@ARTICLE{Achdou:1995:SPF, OLDTAG = "achkuz", AUTHOR = "Yves Achdou and Yuri A. Kuznetsov", TITLE = "Substructuring Preconditioners for Finite Element Methods on Nonmatching Grids", YEAR = 1995, VOLUME = 3, NUMBER = 1, JOURNAL = "East-West J. Numer. Math.", PAGES = "1--28" } @ARTICLE{Achdou:1995:SPM, OLDTAG = "1ackupi", AUTHOR = "Yves Achdou and Yuri A. Kuznetsov and Olivier Pironneau", TITLE = "Substructuring Preconditioners for the ${Q}_1$ Mortar Element Method", YEAR = 1995, JOURNAL = "Numer. Math.", VOLUME = 71, NUMBER = 4, PAGES = "419--449" } @TECHREPORT{Achdou:1996:ISP, OLDTAG = "achmadwid1", AUTHOR = "Yves Achdou and Yvon Maday and Olof B. Widlund", TITLE = "Iterative Substructuring Preconditioners for the Mortar Finite Element Method in Two Dimensions", INSTITUTION = "Department of Computer Science, Courant Institute", YEAR = 1996, NOTE = "In preparation." } @ARTICLE{Achdou:1996:MIS, OLDTAG = "achmadwid0", AUTHOR = "Yves Achdou and Yvon Maday and Olof B. Widlund", TITLE = "M\'{e}thode it\'{e}rative de sous-structuration pour les \'{e}l\'{e}ments avec joints", YEAR = 1996, JOURNAL = "C.R. Acad. Sci. Paris", SERIES = "I", NUMBER = 322, PAGES = "185--190" } @INPROCEEDINGS{Agoshkov:1988:PSO, OLDTAG = "agos", AUTHOR = "V. I. Agoshkov", TITLE = "Poincar{\'e}-{S}teklov Operators and Domain Decomposition Methods in Finite Dimensional Spaces", BOOKTITLE = "{F}irst {I}nternational {S}ymposium on {D}omain {D}ecomposition {M}ethods for {P}artial {D}ifferential {E}quations", YEAR = 1988, EDITOR = "Roland Glowinski and Gene H. Golub and G{\'e}rard A. Meurant and Jacques P{\'e}riaux", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @ARTICLE{Argyris:1959:AFA, OLDTAG = "arg-kel1", AUTHOR = "J. H. Argyris and S. Kelsey", JOURNAL = "Aircraft Engineering", VOLUME = 31, YEAR = 1959, TITLE = "The analysis of fuselages of arbitrary cross-section and taper" } @ARTICLE{Argyris:1960:AFA, OLDTAG = "arg-kel2", AUTHOR = "J. H. Argyris and S. Kelsey", JOURNAL = "Aircraft Engineering", VOLUME = 33, YEAR = 1960, TITLE = "The analysis of fuselages of arbitrary cross-section and taper" } @ARTICLE{Astrakhatsev:1978:MFD, OLDTAG = "astra1", AUTHOR = "G. P. Astrakhatsev", TITLE = "Method of fictitious domains for a second-order elliptic equation with natural boundary conditions", JOURNAL = "U.S.S.R. Computational Math. and Math. Phys.", VOLUME = 18, YEAR = 1978, PAGES = "114--121" } @BOOK{Axelsson:1994:ISM, OLDTAG = "axel", AUTHOR = "Owe Axelsson", TITLE = "Iterative Solution Methods", YEAR = 1994, PUBLISHER = "Cambridge University Press", ADDRESS = "New York" } @ARTICLE{Babuska:1957:USA, OLDTAG = "1babu", AUTHOR = "Ivo Babu\v{s}ka", TITLE = "{\"U}ber {S}chwarzsche {A}lgorithmen in partiellen {D}ifferentialgleichungen der mathematischen {P}hysik", JOURNAL = "ZAMM", YEAR = 1957, VOLUME = 37, NUMBER = "7/8", PAGES = "243--245" } @ARTICLE{Babuska:1958:SAP, OLDTAG = "2babu", AUTHOR = "Ivo Babu\v{s}ka", TITLE = "The {S}chwarz Algorithm in Partial Differential Equations of Mathematical Physics", JOURNAL = "Czech. Math. J. ", YEAR = 1958, VOLUME = 83, NUMBER = 8, PAGES = "328--343", NOTE = "In Russian" } @ARTICLE{Babuska:1989:API, OLDTAG = "1bael", AUTHOR = "Ivo Babu\v{s}ka and Howard C. Elman", TITLE = "Some Aspects of Parallel Implementation of the Finite-Element Method on Message Passing Architectures", YEAR = 1989, VOLUME = 27, PAGES = "157--187", JOURNAL = "J. Comp. Appl. Math." } @ARTICLE{Babuska:1989:PSS, OLDTAG = "1bgp", AUTHOR = "Ivo Babu\v{s}ka and Michael Griebel and Juhani Pitk{\"{a}}ranta", TITLE = "The Problem of Selecting the Shape Functions for a p-type Finite Element", PAGES = "1891 -- 1908", VOLUME = 28, JOURNAL = "Int. J. Numer. Meth. Eng.", YEAR = 1989 } @ARTICLE{Babuska:1991:EPP, OLDTAG = "bcmp", AUTHOR = "Ivo Babu\v{s}ka and Alan Craig and Jan Mandel and Juhani Pitk{\"a}ranta", TITLE = "Efficient Preconditioning for the p-Version Finite Element Method in Two Dimensions", YEAR = 1991, VOLUME = 28, NUMBER = 3, PAGES = "624--661", JOURNAL = "SIAM J. Numer. Anal." } @ARTICLE{Bakhvalov:1966:CRM, OLDTAG = "bak", AUTHOR = "N. S. Bakhvalov", TITLE = "On the