{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T01:25:41Z","timestamp":1768785941000,"version":"3.49.0"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,5,29]],"date-time":"2023-05-29T00:00:00Z","timestamp":1685318400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,5,29]],"date-time":"2023-05-29T00:00:00Z","timestamp":1685318400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["DMS-1912626"],"award-info":[{"award-number":["DMS-1912626"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2023,7]]},"DOI":"10.1007\/s10915-023-02251-0","type":"journal-article","created":{"date-parts":[[2023,5,29]],"date-time":"2023-05-29T11:01:43Z","timestamp":1685358103000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Fast and Accuracy-Preserving Domain Decomposition Methods for Reduced Fracture Models with Nonconforming Time Grids"],"prefix":"10.1007","volume":"96","author":[{"given":"Phuoc-Toan","family":"Huynh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanzhao","family":"Cao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0694-7460","authenticated-orcid":false,"given":"Thi-Thao-Phuong","family":"Hoang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,5,29]]},"reference":[{"key":"2251_CR1","first-page":"365","volume-title":"Domain Decomposition Methods in Science and Engineering","author":"C Alboin","year":"1999","unstructured":"Alboin, C., Jaffr\u00e9, J., Roberts, J.E., Serres, C.: Domain decomposition for flow in fractured porous media. In: Lai, C.H., Bjorstad, P.E., Cross, M., Widlund, O.B. (eds.) Domain Decomposition Methods in Science and Engineering, pp. 365\u2013373. Domain Decomposition Press, Bergen (1999)"},{"key":"2251_CR2","doi-asserted-by":"crossref","unstructured":"Alboin, C., Jaffre, J., Roberts, J.E., Serres, C.: Modeling fractures as interfaces for flow and transport in porous media. In: Fluid Flow and Transport in Porous Media: Mathematical and Numerical Treatment (South Hadley, MA), vol. 295 of Contemp. Math. Amer. Math. Soc. Providence, RI, vol. 2002, pp. 13\u201324 (2001)","DOI":"10.1090\/conm\/295\/04999"},{"key":"2251_CR3","first-page":"11","volume":"5","author":"L Amir","year":"2006","unstructured":"Amir, L., Kern, M., Martin, V., Roberts, J.E.: D\u00e9compositionn de domaine pour un milieu poreux fracture\u00e9: Un mo\u00e8le en 3D avec fractures qui s\u2019intersectent. Arima 5, 11\u201325 (2006)","journal-title":"Arima"},{"key":"2251_CR4","doi-asserted-by":"publisher","DOI":"10.1080\/00036811.2021.1981878","author":"L Amir","year":"2021","unstructured":"Amir, L., Kern, M., Mghazli, Z., Roberts, J.E.: Intersecting fractures in porous media: mathematical and numerical analysis. Appl. Anal. (2021). https:\/\/doi.org\/10.1080\/00036811.2021.1981878","journal-title":"Appl. Anal."},{"issue":"2","key":"2251_CR5","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1051\/m2an\/2008052","volume":"43","author":"P Angot","year":"2009","unstructured":"Angot, P., Boyer, F., Hubert, F.: Asymptotic and numerical modelling of flows in fractured porous media. M2AN Math. Model. Numer. Anal. 43(2), 239\u2013275 (2009)","journal-title":"M2AN Math. Model. Numer. Anal."},{"issue":"265","key":"2251_CR6","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1090\/S0025-5718-08-02145-5","volume":"78","author":"D Bennequin","year":"2009","unstructured":"Bennequin, D., Gander, M.J., Gouarin, L., Halpern, L.: A homographic best approximation problem with application to optimized Schwarz waveform relaxation. Math. Comput. 78(265), 185\u2013223 (2009)","journal-title":"Math. Comput."