{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T17:17:35Z","timestamp":1773249455074,"version":"3.50.1"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2013,1,19]],"date-time":"2013-01-19T00:00:00Z","timestamp":1358553600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computing"],"published-print":{"date-parts":[[2013,12]]},"DOI":"10.1007\/s00607-013-0293-5","type":"journal-article","created":{"date-parts":[[2013,1,18]],"date-time":"2013-01-18T06:38:29Z","timestamp":1358491109000},"page":"1087-1119","source":"Crossref","is-referenced-by-count":41,"title":["Adaptive-Multilevel BDDC and its parallel implementation"],"prefix":"10.1007","volume":"95","author":[{"given":"Bed\u0159ich","family":"Soused\u00edk","sequence":"first","affiliation":[]},{"given":"Jakub","family":"\u0160\u00edstek","sequence":"additional","affiliation":[]},{"given":"Jan","family":"Mandel","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,1,19]]},"reference":[{"key":"293_CR1","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1016\/S0045-7825(99)00242-X","volume":"184","author":"PR Amestoy","year":"2000","unstructured":"Amestoy PR, Duff IS, L\u2019Excellent JY (2000) Multifrontal parallel distributed symmetric and unsymmetric solvers. Comput Methods Appl Mech Eng 184:501\u2013520","journal-title":"Comput Methods Appl Mech Eng"},{"key":"293_CR2","volume-title":"Proceedings of the twelfth international conference on civil, structural and environmental engineering computing","author":"R Blaheta","year":"2009","unstructured":"Blaheta R, Jakl O, Star\u00fd J, Kre\u010dmer K (2009) The Schwarz domain decomposition method for analysis of geocomposites. In: Topping B, Neves LC, Barros R (eds) Proceedings of the twelfth international conference on civil, structural and environmental engineering computing. Civil-Comp Press, Stirlingshire"},{"issue":"8","key":"293_CR3","doi-asserted-by":"crossref","first-page":"1429","DOI":"10.1016\/j.cma.2006.03.012","volume":"196","author":"SC Brenner","year":"2007","unstructured":"Brenner SC, Sung LY (2007) BDDC and FETI-DP without matrices or vectors. Comput Methods Appl Mech Eng 196(8):1429\u20131435","journal-title":"Comput Methods Appl Mech Eng"},{"key":"293_CR4","unstructured":"Bro\u017e J, Kruis J, (2009) An algorithm for corner nodes selection in the FETI-DP method. In: Enginnering mechanics 2009\u2014CDROM [CD-ROM]. Institute of Theoretical and Applied Mechanics AS CR, Prague, pp 129\u2013140"},{"key":"293_CR5","unstructured":"Cros JM (2003) A preconditioner for the Schur complement domain decomposition method. In: Herrera I, Keyes DE, Widlund OB (eds) Domain decomposition methods in science and engineering. In: 14th international conference on domain decomposition methods, Cocoyoc, Mexico, January 6\u201312, 2002. National Autonomous University of Mexico (UNAM), M\u00e9xico (2003) , pp 373\u2013380"},{"key":"293_CR6","doi-asserted-by":"crossref","unstructured":"Demmel JW (1997) Applied numerical linear algebra. Society for Industrial and Applied Mathematics (SIAM), Philadelphia","DOI":"10.1137\/1.9781611971446"},{"issue":"1","key":"293_CR7","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1137\/S1064827502412887","volume":"25","author":"CR Dohrmann","year":"2003","unstructured":"Dohrmann CR (2003) A preconditioner for substructuring based on constrained energy minimization. SIAM J Sci Comput 25(1):246\u2013258","journal-title":"SIAM J Sci Comput"},{"key":"293_CR8","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1002\/1099-1506(200010\/12)7:7\/8<687::AID-NLA219>3.0.CO;2-S","volume":"7","author":"C Farhat","year":"2000","unstructured":"Farhat C, Lesoinne M, Pierson K (2000) A scalable dual-primal domain decomposition method. Numer Linear Algebra Appl 7:687\u2013714","journal-title":"Numer Linear Algebra Appl"},{"key":"293_CR9","doi-asserted-by":"crossref","first-page":"3799","DOI":"10.1016\/S0045-7825(03)00374-8","volume":"192","author":"Y Fragakis","year":"2003","unstructured":"Fragakis Y, Papadrakakis M (2003) The mosaic of high performance domain decomposition methods for structural mechanics: formulation, interrelation and numerical efficiency of primal and dual methods. Comput Methods Appl Mech