Convergence of a Relaxation Method with Natural Constraints on the Elliptic Operator", JOURNAL = "USSR Comput. Math. and Math. Phys.", VOLUME = 6, YEAR = 1966, PAGES = "101--135" } @ARTICLE{Bank:1988:HBM, OLDTAG = "baduys", AUTHOR = "Randolph E. Bank and Todd F. Dupont and Harry Yserentant", TITLE = "The Hierarchical Basis Multigrid Method", JOURNAL = "Numer. Math.", YEAR = 1988, VOLUME = 52, PAGES = "427 -- 458" } @ARTICLE{Bank:1990:CIM, OLDTAG = "baduys", AUTHOR = "Randolph E. Bank and Bruno D. Welfert and Harry Yserentant", TITLE = "A Class of Iterative Methods for Solving Saddle Point Problems", JOURNAL = "Numer. Math.", YEAR = 1990, VOLUME = 56, PAGES = "645 -- 666" } @BOOK{Bank:1990:PSP, OLDTAG = "bank1", AUTHOR = "Randolph E. Bank", TITLE = "PLTMG: A Software Package for Solving Elliptic Partial Differential Equations. Users' Guide 7.0", YEAR = 1990, PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @TECHREPORT{Belgacem:1992:AME, OLDTAG = "benbelg-maday0", AUTHOR = "Ben Belgacem, Faker and Yvon Maday", TITLE = "Adaption de la m\'{e}thode des \'{e}l\'{e}ments avec joints au couplage spectral \'{e}l\'ments finis en dimension 3. {E}tude de l'\'{e}rreur pour l'\'{e}quation de {P}oisson", YEAR = 1992, MONTH = "April", NOTE = "Tech. Rep. HI-72/7095", INSTITUTION = "Electricit\'{e} de France" } @TECHREPORT{Belgacem:1992:RPC, OLDTAG = "benbelg", AUTHOR = "Ben Belgacem, Faker", TITLE = "Rel\`{e}vement Polyn\^{o}miaux sur un Cube", INSTITUTION = "Electricit\'{e} de France", YEAR = 1992, NUMBER = "HI-72/7780" } @PHDTHESIS{Belgacem:1993:D3N, OLDTAG = "benbelg_thesis", AUTHOR = "Ben Belgacem, Faker", TITLE = "Discretisations 3{D} Non Conformes pour la M\'{e}thode de Decomposition de Domaine des {E}l\'{e}ment avec Joints: Analyse Math\'{e}matique et Mise en {\OE}vre pour le Probleme de {P}oisson", SCHOOL = "Universit\'{e} {P}ierre et {M}arie Curie, {P}aris, {F}rance", YEAR = 1993, MONTH = "January", NOTE = "Tech. Rep. HI-72/93017, Electricit\'{e} de France" } @UNPUBLISHED{Belgacem:1993:MEM, OLDTAG = "benbelg-maday2", AUTHOR = "Ben Belgacem, Faker and Yvon Maday", TITLE = "The Mortar Element Method for Three Dimensional Finite Elements", NOTE = "Unpublished paper based on Yvon Maday's talk at the Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing, held at Penn State University, October 27-30, 1993", YEAR = 1993 } @TECHREPORT{Belgacem:1993:NSE, OLDTAG = "benbelg-maday1", AUTHOR = "Ben Belgacem, Faker and Yvon Maday", TITLE = "Non-conforming Spectral Element Method for Second Order Elliptic Problem in {3D}", INSTITUTION = "Laboratoire d'Analyse Num\'{e}rique, Universit\'{e} Pierre et Marie Curie -- Centre National de la Recherche Scientifique", YEAR = 1993, NUMBER = "R93039" } @UNPUBLISHED{Belgacem:1994:MEM, OLDTAG = "benbelg2", AUTHOR = "Ben Belgacem, Faker", TITLE = "The Mortar Element Method with {L}agrange Multipliers", NOTE = "Universit\'{e} Paul Sabatier, % 118 route de Narbonne, 31062 Toulouse, France", YEAR = 1994 } @BOOK{Bell:1973:NPS, OLDTAG = "norsam", AUTHOR = "Bell, K. and Hatlestad, B. and Hansteen, O. E. and Araldsen, Per O.", TITLE = "NORSAM, a programming system for the finite element method. {U}sers manual, {P}art 1, {G}eneral description.", PUBLISHER = "NTH, Trondheim", YEAR = 1973 } @ARTICLE{Bellman:1944:NIE, OLDTAG = "bell", AUTHOR = "Richard Bellman", TITLE = "A Note on an Inequality of {E}. {S}chmidt", JOURNAL = "Bull. Amer. Math. Soc.", VOLUME = 50, YEAR = 1944, PAGES = "734--736" } @INPROCEEDINGS{Benamou:1995:DDM, AUTHOR = "J. D. Benamou", TITLE = "A domain decomposition method for the optimal control of system governed by the Helmholtz equation", BOOKTITLE = "Third international conference on mathematical and numerical wave propagation phenomena", YEAR = 1995, EDITOR = "G. Cohen", PUBLISHER = "SIAM" } @ARTICLE{Benamou:1995:DPF, AUTHOR = "J. D. Benamou", TITLE = "A domain decomposition method for the polar factorization of vector valued mappings", YEAR = 1995, JOURNAL = "SIAM J. on Numer. Anal.", VOLUME = 32, PAGES = "1808--1838" } @ARTICLE{Benamou:1996:DMC, AUTHOR = "J. D. Benamou", TITLE = "Domain Decomposition