{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T11:11:22Z","timestamp":1760267482304,"version":"3.37.3"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,6,29]],"date-time":"2017-06-29T00:00:00Z","timestamp":1498694400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2018,5]]},"DOI":"10.1007\/s11075-017-0364-3","type":"journal-article","created":{"date-parts":[[2017,6,29]],"date-time":"2017-06-29T01:19:50Z","timestamp":1498699190000},"page":"1-20","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Pipeline implementations of Neumann\u2013Neumann and Dirichlet\u2013Neumann waveform relaxation methods"],"prefix":"10.1007","volume":"78","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2315-987X","authenticated-orcid":false,"given":"Benjamin W.","family":"Ong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bankim C.","family":"Mandal","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,6,29]]},"reference":[{"issue":"6","key":"364_CR1","doi-asserted-by":"publisher","first-page":"1097","DOI":"10.1137\/0723075","volume":"23","author":"PE Bj\u00f8rstad","year":"1986","unstructured":"Bj\u00f8rstad, P.E., Widlund, O.B.: Iterative methods for the solution of elliptic problems on regions partitioned into substructures. SIAM J. Numer. Anal. 23(6), 1097\u20131120 (1986). doi:\n                        10.1137\/0723075","journal-title":"SIAM J. Numer. Anal."},{"key":"364_CR2","unstructured":"Bourgat, J.F., Glowinski, R., Le Tallec, P., Vidrascu, M.: Variational formulation and algorithm for trace operator in domain decomposition calculations. In: Domain Decomposition Methods (Los Angeles, CA, 1988), pp. 3\u201316. SIAM, Philadelphia (1989)"},{"issue":"174","key":"364_CR3","doi-asserted-by":"publisher","first-page":"361","DOI":"10.2307\/2007981","volume":"46","author":"JH Bramble","year":"1986","unstructured":"Bramble, J.H., Pasciak, J.E., Schatz, A.H.: An iterative method for elliptic problems on regions partitioned into substructures. Math. Comp. 46(174), 361\u2013369 (1986). doi:\n                        10.2307\/2007981","journal-title":"Math. Comp."},{"key":"364_CR4","unstructured":"De Roeck, Y.H., Le Tallec, P.: Analysis and Test of a Local Domain-Decomposition Preconditioner. In: 4th International Symposium on Domain Decomposition Methods for Partial Differential Equations (Moscow, 1990), pp. 112\u2013128. SIAM, Philadelphia (1991)"},{"issue":"6","key":"364_CR5","doi-asserted-by":"publisher","first-page":"1213","DOI":"10.1137\/0725069","volume":"25","author":"D Funaro","year":"1988","unstructured":"Funaro, D., Quarteroni, A., Zanolli, P.: An iterative procedure with interface relaxation for domain decomposition methods. SIAM J. Numer. Anal. 25(6), 1213\u20131236 (1988). doi:\n                        10.1137\/0725069","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"364_CR6","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 methods for advection reaction diffusion problems. SIAM J. Numer. Anal. 45(2), 666\u2013697 (2007). doi:\n                        10.1137\/050642137\n                        \n                    . (electronic)","journal-title":"SIAM J. Numer. Anal."},{"issue":"5","key":"364_CR7","doi-asserted-by":"publisher","first-page":"1643","DOI":"10.1137\/S003614290139559X","volume":"41","author":"MJ Gander","year":"2003","unstructured":"Gander, M.J., Halpern, L., Nataf, F.: Optimal Schwarz waveform relaxation for the one dimensional wave equation. SIAM J. Numer. Anal. 41(5), 1643\u20131681 (2003). doi:\n                        10.1137\/S003614290139559X","journal-title":"SIAM J. Numer. Anal."},{"key":"364_CR8","first-page":"424","volume":"45","author":"MJ Gander","year":"2016","unstructured":"Gander, M.J., Kwok, F., Mandal, B.C.: Dirichlet-neumann and neumann-neumann waveform relaxation algorithms for parabolic problems. Electron. Trans. Numer. Anal. 45, 424\u2013456 (2016)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"364_CR9","doi-asserted-by":"publisher","unstructured":"Gander, M.J., Kwok, F., Mandal, B.C.: Dirichlet-neumann and neumann-neumann waveform relaxation for the wave equation. In: Dickopf, T., Gander, M. J., Halpern, L., Krause, R., Pavarino, L. (eds.) Domain Decomposition Methods in Science and Engineering XXII, Lecture Notes in Computational Science and Engineering pp. 501\u2013509, Springer International Publishing (2016). doi:\n                        10.1007\/978-3-319-18827-0_51","DOI":"10.1007\/978-3-319-18827-0_51"},{"key":"364_CR10","unstructured":"Gander, M.J., Kwok, F., Mandal, B.C.: Dirichlet-Neumann Waveform Relaxation Method for the 1D and 2D Heat and Wave Equations in Multiple subdomains. to appear (arXiv:\n                        1507.04011\n                        \n                    )"},{"issue":"6","key":"364_CR11","doi-asserted-by":"publisher","first-page":"2014","DOI":"10.1137\/S1064827596305337","volume":"19","author":"MJ Gander","year":"1998","unstructured":"Gander, M.J., Stuart, A.M.: Space-time continuous analysis of waveform relaxation for the heat equation. SIAM J. Sci. Comput. 19(6), 2014\u20132031 (1998). doi:\n                        10.1137\/S1064827596305337","journal-title":"SIAM J. Sci. Comput."