{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T00:00:58Z","timestamp":1769212858981,"version":"3.49.0"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2014,12,4]],"date-time":"2014-12-04T00:00:00Z","timestamp":1417651200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2015,10]]},"DOI":"10.1007\/s00211-014-0693-2","type":"journal-article","created":{"date-parts":[[2014,12,3]],"date-time":"2014-12-03T19:06:47Z","timestamp":1417633607000},"page":"369-404","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Analysis and optimization of the generalized Schwarz method for elliptic problems with application to fluid\u2013structure interaction"],"prefix":"10.1007","volume":"131","author":[{"given":"Giacomo","family":"Gigante","sequence":"first","affiliation":[]},{"given":"Christian","family":"Vergara","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,12,4]]},"reference":[{"issue":"6","key":"693_CR1","doi-asserted-by":"crossref","first-page":"4041","DOI":"10.1137\/090749694","volume":"31","author":"M Astorino","year":"2009","unstructured":"Astorino, M., Chouly, F., Fern\u00e1ndez, M.: Robin based semi-implicit coupling in fluid\u2013structure interaction: stability analysis and numerics. SIAM J. Sci. Comput. 31(6), 4041\u20134065 (2009)","journal-title":"SIAM J. Sci. Comput."},{"key":"693_CR2","doi-asserted-by":"crossref","first-page":"7027","DOI":"10.1016\/j.jcp.2008.04.006","volume":"227","author":"S Badia","year":"2008","unstructured":"Badia, S., Nobile, F., Vergara, C.: Fluid\u2013structure partitioned procedures based on Robin transmission conditions. J. Comput. Phys. 227, 7027\u20137051 (2008)","journal-title":"J. Comput. Phys."},{"issue":"33\u201336","key":"693_CR3","doi-asserted-by":"crossref","first-page":"2768","DOI":"10.1016\/j.cma.2009.04.004","volume":"198","author":"S Badia","year":"2009","unstructured":"Badia, S., Nobile, F., Vergara, C.: Robin\u2013Robin preconditioned Krylov methods for fluid\u2013structure interaction problems. Comput. Methods Appl. Mech. Eng. 198(33\u201336), 2768\u20132784 (2009)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"4","key":"693_CR4","doi-asserted-by":"crossref","first-page":"1778","DOI":"10.1137\/070680497","volume":"30","author":"S Badia","year":"2008","unstructured":"Badia, S., Quaini, A., Quarteroni, A.: Splitting methods based on algebraic factorization for fluid\u2013structure interaction. SIAM J. Sci. Comput. 30(4), 1778\u20131805 (2008)","journal-title":"SIAM J. Sci. Comput."},{"issue":"42\u201344","key":"693_CR5","doi-asserted-by":"crossref","first-page":"4506","DOI":"10.1016\/j.cma.2004.12.005","volume":"194","author":"P Causin","year":"2005","unstructured":"Causin, P., Gerbeau, J.F., Nobile, F.: Added-mass effect in the design of partitioned algorithms for fluid\u2013structure problems. Comput. Methods Appl. Mech. Eng. 194(42\u201344), 4506\u20134527 (2005)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"41\u201343","key":"693_CR6","doi-asserted-by":"crossref","first-page":"5797","DOI":"10.1016\/j.cma.2005.09.029","volume":"195","author":"S Deparis","year":"2006","unstructured":"Deparis, S., Discacciati, M., Fourestey, G., Quarteroni, A.: Fluid\u2013structure algorithms based on Steklov\u2013Poincar\u00e9 operators. Comput. Methods Appl. Mech. Eng. 195(41\u201343), 5797\u20135812 (2006)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"3","key":"693_CR7","doi-asserted-by":"crossref","first-page":"2193","DOI":"10.1137\/080728536","volume":"31","author":"V Dolean","year":"2009","unstructured":"Dolean, V., Gander, M.J., Gerardo Giorda, L.: Optimized Schwarz methods for Maxwell\u2019s equations. SIAM J. Sci. Comput. 31(3), 2193\u20132213 (2009)","journal-title":"SIAM J. Sci. Comput."},{"key":"693_CR8","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1016\/0045-7825(82)90128-1","volume":"33","author":"J Donea","year":"1982","unstructured":"Donea, J.: An arbitrary Lagrangian\u2013Eulerian finite element method for transient dynamic fluid\u2013structure interaction. Comput. Methods Appl. Mech. Eng. 33, 689\u2013723 (1982)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"693_CR9","first-page":"181","volume-title":"Domain Decomposition Methods in Science and Engineering XVI","author":"O Dubois","year":"2006","unstructured":"Dubois, O.: Optimized Schwarz methods with Robin conditions for the advection\u2013diffusion equation. In: Widlund, O.B., Keyes, D.E. (eds.) Domain Decomposition Methods in Science and Engineering XVI, pp. 181\u2013188. Springer-Verlag, New York (2006)"},{"issue":"4","key":"693_CR10","doi-asserted-by":"crossref","first-page":"794","DOI":"10.1002\/nme.1792","volume":"69","author":"MA Fern\u00e1ndez","year":"2007","unstructured":"Fern\u00e1ndez, M.A., Gerbeau, J.F., Grandmont, C.: A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid. Int. J. Numer. Methods Eng. 69(4), 794\u2013821 (2007)","journal-title":"Int. J. Numer. Methods Eng."