Methods with Coupled Transmission Conditions for the Optimal Control of Systems Governed by Elliptic partial Differential Equations", YEAR = 1996, JOURNAL = "SINUM", VOLUME = 33 } @ARTICLE{Bernardi:1990:RPT, OLDTAG = "bernmada1", AUTHOR = "Christine Bernardi and Yvon Maday", TITLE = "Rel\`{e}vement Polynomial de Traces et Applications", JOURNAL = "$M^{2}AN$", VOLUME = 24, NUMBER = 5, YEAR = 1990, PAGES = "557--611" } @BOOK{Bernardi:1992:ASP, OLDTAG = "bernmada2", AUTHOR = "Christine Bernardi and Yvon Maday", TITLE = "Approximations Spectrales de Probl\`{e}mes aux Limites Elliptiques", PUBLISHER = "Springer-Verlag France", ADDRESS = "Paris", SERIES = "Math\`{e}matiques \& Applications", VOLUME = 10, YEAR = 1992 } @ARTICLE{Bernardi:1992:PIR, OLDTAG = "bm92", AUTHOR = "C. Bernardi and Y. Maday", TITLE = "Polynomial interpolation results in {S}obolev spaces", YEAR = 1992, VOLUME = 43, PAGES = "53 -- 80", JOURNAL = "J. Comput. Appl. Math." } @INCOLLECTION{Bernardi:1994:NNA, OLDTAG = "bermadpat", AUTHOR = "Christine Bernardi and Yvon Maday and Anthony T.\ Patera", TITLE = "A New Non Conforming Approach to Domain Decomposition: The Mortar Element Method", BOOKTITLE = "Coll\`{e}ge de France Seminar", PUBLISHER = "Pitman", YEAR = 1994, EDITOR = "Haim Brezis and Jacques-Louis Lions", NOTE = "This paper appeared as a technical report about five years earlier." } @TECHREPORT{Bernardi:1995:MAF, OLDTAG = "bernmada3", AUTHOR = "Christine Bernardi and Yvon Maday", TITLE = "Mesh adaptivity in finite elements by the mortar method", INSTITUTION = "Laboratoire d'Analyse Num\'{e}rique, Universit\'{e} Pierre et Marie Curie -- Centre National de la Recherche Scientifique", YEAR = 1995, MONTH = "January", NUMBER = "R94029" } @PHDTHESIS{Bjorstad:1980:NSB, OLDTAG = "bjthesis", AUTHOR = "Petter E. Bj{\o}rstad", SCHOOL = "Stanford University, Stanford, CA", TITLE = "Numerical solution of the biharmonic equation", YEAR = 1980 } @INPROCEEDINGS{Bjorstad:1984:SEP, OLDTAG = "1bjw", AUTHOR = "Petter E. Bj{\o}rstad and Olof B. Widlund", TITLE = "Solving elliptic problems on regions partitioned into substructures", BOOKTITLE = "Elliptic Problem Solvers {II}", YEAR = 1984, EDITOR = "Garrett Birkhoff and Arthur Schoenstadt", PAGES = "245--256", PUBLISHER = "Academic Press", ADDRESS = "New York" } @ARTICLE{Bjorstad:1986:IMS , OLDTAG = "2bjw", AUTHOR = "Petter E. Bj{\o}rstad and Olof B. Widlund", TITLE = "Iterative methods for the solution of elliptic problems on regions partitioned into substructures", JOURNAL = "SIAM J. Numer. Anal.", YEAR = 1986, VOLUME = 23, NUMBER = "6 ", PAGES = "1093--1120" } @ARTICLE{Bjorstad:1987:LSS, OLDTAG = "pb-loen", AUTHOR = "Petter E. Bj{\o}rstad", TITLE = "A large scale, sparse, secondary storage, direct linear equation solver for structural analysis and its implementation on vector and parallel architectures.", JOURNAL = "Journal on Parallel Computing", YEAR = 1987, VOLUME = 5 } @INPROCEEDINGS{Bjorstad:1988:IMS, OLDTAG = "bjhv", AUTHOR = "Petter E. Bj{\o}rstad and Anders Hvidsten", TITLE = "Iterative Methods for Substructured Elasticity Problems in Structural Analysis", BOOKTITLE = "Domain Decomposition Methods for Partial Differential Equations", PUBLISHER = "SIAM", YEAR = 1988, EDITOR = "Roland Glowinski and Gene H. Golub and G{\'e}rard A. Meurant and Jacques P{\'e}riaux", ADDRESS = "Philadelphia, PA", PAGES = "301--312" } @INPROCEEDINGS{Bjorstad:1989:MAS, OLDTAG = "bjoe", AUTHOR = "Petter E. Bj{\o}rstad", TITLE = "{M}ultiplicative and {A}dditive {S}chwarz {M}ethods: {C}onvergence in the 2 domain case", BOOKTITLE = "Domain Decomposition Methods", YEAR = 1989, EDITOR = "Tony Chan and Roland Glowinski and Jacques P{\'e}riaux and Olof Widlund", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", PAGES = "147--159" } @ARTICLE{Bjorstad:1989:OON, OLDTAG = "3bjw", AUTHOR = "Petter E. Bj{\o}rstad and Olof B. Widlund", TITLE = "To Overlap or Not to Overlap: {A} Note on a Domain Decomposition Method for Elliptic Problems", JOURNAL = "SIAM J. Sci. Stat. Comput.", YEAR = 1989, VOLUME = 10, NUMBER = 5, PAGES = "1053--1061" } @INPROCEEDINGS{Bjorstad:1990:PDI, OLDTAG = "bjmosk", AUTHOR = "Petter E. Bj{\o}rstad and Randi Moe and Morten Skogen", TITLE = "Parallel Domain Decomposition and Iterative Refinement Algorithms", EDITOR = "Wolfgang Hackbusch", BOOKTITLE = "Parallel Algorithms for PDEs, Proceedings of the 6th GAMM-Seminar held in Kiel, Germany, January 19--21, 1990", PUBLISHER = "Vieweg-Verlag", ADDRESS = "Braunschweig, Wiesbaden", YEAR = 1990 } @INPROCEEDINGS{Bjorstad:1991:PSM, AUTHOR = "Petter E. Bj{\o}rstad and Jon Br{\ae}khus and Anders Hvidsten", TITLE = "Parallel Substructuring Algorithms in Structural Analysis, Direct and Iterative Methods", BOOKTITLE = "Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations", YEAR = 1991, EDITOR = "Roland Glowinski and Yuri A. Kuznetsov and G{\'e}rard A. Meurant and Jacques P{\'e}riaux and Olof B. Widlund", PAGES = "321--340", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", NOTE = "Proceedings from the fourth international symposium on domain decomposition, Moscow May 1990", URL = "http://www.ii.uib.no/~petter/reports/moscow_siam.ps.gz" } @ARTICLE{Bjorstad:1991:SSO, OLDTAG = "bjma", AUTHOR = "Petter E. Bj{\o}rstad and Jan Mandel", TITLE = "On the Spectra of Sums of Orthogonal Projections with Applications to Parallel Computing", JOURNAL = "BIT", PAGES = "76--88", VOLUME = 31, YEAR = 1991 } @INPROCEEDINGS{Bjorstad:1992:DAS, OLDTAG = "bjsk", AUTHOR = "Petter E. Bj{\o}rstad and Morten Skogen", TITLE = "Domain Decomposition Algorithms of {S}chwarz Type, Designed for Massively Parallel Computers", EDITOR = "David E. Keyes and Tony F. Chan and G{\'e}rard A. Meurant and Jeffrey S. Scroggs and Robert G. Voigt", BOOKTITLE = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations", PUBLISHER = "SIAM", YEAR = 1992, ADDRESS = "Philadelphia, PA", PAGES = "362--375" } @INPROCEEDINGS{Bjorstad:1994:DAO, OLDTAG = "bj-db-book", AUTHOR = "Petter Bj{\o}stad", TITLE = "Domain Decomposition Applied to Oil Reservoir Simulation", BOOKTITLE = "Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering", EDITOR = "D. Keyes and Y. Saad and D. Truhlar", YEAR = 1994, PUBLISHER = "SIAM", NOTE = "To appear." } @INPROCEEDINGS{Bjorstad:1996:PIS, AUTHOR = "Petter E. Bj{\o}rstad and Maksimilian Dryja and Eero Vainikko", TITLE = "Parallel implementation of a {S}chwarz Domain Decomposition Algorithm", BOOKTITLE = "Applied Parallel Computing in Industrial Problems and Optimization", YEAR = 1996, EDITOR = "Jerzy Wasniewski and Jack Dongarra and Kaj Madsen and Dorte Olesen", PUBLISHER = "Springer", MONTH = "December", NOTE = "Lecture Notes in Computer Science volume 1184", URL = "http://www.ii.uib.no/~petter/reports/para96.ps.gz" } @INPROCEEDINGS{Bjorstad:1997:ASM, AUTHOR = "Petter E. Bj{\o}rstad and Maksymilian Dryja and Eero Vainikko", TITLE = "Additive {S}chwarz Methods without Subdomain Overlap and with New Coarse Spaces", BOOKTITLE = "Domain Decomposition Methods in Sciences and Engineering", YEAR = 1997, EDITOR = "R. Glowinski and J. P\'{e}riaux and Z. Shi and O. B. Widlund", PUBLISHER = "John Wiley \& Sons", NOTE = "Proceedings from the Eight International Conference on Domain Decomposition Metods, May 1995, Beijing" } @INPROCEEDINGS{Bjorstad:1997:RAS, AUTHOR = "Petter E. Bj{\o}rstad and Maksymilian Dryja and Eero Vainikko", TITLE = "Robust Additive {S}chwarz Methods on Unstructured Grids", BOOKTITLE = "Domain Decomposition Methods in Sciences and Engineering", YEAR = 1997, EDITOR = "Petter E. Bj{\o}rstad and Magne Espedal and David Keyes", PUBLISHER = "John Wiley \& Sons", NOTE = "Proceedings from the Ninth International Conference, June 1996, Bergen, Norway" } @ARTICLE{Borgers:1989:DLS, OLDTAG = "2bowi", AUTHOR = "Christoph B{\"o}rgers and Olof B. Widlund", TITLE = "A Domain Decomposition {L}aplace Solver for Internal Combustion Modeling", JOURNAL = "SIAM J. Sci. Stat. Comput.", YEAR = 1989, VOLUME = 10, NUMBER = 4, PAGES = "211--226" } @ARTICLE{Borgers:1989:NDD, OLDTAG = "1bor", AUTHOR = "Christoph B{\"o}rgers", TITLE = "The {N}eumann--{D}irichlet domain decomposition method with inexact solvers on the subdomains", JOURNAL = "Numer. Math.", VOLUME = 55, YEAR = 