},{"key":"2251_CR7","first-page":"170","volume":"40","author":"E Blayo","year":"2013","unstructured":"Blayo, E., Debreu, L., Lemari\u00e9, F.: Toward an optimized global-in-time Schwarz algorithm for diffusion equation with discontinuous and spatially variable coefficients. Part 1: the constant coefficients case. Electron. Trans. Numer. Anal. 40, 170\u2013186 (2013)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"2251_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-36519-5","volume-title":"Mixed Finite Elements Methods and Applications","author":"D Boffi","year":"2013","unstructured":"Boffi, D., Brezzi, F., Fortin, M.: Mixed Finite Elements Methods and Applications. Springer, Heidelberg (2013)"},{"key":"2251_CR9","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1137\/130908191","volume":"52","author":"F Brunner","year":"2014","unstructured":"Brunner, F., Radu, F.A., Knabner, P.: Analysis of an upwind-mixed hybrid finite element method for transport problems. SIAM J. Numer. Anal. 52, 83\u2013102 (2014)","journal-title":"SIAM J. Numer. Anal."},{"key":"2251_CR10","doi-asserted-by":"publisher","first-page":"989","DOI":"10.1090\/S0025-5718-1995-1297465-9","volume":"64","author":"LC Cowsar","year":"1995","unstructured":"Cowsar, L.C., Mandel, J., Wheeler, M.F.: Balancing domain decomposition for mixed finite elements. Math. Comput. 64, 989\u20131015 (1995)","journal-title":"Math. Comput."},{"key":"2251_CR11","doi-asserted-by":"publisher","first-page":"3831","DOI":"10.1002\/nme.1620382207","volume":"38","author":"C Farhat","year":"1995","unstructured":"Farhat, C., Chen, P.S., Mandel, J.: A scalable Lagrange multiplier based domain decomposition method for implicit time-dependent problems. Int. J. Numer. Methods Eng. 38, 3831\u20133858 (1995)","journal-title":"Int. J. Numer. Methods Eng."},{"key":"2251_CR12","doi-asserted-by":"publisher","first-page":"1205","DOI":"10.1002\/nme.1620320604","volume":"32","author":"C Farhat","year":"1991","unstructured":"Farhat, C., Roux, F.X.: A method of finite element tearing and interconnecting and its parallel solution algorithm. Int. J. Numer. Methods Eng. 32, 1205\u20131227 (1991)","journal-title":"Int. J. Numer. Methods Eng."},{"key":"2251_CR13","first-page":"1","volume":"3","author":"A Fumagalli","year":"2011","unstructured":"Fumagalli, A., Scotti, A.: Numerical modeling of multiphase subsurface flow in the presence of fractures. Commun. Appl. Ind. Math. 3, 1\u201323 (2011)","journal-title":"Commun. Appl. Ind. Math."},{"issue":"2","key":"2251_CR14","doi-asserted-by":"publisher","first-page":"666","DOI":"10.1137\/050642137","volume":"45","author":"MJ Gander","year":"2007","unstructured":"Gander, M.J., Halpern, L.: Optimized Schwarz waveform relaxation for advection reaction diffusion problems. SIAM J. Numer. Anal. 45(2), 666\u2013697 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"2251_CR15","doi-asserted-by":"crossref","unstructured":"Gander, M.J., Halpern, L., Kern, M.: A Schwarz waveform relaxation method for advection\u2013diffusion\u2013reaction problems with continuous coefficients and non-matching grids. In: Domain Decomposition Methods in Science and Engineering XVI, vol. 55 of Lect. Notes Comput. Sci. Eng., pp. 283\u2013290. Springer, Berlin (2007)","DOI":"10.1007\/978-3-540-34469-8_33"},{"key":"2251_CR16","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1145\/2513109.2513115","volume":"40","author":"MJ Gander","year":"2013","unstructured":"Gander, M.J., Japhet, C.: Algorithm 932: PANG: software for nonmatching grid projections in 2D and 3D with linear complexity. ACM Trans. Math. Softw. 40, 25 (2013)","journal-title":"ACM Trans. Math. Softw."