},{"key":"693_CR11","volume-title":"Introduction to Partial Differential Equations","author":"GB Folland","year":"1995","unstructured":"Folland, G.B.: Introduction to Partial Differential Equations. Princeton University Press, Princeton (1995)"},{"key":"693_CR12","doi-asserted-by":"crossref","unstructured":"Formaggia, L., Quarteroni, A., Veneziani, A. (eds.): Cardiovascular Mathematics-Modeling and Simulation of the Circulatory System. Springer, Milan (2009)","DOI":"10.1007\/978-88-470-1152-6"},{"key":"693_CR13","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.jcp.2012.08.001","volume":"244","author":"L Formaggia","year":"2013","unstructured":"Formaggia, L., Quarteroni, A., Vergara, C.: On the physical consistency between three-dimensional and one-dimensional models in haemodynamics. J. Comput. Phys. 244, 97\u2013112 (2013)","journal-title":"J. Comput. Phys."},{"issue":"7","key":"693_CR14","doi-asserted-by":"crossref","first-page":"1278","DOI":"10.1016\/j.cma.2006.09.002","volume":"196","author":"C Forster","year":"2007","unstructured":"Forster, C., Wall, W., Ramm, E.: Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flow. Comput. Methods Appl. Mech. Eng. 196(7), 1278\u20131293 (2007)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"2","key":"693_CR15","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1137\/S0036142903425409","volume":"44","author":"MJ Gander","year":"2006","unstructured":"Gander, M.J.: Optimized Schwarz methods. SIAM J. Numer. Anal. 44(2), 699\u2013731 (2006)","journal-title":"SIAM J. Numer. Anal."},{"key":"693_CR16","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1137\/S1064827501387012","volume":"24","author":"MJ Gander","year":"2002","unstructured":"Gander, M.J., Magoul\u00e8s, F., Nataf, F.: Optimized Schwarz methods without overlap for the Helmholtz equation. SIAM J. Sci. Comput. 24, 38\u201360 (2002)","journal-title":"SIAM J. Sci. Comput."},{"issue":"6","key":"693_CR17","doi-asserted-by":"crossref","first-page":"2091","DOI":"10.1137\/09076605X","volume":"48","author":"L Gerardo Giorda","year":"2010","unstructured":"Gerardo Giorda, L., Nobile, F., Vergara, C.: Analysis and optimization of Robin\u2013Robin partitioned procedures in fluid\u2013structure interaction problems. SIAM J. Numer. Anal. 48(6), 2091\u20132116 (2010)","journal-title":"SIAM J. Numer. Anal."},{"issue":"6","key":"693_CR18","doi-asserted-by":"crossref","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\u2013reaction problem with cylindrical interfaces. SIAM J. Numer. Anal. 51(6), 3402\u20133430 (2013)","journal-title":"SIAM J. Numer. Anal."},{"key":"693_CR19","unstructured":"Hairer, E., N\u00f8rsett, S.P., Wanner, G.: Springer Series in Computational Mathematics. Solving ordinary differential equations: nonstiff problems. Springer, Berlin (1993)"},{"key":"693_CR20","unstructured":"Japhet, C.: Optimized Krylov\u2013Ventcell method. Application to convection\u2013diffusion problems. In: Bjorstad, P.E., Espedal, M.S., Keyes, D.E. (eds.) Proceedings of the Ninth International Conference on Domain Decomposition Methods, pp. 382\u2013389 (1998)"},{"key":"693_CR21","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/S0167-739X(00)00072-8","volume":"18","author":"C Japhet","year":"2001","unstructured":"Japhet, C., Nataf, N., Rogier, F.: The optimized order 2 method. Application to convection\u2013diffusion problems. Fut. Gen. Comput. Syst. 18, 17\u201330 (2001)","journal-title":"Fut. Gen. Comput. Syst."},{"issue":"1","key":"693_CR22","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s00466-008-0255-5","volume":"43","author":"U K\u00fcttler","year":"2008","unstructured":"K\u00fcttler, U., Wall, W.A.: Fixed-point fluidstructure interaction solvers with dynamic relaxation. Comput. Mech. 43(1), 61\u201372 (2008)","journal-title":"Comput. Mech."