{"issue":"3","key":"961_CR5","doi-asserted-by":"publisher","first-page":"1072","DOI":"10.1137\/S0036142994273343","volume":"34","author":"JH Bramble","year":"1997","unstructured":"Bramble, J. H., Pasciak, J. E., Vassilev, A. T.: Analysis of the inexact Uzawa algorithm for saddle point problems. SIAM J. Numer. Anal. 34 (3), 1072\u20131092 (1997)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"961_CR6","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/s007910100066","volume":"4","author":"S \u010cani\u0107","year":"2002","unstructured":"\u010cani\u0107, S.: Blood flow through compliant vessels after endovascular repair: wall deformations induced by the discontinuous wall properties. Comput. Vis. Sci. 4(3), 147\u2013155 (2002)","journal-title":"Comput. Vis. Sci."},{"issue":"186","key":"961_CR7","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1090\/S0025-5718-1989-0958871-X","volume":"52","author":"J Douglas","year":"1989","unstructured":"Douglas, J., Wang, J. P.: An absolutely stabilized finite element method for the Stokes problem. Math. Comput. 52(186), 495\u2013508 (1989)","journal-title":"Math. Comput."},{"issue":"8","key":"961_CR8","doi-asserted-by":"publisher","first-page":"755","DOI":"10.1002\/(SICI)1097-0363(19960430)22:8<755::AID-FLD377>3.0.CO;2-1","volume":"22","author":"HC Elman","year":"1996","unstructured":"Elman, H. C.: Multigrid and Krylov subspace methods for the discrete Stokes equations. Int. J. Numer. Methods Fluids 22(8), 755\u2013770 (1996)","journal-title":"Int. J. Numer. Methods Fluids"},{"issue":"6","key":"961_CR9","doi-asserted-by":"publisher","first-page":"1645","DOI":"10.1137\/0731085","volume":"31","author":"HC Elman","year":"1994","unstructured":"Elman, H. C., Golub, G. H.: Inexact and preconditioned Uzawa algorithms for saddle point problems. SIAM J. Numer. Anal. 31(6), 1645\u20131661 (1994)","journal-title":"SIAM J. Numer. Anal."},{"issue":"6-7","key":"961_CR10","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1016\/S0045-7825(01)00302-4","volume":"191","author":"L Formaggia","year":"2001","unstructured":"Formaggia, L., Gerbeau, J. F., Nobile, F., Quarteroni, A.: On the coupling of 3D and 1D Navier\u2013Stokes equations for flow problems in compliant vessels. Comput. Methods Appl. Mech. Eng. 191(6-7), 561\u2013582 (2001)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"3-4","key":"961_CR11","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1023\/B:ENGI.0000007980.01347.29","volume":"47","author":"L Formaggia","year":"2003","unstructured":"Formaggia, L., Lamponi, D., Quarteroni, A.: One-dimensional models for blood flow in arteries. J. Eng. Math. 47(3-4), 251\u2013276 (2003)","journal-title":"J. Eng. Math."},{"key":"961_CR12","doi-asserted-by":"crossref","unstructured":"Formaggia, L., Nobile, F., Quarteroni, A.: A One Dimensional Model for Blood Flow: Application to Vascular Prosthesis. In: Mathematical Modeling and Numerical Simulation in Continuum Mechanics, pp. 137\u2013153. Springer (2002)","DOI":"10.1007\/978-3-642-56288-4_10"},{"issue":"2-3","key":"961_CR13","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/s007910050030","volume":"2","author":"L Formaggia","year":"1999","unstructured":"Formaggia, L., Nobile, F., Quarteroni, A., Veneziani, A.: Multiscale modelling of the circulatory system: a preliminary analysis. Comput. Vis. Sci. 2(2-3), 75\u201383 (1999)","journal-title":"Comput. Vis. Sci."},{"key":"961_CR14","doi-asserted-by":"crossref","unstructured":"Gander, M., Xu, Y.: Optimized Schwarz methods with nonoverlapping circular domain decomposition. Mathematics of Computation 86 (2017)","DOI":"10.1090\/mcom\/3127"},{"issue":"4","key":"961_CR15","doi-asserted-by":"publisher","first-page":"1981","DOI":"10.1137\/130946125","volume":"52","author":"MJ Gander","year":"2014","unstructured":"Gander, M. J., Xu, Y.: Optimized Schwarz methods for circular domain decompositions with overlap. SIAM J. Numer. Anal. 52(4), 1981\u20132004 (2014)","journal-title":"SIAM J. Numer. Anal."},{"issue":"6","key":"961_CR16","doi-asserted-by":"publisher","first-page":"3402","DOI":"10.1137\/120887758","volume":"51","author":"G Gigante","year":"2013","unstructured":"Gigante, G., Pozzoli, M., Vergara, C.: Optimized Schwarz methods for the diffusion-reaction problem with cylindrical interfaces. SIAM J. Numer. Anal. 51(6), 3402\u20133430 (2013)","journal-title":"SIAM J. Numer. Anal."