},{"key":"2251_CR17","doi-asserted-by":"crossref","unstructured":"Gander, M.J., Japhet, C., Maday, Y., Nataf, F.: A new cement to glue nonconforming grids with Robin interface conditions: the finite element case. In: Domain Decomposition Methods in Science and Engineering. Lect. Notes Comput. Sci. Eng., vol. 40, pp. 259\u2013266. Springer, Berlin (2005)","DOI":"10.1007\/3-540-26825-1_24"},{"key":"2251_CR18","first-page":"424","volume":"45","author":"MJ Gander","year":"2016","unstructured":"Gander, M.J., Kwok, F., Mandal, B.C.: Dirichlet\u2013Neumann and Neumann-Neumann waveform relaxation algorithms for parabolic problems. Electron. Trans. Numer. Anal. 45, 424\u2013456 (2016)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"2251_CR19","doi-asserted-by":"crossref","unstructured":"Gander, M.J., Kwok, F., Mandal, B.C.: Dirichlet\u2013Neumann waveform relaxation methods for parabolic and hyperbolic problems in multiple subdomains. BIT Numer. Math. 1\u201335 (2020)","DOI":"10.1007\/s10543-020-00823-2"},{"issue":"1","key":"2251_CR20","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1137\/20M1312125","volume":"59","author":"MJ Gander","year":"2021","unstructured":"Gander, M.J., Hennicker, J., Masson, R.: Modeling and analysis of the coupling in discrete fracture matrix models. SIAM J. Numer. Anal. 59(1), 195\u2013218 (2021)","journal-title":"SIAM J. Numer. Anal."},{"key":"2251_CR21","unstructured":"Glowinski, R., Wheeler, M.F.: Domain decomposition and mixed finite element methods for elliptic problems. In: First International Symposium on Domain Decomposition Methods for Partial Differential Equations (Paris, 1987), pp. 144\u2013172. SIAM, Philadelphia, PA (1988)"},{"key":"2251_CR22","unstructured":"Halpern, L., Japhet, C., Omnes, P.: Nonconforming in time domain decomposition methods for porous method applications. In: Pereira, J.C.F., Sequeira, A. (eds.) Proceedings of the 5th European Conference on Computational Fluid Dynamics ECCOMAS CFD 2010. Lisbon, Portugal (2010)"},{"issue":"5","key":"2251_CR23","doi-asserted-by":"publisher","first-page":"2588","DOI":"10.1137\/120865033","volume":"50","author":"L Halpern","year":"2012","unstructured":"Halpern, L., Japhet, C., Szeftel, J.: Optimized Schwarz waveform relaxation and discontinuous Galerkin time stepping for heterogeneous problems. SIAM J. Numer. Anal. 50(5), 2588\u20132611 (2012)","journal-title":"SIAM J. Numer. Anal."},{"issue":"6","key":"2251_CR24","doi-asserted-by":"publisher","first-page":"3532","DOI":"10.1137\/130914401","volume":"51","author":"TTP Hoang","year":"2013","unstructured":"Hoang, T.T.P., Jaffre, J., Japhet, C., Kern, M., Roberts, J.E.: Space-time domain decomposition methods for diffusion problems in mixed formulations. SIAM J. Numer. Anal. 51(6), 3532\u20133559 (2013)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"2251_CR25","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1137\/15M1009651","volume":"54","author":"TTP Hoang","year":"2016","unstructured":"Hoang, T.T.P., Japhet, C., Kern, M., Roberts, J.E.: Space-time domain decomposition for reduced fracture models in mixed formulation. SIAM J. Numer. Anal. 54(1), 288\u2013316 (2016)","journal-title":"SIAM J. Numer. Anal."},{"key":"2251_CR26","doi-asserted-by":"publisher","first-page":"366","DOI":"10.1016\/j.matcom.2016.11.002","volume":"137","author":"TTP Hoang","year":"2017","unstructured":"Hoang, T.T.P., Japhet, C., Kern, M., Roberts, J.E.: Space-time domain decomposition for advection\u2013diffusion problems in mixed formulations. Math. Comput. Simul. 137, 366\u2013389 (2017)","journal-title":"Math. Comput. Simul."