Eng 192:3799\u20133830","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"10","key":"293_CR10","doi-asserted-by":"crossref","first-page":"904","DOI":"10.2307\/2975268","volume":"102","author":"ICF Ipsen","year":"1995","unstructured":"Ipsen ICF, Meyer CD (1995) The angle between complementary subspaces. Am Math Monthly 102(10):904\u2013911","journal-title":"Am Math Monthly"},{"key":"293_CR11","unstructured":"Karypis G, Kumar V (1998) METIS: a software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices, version 4.0. Technical report, Department of Computer Science, University of Minnesota. http:\/\/glaros.dtc.umn.edu\/gkhome\/views\/metis"},{"issue":"2","key":"293_CR12","doi-asserted-by":"crossref","first-page":"1576","DOI":"10.1137\/07069081X","volume":"47","author":"HH Kim","year":"2009","unstructured":"Kim HH, Tu X (2009) A three-level BDDC algorithm for mortar discretizations. SIAM J Numer Anal 47(2):1576\u20131600. doi: 10.1137\/07069081X","journal-title":"SIAM J Numer Anal"},{"issue":"5","key":"293_CR13","doi-asserted-by":"crossref","first-page":"2484","DOI":"10.1137\/070688675","volume":"46","author":"A Klawonn","year":"2008","unstructured":"Klawonn A, Rheinbach O, Widlund OB (2008) An analysis of a FETI-DP algorithm on irregular subdomains in the plane. SIAM J Numer Anal 46(5):2484\u20132504. doi: 10.1137\/070688675","journal-title":"SIAM J Numer Anal"},{"issue":"11","key":"293_CR14","doi-asserted-by":"crossref","first-page":"1523","DOI":"10.1002\/cpa.20156","volume":"59","author":"A Klawonn","year":"2006","unstructured":"Klawonn A, Widlund OB (2006) Dual-primal FETI methods for linear elasticity. Commun Pure Appl Math 59(11):1523\u20131572","journal-title":"Commun Pure Appl Math"},{"issue":"1","key":"293_CR15","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1137\/S0036142901388081","volume":"40","author":"A Klawonn","year":"2002","unstructured":"Klawonn A, Widlund OB, Dryja M (2002) Dual-primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients. SIAM J Numer Anal 40(1):159\u2013179","journal-title":"SIAM J Numer Anal"},{"key":"293_CR16","doi-asserted-by":"crossref","unstructured":"Knyazev AV (2001) Toward the optimal preconditioned eigensolver: locally optimal block preconditioned conjugate gradient method. Copper Mountain conference, 2000. SIAM J Sci Comput 23(2):517\u2013541","DOI":"10.1137\/S1064827500366124"},{"key":"293_CR17","volume-title":"Domain decomposition methods for distributed computing","author":"J Kruis","year":"2006","unstructured":"Kruis J (2006) Domain decomposition methods for distributed computing. Saxe-Coburg Publications, Kippen"},{"key":"293_CR18","unstructured":"Lesoinne M (2003) A FETI-DP corner selection algorithm for three-dimensional problems. In: Herrera I, Keyes DE, Widlund OB (eds) Domain decomposition methods in science and engineering. In: 14th international conference on domain decomposition methods, Cocoyoc, Mexico, January 6\u201312, 2002. National Autonomous University of Mexico (UNAM), M\u00e9xico, pp 217\u2013223. http:\/\/www.ddm.org"},{"issue":"2","key":"293_CR19","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1002\/nme.1553","volume":"66","author":"J Li","year":"2006","unstructured":"Li J, Widlund OB (2006) FETI-DP, BDDC, and block Cholesky methods. Int J Numer Methods Eng 66(2):250\u2013271","journal-title":"Int J Numer Methods Eng"},{"issue":"7","key":"293_CR20","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1002\/nla.341","volume":"10","author":"J Mandel","year":"2003","unstructured":"Mandel J, Dohrmann CR (2003) Convergence of a balancing domain decomposition by constraints and energy minimization. Numer Linear Algebra Appl 10(7):639\u2013659","journal-title":"Numer Linear Algebra Appl"},{"issue":"2","key":"293_CR21","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.apnum.2004.09.022","volume":"54","author":"J Mandel","year":"2005","unstructured":"Mandel J, Dohrmann CR, Tezaur R (2005) An algebraic theory for primal and dual substructuring methods by constraints. Appl Numer Math 54(2):167\u2013193","journal-title":"Appl Numer Math"},{"key":"293_CR22","first-page":"421","volume-title":"Domain decomposition methods in science and engineering