},{"key":"961_CR17","unstructured":"Gunzburger, M. D.: Finite element methods for viscous incompressible flows: a guide to theory, practice, and algorithms. Elsevier (2012)"},{"issue":"1","key":"961_CR18","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/0045-7825(87)90184-8","volume":"65","author":"TJ Hughes","year":"1987","unstructured":"Hughes, T. J., Franca, L. P.: A new finite element formulation for computational fluid dynamics: VII. The Stokes problem with various well-posed boundary conditions: symmetric formulations that converge for all velocity\/pressure spaces. Comput. Methods Appl. Mech. Eng. 65(1), 85\u201396 (1987)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"1","key":"961_CR19","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/0045-7825(86)90025-3","volume":"59","author":"TJ Hughes","year":"1986","unstructured":"Hughes, T. J., Franca, L. P., Balestra, M.: A new finite element formulation for computational fluid dynamics: V. Circumventing the babu\u0161ka-brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput. Methods Appl. Mech. Eng. 59(1), 85\u201399 (1986)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"6","key":"961_CR20","doi-asserted-by":"publisher","first-page":"4142","DOI":"10.1137\/080731876","volume":"47","author":"HH Kim","year":"2010","unstructured":"Kim, H. H., Lee, C. O., Park, E. H.: A FETI-DP formulation for the Stokes problem without primal pressure components. SIAM J. Numer. Anal. 47(6), 4142\u20134162 (2010)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"961_CR21","doi-asserted-by":"publisher","first-page":"540","DOI":"10.1137\/S1064827595279575","volume":"19","author":"A Klawonn","year":"1998","unstructured":"Klawonn, A.: An optimal preconditioner for a class of saddle point problems with a penalty term. SIAM J. Sci. Comput. 19(2), 540\u2013552 (1998)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"961_CR22","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1137\/S1064827596303624","volume":"19","author":"A Klawonn","year":"1998","unstructured":"Klawonn, A.: Block-triangular preconditioners for saddle point problems with a penalty term. SIAM J. Sci. Comput. 19(1), 172\u2013184 (1998)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1-4","key":"961_CR23","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1016\/S0045-7825(98)00059-0","volume":"165","author":"A Klawonn","year":"1998","unstructured":"Klawonn, A., Pavarino, L. F.: Overlapping Schwarz methods for mixed linear elasticity and Stokes problems. Comput. Methods Appl. Mech. Eng. 165(1-4), 233\u2013245 (1998)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"1","key":"961_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/(SICI)1099-1506(200001\/02)7:1<1::AID-NLA183>3.0.CO;2-J","volume":"7","author":"A Klawonn","year":"2000","unstructured":"Klawonn, A., Pavarino, L. F.: A comparison of overlapping Schwarz methods and block preconditioners for saddle point problems. Numer. Linear Algebra Appl. 7(1), 1\u201325 (2000)","journal-title":"Numer. Linear Algebra Appl."},{"issue":"2","key":"961_CR25","doi-asserted-by":"publisher","first-page":"C73","DOI":"10.1137\/15M1010567","volume":"38","author":"F Kong","year":"2016","unstructured":"Kong, F., Cai, X. C.: A highly scalable multilevel Schwarz method with boundary geometry preserving coarse spaces for 3D elasticity problems on domains with complex geometry. SIAM J. Sci. Comput. 38(2), C73\u2013C95 (2016)","journal-title":"SIAM J. Sci. Comput."},{"key":"961_CR26","doi-asserted-by":"publisher","first-page":"498","DOI":"10.1016\/j.jcp.2017.03.043","volume":"340","author":"F Kong","year":"2017","unstructured":"Kong, F., Cai, X. C.: A scalable nonlinear fluid\u2013structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D. J. Comput. Phys. 340, 498\u2013518 (2017)","journal-title":"J. Comput. Phys."},{"issue":"4","key":"961_CR27","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1243\/09544119JEIM308","volume":"222","author":"J Lee","year":"2008","unstructured":"Lee, J., Smith, N.: Development and application of a one-dimensional blood flow model for microvascular networks. Proc. Inst. Mech. Eng. Part H: J. Eng. Med. 222(4), 487\u2013511 (2008)","journal-title":"Proc. Inst. Mech. Eng. Part H: J. Eng. Med."},{"issue":"2","key":"961_CR28","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1007\/s00211-005-0653-y","volume":"102","author":"J Li","year":"2005","unstructured":"Li, J.: A dual-primal FETI method for incompressible Stokes equations. Numer. Math. 102(2), 257\u2013275 (2005)","journal-title":"Numer. Math."