1989, PAGES = "123--136" } @ARTICLE{Borgers:1990:FED, OLDTAG = "1bowi", AUTHOR = "Christoph B{\"o}rgers and Olof B. Widlund", TITLE = "On Finite Element Domain Imbedding Methods", JOURNAL = "SIAM J. Numer. Anal.", YEAR = 1990, MONTH = "August", VOLUME = 27, NUMBER = 4 } @ARTICLE{Bornemann:1993:BNE, OLDTAG = "boys", AUTHOR = "Folkmar Bornemann and Harry Yserentant", TITLE = "A Basic Norm Equivalence for the Theory of Multilevel Methods", YEAR = 1993, JOURNAL = "Numer. Math.", VOLUME = 64, NUMBER = 4, PAGES = "455--476" } @INPROCEEDINGS{Bourgat:1989:VFA, OLDTAG = "bgltv", AUTHOR = "Jean-Fran\c{c}ois Bourgat and Roland Glowinski and Le Tallec, Patrick and Marina Vidrascu", TITLE = "Variational Formulation and Algorithm for Trace Operator in Domain Decomposition Calculations", BOOKTITLE = "Domain Decomposition Methods", YEAR = 1989, EDITOR = "Tony Chan and Roland Glowinski and Jacques P{\'e}riaux and Olof Widlund", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", PAGES = "3--16" } @INPROCEEDINGS{Bourgat:1994:CBE, OLDTAG = "blpq", AUTHOR = "J. F. Bourgat and P. Le Tallec and B. Perthame and Y. Qiu", TITLE = "Coupling Boltzmann and Euler equations without overlapping", YEAR = 1994, PAGES = "377-398", BOOKTITLE = "Domain Decomposition Methods in Science and Engineering", EDITOR = "Alfio Quarteroni and Jacques P{\'e}riaux and Yuri A. Kuznetsov and Olof Widlund", PUBLISHER = "AMS", ADDRESS = "Providence, RI" } @ARTICLE{Bramble:1966:SOF, OLDTAG = "bram", AUTHOR = "James H. Bramble", TITLE = "A second order finite difference analogue of the first biharmonic boundary value problem", JOURNAL = "Numer. Math.", YEAR = 1966, VOLUME = 9, PAGES = "236--249" } @ARTICLE{Bramble:1986:CPE, OLDTAG = "2bps", AUTHOR = "James H. Bramble and Joseph E. Pasciak and Alfred H. Schatz", TITLE = "The construction of preconditioners for elliptic problems by substructuring, {I}", JOURNAL = "Math. Comp.", YEAR = 1986, VOLUME = 47, NUMBER = 175, PAGES = "103--134" } @ARTICLE{Bramble:1986:IME, OLDTAG = "1bps", AUTHOR = "James H. Bramble and Joseph E. Pasciak and Alfred H. Schatz", TITLE = "An iterative method for elliptic problems on regions partitioned into substructures", JOURNAL = "Math. Comp.", YEAR = 1986, VOLUME = 46, NUMBER = 173, PAGES = "361--369" } @ARTICLE{Bramble:1987:CPE, OLDTAG = "3bps", AUTHOR = "James H. Bramble and Joseph E. Pasciak and Alfred H. Schatz", TITLE = "The construction of preconditioners for elliptic problems by substructuring, {II}", JOURNAL = "Math. Comp.", YEAR = "1987 ", VOLUME = "49 ", PAGES = "1--16" } @TECHREPORT{Bramble:1987:PTI, OLDTAG = "brpa", AUTHOR = "James H. Bramble and Joseph E. Pasciak", TITLE = "A Preconditioning Technique for Indefinite Systems Resulting from Mixed Approximations of Elliptic Problems", INSTITUTION = "Cornell University", YEAR = 1987 } @ARTICLE{Bramble:1988:CPE, OLDTAG = "4bps", AUTHOR = "James H. Bramble and Joseph E. Pasciak and Alfred H. Schatz", TITLE = "The construction of preconditioners for elliptic problems by substructuring, {III}", JOURNAL = "Math. Comp.", YEAR = "1988 ", VOLUME = "51 ", PAGES = "415--430" } @ARTICLE{Bramble:1988:PTE, OLDTAG = "beps", AUTHOR = "James H. Bramble and Richard E. Ewing and Joseph E. Pasciak and Alfred H. Schatz", TITLE = "A preconditioning technique for the efficient solution of problems with local grid refinement", JOURNAL = "Comp. Methods Appl. Mech. Eng.", VOLUME = 67, YEAR = 1988, PAGES = "149--159" } @ARTICLE{Bramble:1989:CPE, OLDTAG = "5bps", AUTHOR = "James H. Bramble and Joseph E. Pasciak and Alfred H. Schatz", TITLE = "The construction of preconditioners for elliptic problems by substructuring, {IV}", JOURNAL = "Math. Comp.", YEAR = "1989 ", VOLUME = "53 ", PAGES = "1--24" } @TECHREPORT{Bramble:1990:DMP, OLDTAG = "bepp", AUTHOR = "James H. Bramble and Richard E. Ewing and Rossen R. Parashkevov and Joseph E. Pasciak", TITLE = "Domain Decomposition Methods for Problems with Partial Refinement", YEAR = 1990, INSTITUTION = "Cornell University" } @ARTICLE{Bramble:1990:PMP, OLDTAG = "bpx", AUTHOR = "James H. Bramble and Joseph E. Pasciak and Jinchao Xu", TITLE = "Parallel