XVI. Lecture notes in computational science and engineering","author":"J Mandel","year":"2006","unstructured":"Mandel J, Soused\u00edk B (2006) Adaptive coarse space selection in the BDDC and the FETI-DP iterative substructuring methods: optimal face degrees of freedom. In: Widlund OB, Keyes DE (eds) Domain decomposition methods in science and engineering XVI. Lecture notes in computational science and engineering, vol 55. Springer, Berlin, pp 421\u2013428"},{"issue":"8","key":"293_CR23","doi-asserted-by":"crossref","first-page":"1389","DOI":"10.1016\/j.cma.2006.03.010","volume":"196","author":"J Mandel","year":"2007","unstructured":"Mandel J, Soused\u00edk B (2007) Adaptive selection of face coarse degrees of freedom in the BDDC and the FETI-DP iterative substructuring methods. Comput Methods Appl Mech Eng 196(8):1389\u20131399","journal-title":"Comput Methods Appl Mech Eng"},{"key":"293_CR24","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/s00607-007-0254-y","volume":"81","author":"J Mandel","year":"2007","unstructured":"Mandel J, Soused\u00edk B (2007) BDDC and FETI-DP under minimalist assumptions. Computing 81:269\u2013280","journal-title":"Computing"},{"key":"293_CR25","doi-asserted-by":"crossref","unstructured":"Mandel J, Soused\u00edk B, Dohrmann CR (2007) On multilevel BDDC. Domain decomposition methods in science and engineering XVII. Lecture notes in computational science and engineering, vol 60, pp 287\u2013294","DOI":"10.1007\/978-3-540-75199-1_33"},{"issue":"2\u20133","key":"293_CR26","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s00607-008-0014-7","volume":"83","author":"J Mandel","year":"2008","unstructured":"Mandel J, Soused\u00edk B, Dohrmann CR (2008) Multispace and multilevel BDDC. Computing 83(2\u20133):55\u201385. doi: 10.1007\/s00607-008-0014-7","journal-title":"Computing"},{"issue":"10","key":"293_CR27","doi-asserted-by":"crossref","first-page":"1812","DOI":"10.1016\/j.matcom.2011.03.014","volume":"82","author":"J Mandel","year":"2001","unstructured":"Mandel J, Soused\u00edk B, \u0160\u00edstek J (2001) Adaptive BDDC in three dimensions. Math Comput Simul 82(10):1812\u20131831. doi: 10.1016\/j.matcom.2011.03.014","journal-title":"Math Comput Simul"},{"key":"293_CR28","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1007\/s211-001-8014-1","volume":"88","author":"J Mandel","year":"2001","unstructured":"Mandel J, Tezaur R (2001) On the convergence of a dual-primal substructuring method. Numer Math 88:543\u2013558","journal-title":"Numer Math"},{"issue":"2","key":"293_CR29","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/s00211-008-0186-2","volume":"111","author":"C Pechstein","year":"2008","unstructured":"Pechstein C, Scheichl R (2008) Analysis of FETI methods for multiscale PDEs. Numer Math 111(2):293\u2013333","journal-title":"Numer Math"},{"issue":"3","key":"293_CR30","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1007\/s00211-011-0359-2","volume":"118","author":"C Pechstein","year":"2011","unstructured":"Pechstein C, Scheichl R (2011) Analysis of FETI methods for multiscale PDEs\u2014Part II: interface variations. Numer Math 118(3):485\u2013529","journal-title":"Numer Math"},{"key":"293_CR31","unstructured":"\u0160\u00edstek J, Mandel J, Soused\u00edk B (2012) Some practical aspects of parallel adaptive BDDC method. In: Brandts J, Chleboun J, Korotov S, Segeth K, \u0160\u00edstek J, Vejchodsk\u00fd T (eds) Proceedings of Applications of Mathematics 2012. Institute of Mathematics AS CR, pp 253\u2013266"},{"key":"293_CR32","doi-asserted-by":"crossref","unstructured":"\u0160\u00edstek J, Mandel J, Soused\u00edk B, Burda P (2013) Parallel implementation of Multilevel BDDC. In: Proceedings of ENUMATH 2011. Springer, Berlin (to appear)","DOI":"10.1007\/978-3-642-33134-3_72"},{"issue":"10","key":"293_CR33","doi-asserted-by":"crossref","first-page":"1799","DOI":"10.1016\/j.matcom.2011.06.007","volume":"82","author":"J \u0160\u00edstek","year":"2012","unstructured":"\u0160\u00edstek J, \u010cert\u00edkov\u00e1 M, Burda P, Novotn\u00fd J (2012) Face-based selection of corners in 3D substructuring. Math Comput Simul 82(10):1799\u20131811. doi: 10.1016\/j.matcom.2011.06.007","journal-title":"Math