{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T07:33:50Z","timestamp":1787384030904,"version":"build-2736575974"},"reference-count":43,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>Dual\u2010primal FETI methods for linear elasticity problems in three dimensions are considered. These are nonoverlapping domain decomposition methods where some primal continuity constraints across subdomain boundaries are required to hold throughout the iterations, whereas most of the constraints are enforced by Lagrange multipliers. An algorithmic framework for dual\u2010primal FETI methods is described together with a transformation of basis to implement the primal constraints. Numerical results obtained from a parallel implementation of these algorithms applied to a model benchmark problem with structured meshes and to problems with more complicated geometries from industrial and biological applications using unstructured meshes are provided. These results show that the presented dual\u2010primal FETI algorithms are numerical and parallel scalable.<\/jats:p>","DOI":"10.1137\/050624364","type":"journal-article","created":{"date-parts":[[2006,11,20]],"date-time":"2006-11-20T18:58:26Z","timestamp":1164049106000},"page":"1886-1906","source":"Crossref","is-referenced-by-count":66,"title":["A Parallel Implementation of Dual\u2010Primal FETI Methods for Three\u2010Dimensional Linear Elasticity Using a Transformation of Basis"],"prefix":"10.1137","volume":"28","author":[{"given":"Axel","family":"Klawonn","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Oliver","family":"Rheinbach","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,11,16]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479899358194"},{"key":"R2","unstructured":"S. Balay, K. Buschelman, V. Eijkhout, W. D. Gropp, D. Kaushik, M. G. Knepley, L. Curfman McInnes, B. F. Smith, and H. Zhang,\n                      PETSc Users Manual\n                      , Technical report ANL\u201095\/11, Revision 2.1.5, Argonne National Laboratory, Argonne, IL, 2004."},{"key":"R3","unstructured":"S. Balay, K. Buschelman, W. D. Gropp, D. Kaushik, M. Knepley, L. Curfman McInnes, B. F. Smith, and H. Zhang,\n                      PETSc Home Page\n                      , http:\/\/www.mcs.anl.gov\/petsc, 2001."},{"key":"R4","doi-asserted-by":"crossref","unstructured":"S. Balay, V. Eijkhout, W. D. Gropp, L. Curfman McInnes, and B. F. Smith,\n                      Efficient management of parallelism in object oriented numerical software libraries\n                      , in Modern Software Tools in Scientific Computing, E. Arge, A. M. Bruaset, and H. P. 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Karypis, K. Schloegel, and V. Kumar,\n                      ParMetis\u2014Parallel Graph Partitioning and Sparse Matrix Ordering\n                      , Version 3.1, Technical report, Department of Computer Science and Engineering, University of Minnesota, 2003."},{"key":"R21","unstructured":"A. Klawonn and O. Rheinbach,\n                      Robust FETI\u2010DP Methods for Heterogeneous Three Dimensional Linear Elasticity Problems\n                      , Technical report TR\u2010SM\u2010E\u2010607, Department of Mathematics, University of Duisburg\u2010Essen, Germany, 2005, revised 2006. Comput. Methods Appl. Mech. Engrg., to appear."},{"key":"R22","unstructured":"A. Klawonn and O. Rheinbach,\n                      Inexact FETI\u2010DP Methods\n                      , Technical report TR\u2010SM\u2010E\u2010609, Department of Mathematics, University of Duisburg\u2010Essen, Germany, 2005, revised 2006. Internat. J. Numer. Methods Engrg., to appear."},{"key":"R23","unstructured":"A. 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Engrg., Springer\u2010Verlag, Berlin, 2005, pp. 67\u201381.","DOI":"10.1007\/3-540-26825-1_5"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901388081"},{"key":"R28","doi-asserted-by":"crossref","unstructured":"A. Klawonn, O. B. Widlund, and M. Dryja,\n                      Dual\u2010Primal FETI methods with face constraints\n                      , in Recent Developments in Domain Decomposition Methods, L. F. Pavarino and A. Toselli, eds., Lecture Notes in Comput. Sci. Engrg. 23, Springer\u2010Verlag, Berlin, 2002, pp. 27\u201340.","DOI":"10.1007\/978-3-642-56118-4_2"},{"key":"R29","unstructured":"M. Lesoinne,\n                      A FETI\u2010DP corner selection algorithm for three\u2010dimensional problems\n                      , in Domain Decomposition Methods in Science and Engineering, I. Herrera, D. E. Keyes, O. B. Widlund, and R. 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Tu,\n                      Three\u2010Level BDDC in Three Dimensions\n                      , Technical report TR2005\u2010862, Department of Computer Science, Courant Institute, New York University, New York, 2005."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/050624364","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:55:20Z","timestamp":1787334920000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/050624364"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":43,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/050624364"],"URL":"https:\/\/doi.org\/10.1137\/050624364","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}