},{"key":"364_CR12","doi-asserted-by":"publisher","unstructured":"Gear, C.W.: Waveform methods for space and time parallelism. In: Proceedings of the International Symposium on Computational Mathematics (Matsuyama, 1990), vol. 38, pp. 137\u2013147 (1991). doi:\n                        10.1016\/0377-0427(91)90166-H","DOI":"10.1016\/0377-0427(91)90166-H"},{"key":"364_CR13","unstructured":"Giladi, E., Keller, H.: Space Time Domain Decomposition for Parabolic Problems. Tech. Rep. 97-4. Center for research on parallel computation CRPC, Caltech (1997)"},{"key":"364_CR14","doi-asserted-by":"crossref","unstructured":"Kwok, F.: Neumann-Neumann 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-Verlag (2014)","DOI":"10.1007\/978-3-319-05789-7_15"},{"issue":"1","key":"364_CR15","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/0377-0427(91)90150-I","volume":"34","author":"P Le Tallec","year":"1991","unstructured":"Le Tallec, P., De Roeck, Y.H., Vidrascu, M.: Domain decomposition methods for large linearly elliptic three-dimensional problems. J. Comput. Appl. Math. 34(1), 93\u2013117 (1991). doi:\n                        10.1016\/0377-0427(91)90150-I","journal-title":"J. Comput. Appl. Math."},{"issue":"3","key":"364_CR16","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1109\/TCAD.1982.1270004","volume":"1","author":"E Lelarasmee","year":"1982","unstructured":"Lelarasmee, E., Ruehli, A., Sangiovanni-Vincentelli, A.: The waveform relaxation method for time-domain analysis of large scale integrated circuits. IEEE Trans. Compt.-Aided Design Integr. Circuits Syst. 1(3), 131\u2013145 (1982)","journal-title":"IEEE Trans. Compt.-Aided Design Integr. Circuits Syst."},{"key":"364_CR17","unstructured":"Lindel\u00f6f, E.: Sur l\u2019application des m\u00e9thodes d\u2019approximations successives \u00e0 l\u2019\u00e9tude des int\u00e9grales r\u00e9elles des \u00e9quations diff\u00e9rentielles ordinaires. Journal de Math\u00e9matiques Pures et Appliqu\u00e9es (1894)"},{"key":"364_CR18","unstructured":"Mandal, B.C.: Convergence Analysis of Substructuring Waveform Relaxation Methods for Space-time Problems and Their Application to Optimal Control Problems. Ph.D. thesis, University of Geneva. \n                        http:\/\/archive-ouverte.unige.ch\/unige:46146\n                        \n                     (2014)"},{"key":"364_CR19","doi-asserted-by":"crossref","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-Verlag (2014)","DOI":"10.1007\/978-3-319-05789-7_44"},{"key":"364_CR20","doi-asserted-by":"publisher","unstructured":"Mandal, B.C.: Neumann-Neumann waveform relaxation algorithm in multiple subdomains for hyperbolic problems in 1d and 2d. Numer. Methods Partial Differ. Equ. doi:\n                        10.1002\/num.22112\n                        \n                     (2016)","DOI":"10.1002\/num.22112"},{"issue":"5","key":"364_CR21","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1007\/BF01398917","volume":"55","author":"LD Marini","year":"1989","unstructured":"Marini, L.D., Quarteroni, A.: A relaxation procedure for domain decomposition methods using finite elements. Numer. Math. 55(5), 575\u2013598 (1989). doi:\n                        10.1007\/BF01398917","journal-title":"Numer. Math."},{"key":"364_CR22","unstructured":"Martini, L., Quarteroni, A.: An Iterative Procedure for Domain Decomposition Methods: a Finite Element Approach. SIAM in Domain Decomposition Methods for PDEs I (1988)"},{"key":"364_CR23","doi-asserted-by":"publisher","unstructured":"Ong, B.W., High, S., Kwok, F.: Pipeline Schwarz waveform relaxation. In: Dickopf, T., Gander, M. J., Halpern, L., Krause, R., Pavarino, L. (eds.) Domain Decomposition Methods in Science and Engineering XXII, Lecture Notes in Computational Science and Engineering, pp. 179\u2013187. Springer International Publishing (2016). doi:\n                        10.1007\/978-3-319-18827-0_36","DOI":"10.1007\/978-3-319-18827-0_36"},{"key":"364_CR24","unstructured":"Picard, E.: Sur l\u2019application des m\u00e9thodes d\u2019approximations successives \u00e0 l\u2019\u00e9tude de certaines \u00e9quations diff\u00e9rentielles ordinaires. Journal de Math\u00e9matiques Pures et Appliqu\u00e9es (1893)"},{"key":"364_CR25","doi-asserted-by":"publisher","unstructured":"Toselli, A., Widlund, O.: Domain decomposition methods\u2014algorithms and theory, Springer Series in Computational Mathematics, vol. 34. Springer-Verlag, Berlin (2005). doi:\n                        10.1007\/b137868","DOI":"10.1007\/b137868"},{"key":"364_CR26","unstructured":"Vandewalle, S.G., Van de Velde, E.F.: Space-time concurrent multigrid waveform relaxation. Ann. Numer. Math. 1(1-4), 347\u2013360 (1994). Scientific computation and differential equations (Auckland, 1993)"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-017-0364-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-017-0364-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-017-0364-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,4,18]],"date-time":"2018-04-18T05:49:40Z","timestamp":1524030580000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-017-0364-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,29]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,5]]}},"alternative-id":["364"],"URL":"https:\/\/doi.org\/10.1007\/s11075-017-0364-3","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2017,6,29]]}}}