},{"key":"693_CR23","volume-title":"Special Functions and Their Applications","author":"N Lebedev","year":"1972","unstructured":"Lebedev, N.: Special Functions and Their Applications. Courier Dover Publications, New York (1972)"},{"key":"693_CR24","unstructured":"LifeV project: http:\/\/www.lifev.org (2004)"},{"key":"693_CR25","first-page":"202","volume-title":"Proceedings of the Third International Symposium on Domain Decomposition Methods for PDE\u2019s","author":"PL Lions","year":"1990","unstructured":"Lions, P.L.: On the Schwarz alternating method III. In: Chan, T., Glowinki, R., Periaux, J., Widlund, O.B. (eds.) Proceedings of the Third International Symposium on Domain Decomposition Methods for PDE\u2019s, pp. 202\u2013223. SIAM, Philadelphia (1990)"},{"key":"693_CR26","doi-asserted-by":"crossref","first-page":"4797","DOI":"10.1016\/j.cma.2004.05.004","volume":"193","author":"F Magoul\u00e8s","year":"2004","unstructured":"Magoul\u00e8s, F., Ivanyi, P., Topping, B.H.V.: Non-overlapping Schwarz method with optimized transmission conditions for the Helmholtz equation. Comput. Methods Appl. Mech. Eng. 193, 4797\u20134818 (2004)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"1\u20132","key":"693_CR27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10237-011-0289-z","volume":"11","author":"P Moireau","year":"2012","unstructured":"Moireau, P., Xiao, N., Astorino, M., Figueroa, C.A., Chapelle, D., Taylor, C.A., Gerbeau, J.-F.: External tissue support and fluidstructure simulation in blood flows. Biomech. Model. Mechanobiol. 11(1\u20132), 1\u201318 (2012)","journal-title":"Biomech. Model. Mechanobiol."},{"key":"693_CR28","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1016\/j.compfluid.2013.07.031","volume":"86","author":"F Nobile","year":"2013","unstructured":"Nobile, F., Pozzoli, M., Vergara, C.: Time accurate partitioned algorithms for the solution of fluid\u2013structure interaction problems in haemodynamics. Comput. Fluids 86, 470\u2013482 (2013)","journal-title":"Comput. Fluids"},{"key":"693_CR29","doi-asserted-by":"crossref","unstructured":"Nobile, F., Pozzoli, M., Vergara, C.: J. Comput. Phys. 273, 598\u2013617 (2014)","DOI":"10.1016\/j.jcp.2014.05.020"},{"issue":"2","key":"693_CR30","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1137\/060678439","volume":"30","author":"F Nobile","year":"2008","unstructured":"Nobile, F., Vergara, C.: An effective fluid\u2013structure interaction formulation for vascular dynamics by generalized Robin conditions. SIAM J. Sci. Comput. 30(2), 731\u2013763 (2008)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"693_CR31","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1007\/s00032-012-0194-7","volume":"80","author":"F Nobile","year":"2012","unstructured":"Nobile, F., Vergara, C.: Partitioned algorithms for fluid\u2013structure interaction problems in haemodynamics. Milan J. Math. 80(2), 443\u2013467 (2012)","journal-title":"Milan J. Math."},{"key":"693_CR32","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1016\/j.apnum.2007.01.015","volume":"58","author":"A Qaddouria","year":"2008","unstructured":"Qaddouria, A., Laayounib, L., Loiselc, S., Cotea, J., Gander, M.J.: Optimized Schwarz methods with an overset grid for the shallow-water equations: preliminary results. Appl. Numer. Math. 58, 459\u2013471 (2008)","journal-title":"Appl. Numer. Math."},{"key":"693_CR33","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1016\/j.jcp.2009.10.015","volume":"229","author":"B Stupfel","year":"2010","unstructured":"Stupfel, B.: Improved transmission conditions for a one-dimensional domain decomposition method applied to the solution of the Helmhotz equation. J. Comput. Phys. 229, 851\u2013874 (2010)","journal-title":"J. Comput. Phys."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-014-0693-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-014-0693-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-014-0693-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,18]],"date-time":"2019-08-18T03:41:05Z","timestamp":1566099665000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-014-0693-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,4]]},"references-count":33,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,10]]}},"alternative-id":["693"],"URL":"https:\/\/doi.org\/10.1007\/s00211-014-0693-2","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12,4]]}}}