{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:55Z","timestamp":1787337235502,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2001,1]]},"abstract":"<jats:p>The solution of elliptic problems is challenging on parallel distributed memory computers since their Green's functions are global. To address this issue, we present a set of preconditioners for the Schur complement domain decomposition method. They implement a global coupling mechanism, through coarse-space components, similar to the one proposed in [Bramble, Pasciak, and Shatz, Math. Comp., 47 (1986), pp. 103--134]. The definition of the coarse-space components is algebraic; they are defined using the mesh partitioning information and simple interpolation operators. These preconditioners are implemented on distributed memory computers without introducing any new global synchronization in the preconditioned conjugate gradient iteration. The numerical and parallel scalability of those preconditioners are illustrated on two-dimensional model examples that have anisotropy and\/or discontinuity phenomena.<\/jats:p>","DOI":"10.1137\/s1064827598340809","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1987-2005","source":"Crossref","is-referenced-by-count":28,"title":["Algebraic Two-Level Preconditioners for the Schur Complement Method"],"prefix":"10.1137","volume":"22","author":[{"given":"L. M.","family":"Carvalho","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L.","family":"Giraud","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P.","family":"Le Tallec","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","unstructured":"E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Oustrouchov, and D. Sorensen,\n                      LAPACK Users\u2019 Guide\n                      , 2nd ed., SIAM, Philadelphia, 1995."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1986-0842125-3"},{"key":"R3","unstructured":"L. Carvalho,\n                      Preconditioned Schur Complement Methods in Distributed Memory Environments\n                      , Ph.D. thesis, INPT\/CERFACS, France, 1997."},{"key":"R4","doi-asserted-by":"crossref","unstructured":"Tony Chan, Tarek Mathew, Domain decomposition algorithms, Acta Numer., Cambridge Univ. Press, Cambridge, 1994, 61\u201314395f:65214","DOI":"10.1017\/S0962492900002427"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/0613018"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/0731086"},{"key":"R7","unstructured":"I. Duff and J. Reid,\n                      MA27\u2014A Set of Fortran Subroutines for Solving Sparse Symmetric Sets of Linear Equations\n                      , Tech. Report AERE R10533, Rutherford Appleton Laboratory, London, 1982."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620320604"},{"key":"R9","volume-title":"Computer solution of large sparse positive definite systems","author":"George Alan","year":"1981"},{"key":"R10","unstructured":"L. Giraud, F. Guevara Vasquez, and R. S. Tuminaro,\n                      Grid Transfer Operators for Highly Variable Coefficient Problems in Two\u2010Level Non\u2010Overlapping Domain Decomposition Methods\n                      , CERFACS Tech. Report TR\/PA\/01\/03, Toulouse, France, 2001."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/19.1.1"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1108\/eb051893"},{"key":"R13","first-page":"121","volume":"1","author":"Le Tallec Patrick","year":"1994","journal-title":"Comput. Mech. Adv."},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.1640090307"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-96-00757-0"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050201"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1137\/0917010"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(99)00127-3"},{"key":"R19","unstructured":"B. Smith,\n                      Domain Decomposition Algorithms for the Partial Differential Equations of Linear Elasticity\n                      , Tech. Report 517, Department of Computer Science, Courant Institute, New York, 1990."},{"key":"R20","unstructured":"B. Smith, P. Bj\u00f8rstad, and W. Gropp,\n                      Domain Decomposition, Parallel Multilevel Methods for Elliptic Partial Differential Equations\n                      , 1st ed., Cambridge University Press, New York, 1996."},{"key":"R21","unstructured":"W. Wan,\n                      Scalable and Multilevel Iteratives Methods\n                      , Ph.D. thesis, Department of Mathematics, UCLA, Los Angeles, 1998."},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598334277"},{"key":"R23","volume-title":"An introduction to multigrid methods","author":"Wesseling Pieter","year":"1992"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827598340809","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:51:29Z","timestamp":1787334689000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827598340809"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,1]]},"references-count":23,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2001,1]]}},"alternative-id":["10.1137\/S1064827598340809"],"URL":"https:\/\/doi.org\/10.1137\/s1064827598340809","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,1]]}}}