Comput Simul"},{"key":"293_CR34","volume-title":"Domain decomposition: parallel multilevel methods for elliptic partial differential equations","author":"BF Smith","year":"1996","unstructured":"Smith BF, Bj\u00f8rstad PE, Gropp WD (1996) Domain decomposition: parallel multilevel methods for elliptic partial differential equations. Cambridge University Press, Cambridge"},{"key":"293_CR35","unstructured":"Soused\u00edk B (2008) Comparison of some domain decomposition methods. Ph.D. thesis, Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mathematics. http:\/\/mat.fsv.cvut.cz\/doktorandi\/files\/BSthesisCZ.pdf . Retrieved December 2011"},{"key":"293_CR36","unstructured":"Soused\u00edk B (2010) Adaptive-Multilevel BDDC. Ph.D. thesis, University of Colorado Denver, Department of Mathematical and Statistical Sciences"},{"key":"293_CR37","unstructured":"Soused\u00edk B (2011) Nested BDDC for a saddle-point problem. submitted to Numerische Mathematik. http:\/\/arxiv.org\/abs\/1109.0580"},{"key":"293_CR38","unstructured":"Soused\u00edk B, Mandel J (2008) On the equivalence of primal and dual substructuring preconditioners. Electron Trans Numer Anal 31:384\u2013402. http:\/\/etna.mcs.kent.edu\/vol.31.2008\/pp384-402.dir\/pp384-402.html . Retrieved December 2011"},{"key":"293_CR39","doi-asserted-by":"crossref","unstructured":"Soused\u00edk B, Mandel J (2011) On Adaptive-Multilevel BDDC. In: Huang Y, Kornhuber R, Widlund O, Xu J (eds) Domain decomposition methods in science and engineering XIX. Lecture notes in computational science and engineering vol 78, Part 1. Springer, Berlin, pp 39\u201350. doi: 10.1007\/978-3-642-11304-8_4","DOI":"10.1007\/978-3-642-11304-8_4"},{"key":"293_CR40","doi-asserted-by":"crossref","unstructured":"Toselli A, Widlund OB (2005) Domain decomposition methods\u2014algorithms and theory. In: Springer series in computational mathematics, vol 34. Springer, Berlin","DOI":"10.1007\/b137868"},{"issue":"4","key":"293_CR41","doi-asserted-by":"crossref","first-page":"1759","DOI":"10.1137\/050629902","volume":"29","author":"X Tu","year":"2007","unstructured":"Tu X (2007) Three-level BDDC in three dimensions. SIAM J Sci Comput 29(4):1759\u20131780. doi: 10.1137\/050629902","journal-title":"SIAM J Sci Comput"},{"issue":"1","key":"293_CR42","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1002\/nme.1753","volume":"69","author":"X Tu","year":"2007","unstructured":"Tu X (2007) Three-level BDDC in two dimensions. Int J Numer Methods Eng 69(1):33\u201359. doi: 10.1002\/nme.1753","journal-title":"Int J Numer Methods Eng"},{"issue":"1","key":"293_CR43","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/s00211-011-0375-2","volume":"119","author":"X Tu","year":"2011","unstructured":"Tu X (2011) A three-level BDDC algorithm for a saddle point problem. Numer Math 119(1):189\u2013217. doi: 10.1007\/s00211-011-0375-2","journal-title":"Numer Math"},{"key":"293_CR44","doi-asserted-by":"crossref","unstructured":"Widlund OB (2009) Accomodating irregular subdomains in domain decomposition theory. In: Bercovier M, Gander M, Kornhuber R, Widlund O (eds) Domain decomposition methods in science and engineering XVIII. Proceedings of 18th international conference on domain decomposition. Jerusalem, Israel, January 2008. Lecture notes in computational science and engineering, vol 70. Springer, Berlin","DOI":"10.1007\/978-3-642-02677-5_8"}],"container-title":["Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00607-013-0293-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00607-013-0293-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00607-013-0293-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,8]],"date-time":"2019-07-08T13:19:52Z","timestamp":1562591992000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00607-013-0293-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,19]]},"references-count":44,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2013,12]]}},"alternative-id":["293"],"URL":"https:\/\/doi.org\/10.1007\/s00607-013-0293-5","relation":{},"ISSN":["0010-485X","1436-5057"],"issn-type":[{"value":"0010-485X","type":"print"},{"value":"1436-5057","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1,19]]}}}