},{"issue":"6","key":"961_CR29","doi-asserted-by":"publisher","first-page":"2432","DOI":"10.1137\/050628556","volume":"44","author":"J Li","year":"2006","unstructured":"Li, J., Widlund, O.: BDDC Algorithms for incompressible Stokes equations. SIAM J. Numer. Anal. 44(6), 2432\u20132455 (2006)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1-2","key":"961_CR30","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/S0045-7825(99)00326-6","volume":"187","author":"LF Pavarino","year":"2000","unstructured":"Pavarino, L. F.: Indefinite overlapping Schwarz methods for time-dependent Stokes problems. Comput. Methods Appl. Mech. Eng. 187(1-2), 35\u201351 (2000)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"3","key":"961_CR31","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1002\/cpa.10020","volume":"55","author":"LF Pavarino","year":"2002","unstructured":"Pavarino, L. F., Widlund, O.: Balancing Neumann-Neumann methods for incompressible Stokes equations. Commun. Pure Appl. Math. J. Issued Cour. Inst. Math. Sci. 55(3), 302\u2013335 (2002)","journal-title":"Commun. Pure Appl. Math. J. Issued Cour. Inst. Math. Sci."},{"key":"961_CR32","first-page":"3","volume":"12","author":"A Quarteroni","year":"2004","unstructured":"Quarteroni, A., Formaggia, L.: Mathematical modelling and numerical simulation of the cardiovascular system. Handb. Numer. Anal. 12, 3\u2013127 (2004)","journal-title":"Handb. Numer. Anal."},{"key":"961_CR33","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1017\/S0962492917000046","volume":"26","author":"A Quarteroni","year":"2017","unstructured":"Quarteroni, A., Manzoni, A., Vergara, C.: The cardiovascular system: mathematical modelling, numerical algorithms and clinical applications. Acta Numer. 26, 365\u2013590 (2017)","journal-title":"Acta Numer."},{"issue":"3","key":"961_CR34","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1115\/1.3426281","volume":"99","author":"AH Shapiro","year":"1977","unstructured":"Shapiro, A. H.: Steady flow in collapsible tubes. J. Biomech. Eng. 99(3), 126\u2013147 (1977)","journal-title":"J. Biomech. Eng."},{"issue":"6-7","key":"961_CR35","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1002\/fld.543","volume":"43","author":"S Sherwin","year":"2003","unstructured":"Sherwin, S., Formaggia, L., Peiro, J., Franke, V.: Computational modelling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system. Int. J. Numer. Methods Fluids 43(6-7), 673\u2013700 (2003)","journal-title":"Int. J. Numer. Methods Fluids"},{"issue":"3-4","key":"961_CR36","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1023\/B:ENGI.0000007979.32871.e2","volume":"47","author":"S Sherwin","year":"2003","unstructured":"Sherwin, S., Franke, V., Peiro, J., Parker, K.: One-dimensional modelling of a vascular network in space-time variables. J. Eng. Math. 47(3-4), 217\u2013250 (2003)","journal-title":"J. Eng. Math."},{"issue":"3","key":"961_CR37","doi-asserted-by":"publisher","first-page":"990","DOI":"10.1137\/S0036139999355199","volume":"62","author":"N Smith","year":"2002","unstructured":"Smith, N., Pullan, A., Hunter, P.: An anatomically based model of transient coronary blood flow in the heart. SIAM J. Appl. Math. 62(3), 990\u20131018 (2002)","journal-title":"SIAM J. Appl. Math."},{"issue":"1","key":"961_CR38","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1161\/01.RES.13.1.3","volume":"13","author":"VL Streeter","year":"1963","unstructured":"Streeter, V. L., Keitzer, W. F., Bohr, D. F.: Pulsatile pressure and flow through distensible vessels. Circ. Res. 13(1), 3\u201320 (1963)","journal-title":"Circ. Res."},{"key":"961_CR39","doi-asserted-by":"crossref","unstructured":"Toselli, A., Widlund, O.: Domain decomposition methods algorithms and theory. Springer, Berlin (2005)","DOI":"10.1007\/b137868"},{"issue":"2","key":"961_CR40","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1137\/0721019","volume":"21","author":"R Verf\u00fcrth","year":"1984","unstructured":"Verf\u00fcrth, R.: A multilevel algorithm for mixed problems. SIAM J. Numer. Anal. 21(2), 264\u2013271 (1984)","journal-title":"SIAM J. Numer. Anal."},{"issue":"5","key":"961_CR41","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1007\/BF01396361","volume":"54","author":"G Wittum","year":"1989","unstructured":"Wittum, G.: Multi-grid methods for Stokes and Navier-Stokes equations. Numer. Math. 54(5), 543\u2013563 (1989)","journal-title":"Numer. Math."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-020-00961-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-020-00961-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-020-00961-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,2]],"date-time":"2021-07-02T23:45:29Z","timestamp":1625269529000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-020-00961-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,3]]},"references-count":41,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,5]]}},"alternative-id":["961"],"URL":"https:\/\/doi.org\/10.1007\/s11075-020-00961-2","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7,3]]},"assertion":[{"value":"29 October 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 June 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 July 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}