Multilevel Preconditioners", JOURNAL = "Math. Comp.", VOLUME = 55, PAGES = "1--22", YEAR = 1990 } @ARTICLE{Bramble:1991:CEM, OLDTAG = "bpwx2", AUTHOR = "James H. Bramble and Joseph E. Pasciak and Junping Wang and Jinchao Xu", TITLE = "Convergence Estimates for Multigrid Algorithms without Regularity Assumptions", JOURNAL = "Math. Comp.", VOLUME = 57, NUMBER = 195, PAGES = "23--45", YEAR = 1991 } @ARTICLE{Bramble:1991:CEP, OLDTAG = "bpwx", AUTHOR = "James H. Bramble and Joseph E. Pasciak and Junping Wang and Jinchao Xu", TITLE = "Convergence Estimates for Product Iterative Methods with Applications to Domain Decomposition", JOURNAL = "Math. Comp.", VOLUME = 57, NUMBER = 195, PAGES = "1--21", YEAR = 1991 } @ARTICLE{Bramble:1991:EWP, OLDTAG = "brxu1", AUTHOR = "James H. Bramble and Jinchao Xu", TITLE = "Some Estimates for a Weighted ${L}^{2}$ Projection", YEAR = 1991, VOLUME = 56, PAGES = "463--476", JOURNAL = "Math. Comp." } @ARTICLE{Bramble:1993:ISN, OLDTAG = "bleykp", AUTHOR = "James H. Bramble and Zbigniew Leyk and Joseph E. Pasciak", TITLE = "Iterative Schemes for Non-symmetric and Indefinite Elliptic Boundary Value Problems", JOURNAL = "Math. Comp.", VOLUME = 60, PAGES = "1--22", YEAR = 1993 } @BOOK{Bramble:1993:MUM, OLDTAG = "bramble_book", AUTHOR = "James H. Bramble", TITLE = "Multigrid Methods", PUBLISHER = "Longman Scientic \& Technical", YEAR = 1993, ADRESS = "Burnt Mill, Harlow, Essex CM20 2JE, England", NOTE = "Pitman Research Notes in Mathematics Series \#294" } @ARTICLE{Bramble:1993:NEM, OLDTAG = "2brpa", AUTHOR = "James H. Bramble and Joseph E. Pasciak", TITLE = "New Estimates for Multilevel Algorithms Including the {V}-cycle", YEAR = 1993, JOURNAL = "Math. Comp.", PAGES = "447--471", VOLUME = 60 } @INPROCEEDINGS{Brandt:1972:MAT, OLDTAG = "1brandt", AUTHOR = "A. Brandt", TITLE = "Multi-level Adaptive Techniques ({MLAT}) for Fast Numerical Solution to Boundary Value Problems", BOOKTITLE = "Proc. 3rd Internat. Conf. on Numer. Method in Fluid Mechanics", YEAR = 1972, PUBLISHER = "Springer", ADDRESS = "Berlin", PAGES = "82-89" } @ARTICLE{Brandt:1977:MAS, OLDTAG = "2brandt", AUTHOR = "A. Brandt", TITLE = "Multi-level Adaptive Solutions to Boundary Value Problems", JOURNAL = "Numer. Math.", YEAR = 1977, VOLUME = 31, PAGES = "333-390" } @ARTICLE{Brenner:1990:NMM, OLDTAG = "2brenner", AUTHOR = "Susanne C. Brenner", TITLE = "A Nonconforming Multigrid Method for the Stationary {S}tokes Equations", JOURNAL = "Math. Comp.", YEAR = 1990, VOLUME = 55, NUMBER = 192, PAGES = "411--437" } @ARTICLE{Brenner:1996:TSP, OLDTAG = "3brenner", AUTHOR = "Susanne C. Brenner", TITLE = "A Two-Level {S}chwarz Preconditioner for Nonconforming Plate Elements", JOURNAL = "Numer. Math.", VOLUME = 72, NUMBER = 4, YEAR = 1996, PAGES = "419--447" } @BOOK{Briggs:1987:MUT, OLDTAG = "briggs", AUTHOR = "William Briggs", TITLE = "A Multigrid Tutorial", YEAR = 1987, PUBLISHER = "SIAM", ADDRESS = "Philadelphia" } @PHDTHESIS{Cai:1989:DAN, OLDTAG = "1cai", AUTHOR = "Xiao-Chuan Cai", TITLE = "Some Domain Decomposition Algorithms for Nonselfadjoint Elliptic and Parabolic Partial Differential Equations", SCHOOL = "Courant Institute of Mathematical Sciences", YEAR = 1989, MONTH = "September", NOTE = "Tech. Rep. 461, Department of Computer Science, Courant Institute" } @INPROCEEDINGS{Cai:1990:ASA, OLDTAG = "2cai", AUTHOR = "Xiao-Chuan Cai", TITLE = "An Additive {S}chwarz Algorithm for Nonselfadjoint Elliptic Equations", BOOKTITLE = "Third International Symposium on Domain Decomposition Methods for Partial Differential Equations", YEAR = 1990, EDITOR = "Tony Chan and Roland Glowinski and Jacques P{\'e}riaux and Olof Widlund", PUBLISHER = "SIAM, Philadelphia, PA", PAGES = "232--244" } @ARTICLE{Cai:1991:ASA, OLDTAG = "3cai", AUTHOR = "Xiao-Chuan Cai", TITLE = "Additive {S}chwarz Algorithms for Parabolic Convection-Diffusion Equations", JOURNAL = "Numer. Math.", YEAR = 1991, VOLUME = 60, NUMBER = 1, PAGES = "41--61" } @INPROCEEDINGS{Cai:1992:CDA, OLDTAG = "1cagrke", AUTHOR = "Xiao-Chuan Cai and William D. Gropp and David E. Keyes", TITLE = "A Comparison of Some Domain Decomposition