},{"issue":"1","key":"2251_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10915-021-01422-1","volume":"87","author":"TTP Hoang","year":"2021","unstructured":"Hoang, T.T.P., Lee, H.: A global-in-time domain decomposition methods for the coupled nonlinear Stokes and Darcy flows. J. Sci. Comput. 87(1), 1\u201322 (2021)","journal-title":"J. Sci. Comput."},{"key":"2251_CR28","doi-asserted-by":"publisher","first-page":"1667","DOI":"10.1137\/S1064827503429363","volume":"26","author":"J Jaffre","year":"2005","unstructured":"Jaffre, J., Martin, V., Roberts, J.E.: Modeling fractures and barriers as interfaces for flow in porous media. SIAM J. Sci. Comput. 26, 1667\u20131691 (2005)","journal-title":"SIAM J. Sci. Comput."},{"key":"2251_CR29","doi-asserted-by":"crossref","unstructured":"Japhet, C., Maday, Y., Nataf, F.: A new interface cement equilibrated mortar method with ventcel conditions. In: Erhel, J., Gander, M., Halpern, L., Pichot, G., Sassi, T., Widlund, O. (eds.) Domain Decomposition Methods in Science and Engineering XXI. Lect. Notes Comput. Sci. Eng., vol. 98, pp. 329\u2013336. Springer (2014)","DOI":"10.1007\/978-3-319-05789-7_35"},{"key":"2251_CR30","doi-asserted-by":"crossref","unstructured":"Japhet, C., Maday, Y.: Mortar methods with optimized transmission conditions for advection\u2013diffusion problems. In: Dickopf, T., Gander, M., Halpern, L., Krause, R., Pavarino, L. (eds.) Domain Decomposition Methods in Science and Engineering XXII. Lecture Notes in Computational Science and Engineering, vol. 104, pp. 541\u2013549. Springer (2016)","DOI":"10.1007\/978-3-319-18827-0_55"},{"key":"2251_CR31","doi-asserted-by":"publisher","DOI":"10.1016\/j.advwatres.2020.103620","volume":"142","author":"T Kadeethum","year":"2020","unstructured":"Kadeethum, T., Nick, H.M., Lee, S., Ballarin, F.: Flow in porous media with low dimensional fractures by employing enriched Galerkin method. Adv. Water Resour. 142, 103620 (2020)","journal-title":"Adv. Water Resour."},{"key":"2251_CR32","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/978-3-319-05789-7_15","volume-title":"Domain Decomposition in Science and Engineering XXI","author":"F Kwok","year":"2014","unstructured":"Kwok, F.: Neumann\u2013Neumann waveform relaxation for the time-dependent heat equation. In: Erhel, J., Gander, M.J., Halpern, L., Pichot, G., Sassi, T., Widlund, O.B. (eds.) Domain Decomposition in Science and Engineering XXI, vol. 98, pp. 189\u2013198. Springer, Berlin (2014)"},{"key":"2251_CR33","volume-title":"Krylov Subspace Methods: Principle and Analysis","author":"J Liesen","year":"2013","unstructured":"Liesen, J., Strako\u0161, Z.: Krylov Subspace Methods: Principle and Analysis. Oxford University Press, Oxford (2013)"},{"key":"2251_CR34","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1007\/978-3-319-05789-7_44","volume-title":"Domain Decomposition in Science and Engineering XXI","author":"BC Mandal","year":"2014","unstructured":"Mandal, B.C.: A time-dependent Dirichlet-Neumann method for the heat equation. In: Erhel, J., Gander, M.J., Halpern, L., Pichot, G., Sassi, T., Widlund, O.B. (eds.) Domain Decomposition in Science and Engineering XXI, vol. 98, pp. 467\u2013475. Springer, Berlin (2014)"},{"key":"2251_CR35","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1002\/cnm.1640090307","volume":"9","author":"J Mandel","year":"1993","unstructured":"Mandel, J.: Balancing domain decomposition. Commun. Numer. Methods Eng. 9, 233\u2013241 (1993)","journal-title":"Commun. Numer. Methods Eng."},{"key":"2251_CR36","doi-asserted-by":"publisher","first-page":"1387","DOI":"10.1090\/S0025-5718-96-00757-0","volume":"65","author":"J Mandel","year":"1996","unstructured":"Mandel, J., Brezina, M.: Balancing domain decomposition for problems with large jumps in coefficients. Math. Comput. 65, 1387\u20131401 (1996)","journal-title":"Math. Comput."},{"key":"2251_CR37","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1016\/j.apnum.2004.08.022","volume":"52","author":"V Martin","year":"2005","unstructured":"Martin, V.: An optimized Schwarz waveform relaxation method for the unsteady convection diffusion equation in two dimensions. Appl. Numer. Math. 52, 401\u2013428 (2005)","journal-title":"Appl. Numer. Math."},{"key":"2251_CR38","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1002\/mma.1555","volume":"35","author":"F Morales","year":"2012","unstructured":"Morales, F., Showalter, R.E.: Interface approximation of Darcy flow in a narrow channel. Math. Methods Appl. Sci. 35, 182\u2013195 (2012)","journal-title":"Math. Methods Appl. Sci."},{"key":"2251_CR39","doi-asserted-by":"crossref","unstructured":"Quarteroni, A., Valli, A.: Theory and application of Steklov\u2013Poincar\u00e9 operators for boundary-value problems: the heterogeneous operator case. In: Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations (Moscow, 1990), pp. 58\u201381. SIAM, Philadelphia, PA (1991)","DOI":"10.1007\/978-94-009-1908-2_14"},{"key":"2251_CR40","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198501787.001.0001","volume-title":"Domain Decomposition Method for Partial Differential Equations","author":"A Quarteroni","year":"1999","unstructured":"Quarteroni, A., Valli, A.: Domain Decomposition Method for Partial Differential Equations. Clarendon Press, Oxford (1999)"},{"key":"2251_CR41","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.advwatres.2010.09.012","volume":"34","author":"FA Radu","year":"2011","unstructured":"Radu, F.A., Suciu, N., Hoffmann, J., Vogel, A., Kolditz, O., Park, C.-H., Attinger, S.: Accuracy of numerical simulations of contaminant transport in heterogeneous aquifers: a comparative study. Adv. Water Resour. 34, 47\u201361 (2011)","journal-title":"Adv. Water Resour."},{"key":"2251_CR42","doi-asserted-by":"crossref","unstructured":"Roberts, J.E., Thomas, J.M.: Mixed and hybrid methods. In: Handbook of Numerical Analysis, Vol. II, Handb. Numer. Anal., II, pp. 523\u2013639. North-Holland, Amsterdam (1991)","DOI":"10.1016\/S1570-8659(05)80041-9"},{"key":"2251_CR43","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1137\/1104014","volume":"4","author":"AD Ventcel","year":"1959","unstructured":"Ventcel, A.D.: On boundary conditions for multidimensional diffusion processes. Theory Probab. Appl. 4, 164\u2013177 (1959)","journal-title":"Theory Probab. Appl."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-023-02251-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-023-02251-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-023-02251-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,14]],"date-time":"2023-12-14T08:37:44Z","timestamp":1702543064000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-023-02251-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,29]]},"references-count":43,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,7]]}},"alternative-id":["2251"],"URL":"https:\/\/doi.org\/10.1007\/s10915-023-02251-0","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,29]]},"assertion":[{"value":"12 February 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 January 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 May 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 May 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declaration"}},{"value":"The authors have not disclosed any competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"23"}}