Algorithms for Nonsymmetric Elliptic Problems", EDITOR = "David E. Keyes and Tony F. Chan and G{\'e}rard A. Meurant and Jeffrey S. Scroggs and Robert G. Voigt", BOOKTITLE = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations", PUBLISHER = "SIAM", YEAR = 1992, ADDRESS = "Philadelphia, PA", PAGES = "224--235" } @ARTICLE{Cai:1992:CRE, OLDTAG = "2cagrke", AUTHOR = "Xiao-Chuan Cai and William D. Gropp and David E. Keyes", TITLE = "Convergence Rate Estimate for a Domain Decomposition Method", YEAR = 1992, PAGES = "153--169", JOURNAL = "Numer. Math.", VOLUME = 61 } @ARTICLE{Cai:1992:DAI, OLDTAG = "1caiwid", AUTHOR = "Xiao-Chuan Cai and Olof Widlund", TITLE = "Domain Decomposition Algorithms for Indefinite Elliptic Problems", JOURNAL = "SIAM J. Sci. Statist. Comput.", YEAR = 1992, MONTH = "January", VOLUME = 13, NUMBER = 1, PAGES = "243--258" } @ARTICLE{Cai:1992:PMN, OLDTAG = "caixu", AUTHOR = "Xiao-Chuan Cai and Jinchao Xu", TITLE = "A preconditioned {GMRES} method for nonsymmetric or indefinite problems", JOURNAL = "Math. Comp.", VOLUME = 59, YEAR = 1992, PAGES = "311--319" } @ARTICLE{Cai:1993:MSA, OLDTAG = "2caiwid", AUTHOR = "Xiao-Chuan Cai and Olof Widlund", TITLE = "Multiplicative {S}chwarz Algorithms for Some Nonsymmetric and Indefinite Problems", JOURNAL = "SIAM J. Numer. Anal.", NUMBER = 4, MONTH = "August", YEAR = 1993, VOLUME = 30, PAGES = "936--952" } @TECHREPORT{Cai:1993:ODA, OLDTAG = "caisaad", AUTHOR = "Xiao-Chuan Cai and Youcef Saad", TITLE = "Overlapping domain decomposition algorithms for general sparse matrices", INSTITUTION = "Army High Performance Computing Research Center, University of Minnesota", YEAR = 1993, NUMBER = "Preprint 93-027", NOTE = "SIAM J. Sci. Comp. (submitted)" } @ARTICLE{Cai:1993:OTO, OLDTAG = "4cai", AUTHOR = "Xiao-Chuan Cai", TITLE = "An Optimal Two-level Overlapping Domain Decomposition Method for Elliptic Problems in Two and Three Dimensions", JOURNAL = "SIAM J. Sci. Comp.", VOLUME = 14, MONTH = "January", YEAR = 1993, PAGES = "239--247" } @ARTICLE{Cai:1994:CDP, OLDTAG = "3cagrke", AUTHOR = "Xiao-Chuan Cai and William D. Gropp and David E. Keyes", TITLE = "A Comparison of Some Domain Decomposition and {ILU} Preconditioned Iterative Methods for Nonsymmetric Elliptic Problems", JOURNAL = "Numer. Lin. Alg. Appl", VOULME = 1, NUMBER = 5, PAGES = "477--504", YEAR = 1994 } @INPROCEEDINGS{Cai:1994:FOS, OLDTAG = "6cai", AUTHOR = "X.-C. Cai", TITLE = "A family of overlapping {S}chwarz algorithms for nonsymmetric and indefinite elliptic problems", BOOKTITLE = "Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering", EDITOR = "D. Keyes and Y. Saad and D. Truhlar", YEAR = 1994, PUBLISHER = "SIAM", NOTE = "To appear." } @ARTICLE{Cai:1994:MSM, OLDTAG = "7cai", AUTHOR = "Xiao-Chuan Cai", TITLE = "Multiplicative {S}chwarz Methods for Parabolic Problems", JOURNAL = "SIAM J. Sci Comput.", YEAR = 1994, VOLUME = 15, NUMBER = 3, PAGES = "587--603" } @INPROCEEDINGS{Cai:1994:NKS, OLDTAG = "cgkt", AUTHOR = "Xiao-Chuan Cai and William D. Gropp and David E. Keyes and M. D. Tidriri", TITLE = "Newton-{K}rylov-{S}chwarz Methods in {CFD}", EDITOR = "R. Rannacher", BOOKTITLE = "Proceedings of the International Workshop on the {N}avier-{S}tokes Equations, Notes in Numerical Fluid Mechanics", PUBLISHER = "Vieweg Verlag, Braunschweig", YEAR = 1994, NOTE = "To appear." } @ARTICLE{Cai:1995:UPI, OLDTAG = "5cai", AUTHOR = "Xiao-Chuan Cai", TITLE = "The Use of Pointwise Interpolation in Domain Decomposition Methods with Non-nested Meshes", JOURNAL = "SIAM J. Sci Comput.", YEAR = 1995, VOLUME = 16, PAGES = "250--256", NUMBER = 1 } @ARTICLE{Canuto:1988:SAS, OLDTAG = "canfun", AUTHOR = "Claudio Canuto and Daniele Funaro", TITLE = "The {S}chwarz Algorithm for Spectral Methods", JOURNAL = "SIAM J. Numer. Anal.", YEAR = 1988, VOLUME = 25, NUMBER = 1, PAGES = "24--40" } @BOOK{Canuto:1988:SMF, OLDTAG = "cahuquza", AUTHOR = "Claudio Canuto and M. Yousuff Hussaini and Alfio Quarteroni and Thomas A. Zang", TITLE = "Spectral Methods in Fluid Dynamics", PUBLISHER = "Springer-Verlag", YEAR = 1988 } @ARTICLE{Canuto:1994:SSM, OLDTAG = "canmontp", AUTHOR = "Claudio Canuto", TITLE = "Stablization of Spectral Methods by Finite Element Bubble Functions", NOTE = "Proceedings of ICOSAHOM 92, a conference held in Montpellier, France, June 1992.", JOURNAL = "Comput. Methods Appl. Mech. Engrg", YEAR = 1994, PAGES = "13--26", VOLUME = 116 } @TECHREPORT{Casarin:1995:DEP, OLDTAG = "2casa", AUTHOR = "Mario A. Casarin", TITLE = "Diagonal Edge Preconditioners in p-Version and Spectral Element Methods", INSTITUTION = "Department of Computer Science, Courant Institute", YEAR = 1995, NUMBER = 704, MONTH = "September", NOTE = "To appear in SIAM J. Sci. Comp." } @INPROCEEDINGS{Casarin:1995:QSMa, OLDTAG = "1casa", AUTHOR = "Mario A. Casarin", TITLE = "Quasi-Optimal {S}chwarz Methods for the Conforming Spectral Element Discretization", YEAR = 1995, BOOKTITLE = "Proceedings of the 1995 Copper Mountain Conference on Multigrid Methods", EDITOR = "N. Duane Melson and Thomas A. Manteuffel and Steve F. McCormick", PUBLISHER = "NASA", ADDRESS = "Hampton VA" } @TECHREPORT{Casarin:1995:QSMb, OLDTAG = "3casa", AUTHOR = "Mario A. Casarin", TITLE = "Quasi-Optimal {S}chwarz Methods for the Conforming Spectral Element Discretization", INSTITUTION = "Department of Computer Science, Courant Institute", YEAR = 1995, NUMBER = 705, MONTH = "September", NOTE = "To appear in SIAM J. Numer. Anal." } @ARTICLE{Casarin:1996:HPM, OLDTAG = "1casa_wid", AUTHOR = "Mario A. Casarin and Olof B. Widlund", TITLE = "A Hierarchical Preconditioner for the Mortar Finite Element Method", JOURNAL = "ETNA", YEAR = 1996, VOLUME = 4, MONTH = "June", PAGES = "75--88" } @PHDTHESIS{Casarin:1996:SPS, OLDTAG = "4casa", AUTHOR = "Mario A. Casarin", TITLE = "{S}chwarz Preconditioners for Spectral and Mortar Finite Element Methods with Applications to Incompressible Fluids", SCHOOL = "Courant Institute of Mathematical Sciences", YEAR = 1996, MONTH = "March", NOTE = "Tech. Rep. 717, Department of Computer Science, Courant Institute" } @INPROCEEDINGS{Champaney:1995:3SA, AUTHOR = "L. Champaney and J.-Y. Cognard and D. Dureisseix and P. Ladev{\`e}ze", TITLE = "3{D} structures assembly analysis with a modular approach suited to parallel computations", BOOKTITLE = "28th International Symposium on Automotive Technology and Automation", YEAR = 1995, EDITOR = "J. I. Soliman and D. Roller", PAGES = "285--292", ADDRESS = "Stuttgart", MONTH = "September" } @INPROCEEDINGS{Champaney:1995:NEP, AUTHOR = "L. Champaney and J.-Y. Cognard and D. Dureisseix and P. Ladev{\`e}ze", TITLE = "Numerical experimentations of parallel strategies in structural non-linear analysis", BOOKTITLE = "Euro{PVM}'95", YEAR = 1995, EDITOR = "J. Dongarra and M. Gengler and B. Tourancheau and X. Vigouroux", PAGES = "221--226", PUBLISHER = "Herm{\`e}s", ADDRESS = "Lyon", MONTH = "September" } @ARTICLE{Champaney:1996:NEP, AUTHOR = "L. Champaney and J.-Y. Cognard and D. Dureisseix and P. Ladev{\`e}ze", TITLE = "Numerical experimentations of parallel strategies in structural non-linear analysis", YEAR = 1996, JOURNAL = "Calculateurs Parall{\`e}les", VOLUME = 8, NUMBER = 2, PAGES = "245--249" } @TECHREPORT{Chan:1985:DPS, OLDTAG = "2tch", AUTHOR = "Tony F. Chan and Diana C. Resasco", TITLE = "A domain-decomposed fast {P}oisson solver on a rectangle", INSTITUTION = "Yale University", YEAR = 1985, NUMBER = "{/DCS/RR-409}" } @TECHREPORT{Chan:1985:SPD, OLDTAG = "3tch", AUTHOR = "Tony F. Chan and Diana C. Resasco", TITLE = "A survey of preconditioners for domain decomposition", INSTITUTION = "Yale University", YEAR = 1985, NUMBER = "{/DCS/RR-414}" } @INPROCEEDINGS{Chan:1987:ADP, OLDTAG = "5tch", AUTHOR = "Tony F. Chan and Diana C. Resasco", TITLE = "Analysis of Domain Decomposition Preconditioners on Irregular Regions", BOOKTITLE = "Advances in Computer Methods for Partial Differential Equations", PUBLISHER = "IMACS", EDITOR = "R. Vichnevetsky and R. Stepleman", YEAR = 1987, PAGES = "317--322" } @ARTICLE{Chan:1987:APD, OLDTAG = "1tch", AUTHOR = "Tony F. Chan", TITLE = "Analysis of preconditioners for domain decomposition", JOURNAL = "SIAM J. Numer. Anal.", YEAR = 1987, VOLUME = 24, NUMBER = 2, PAGES = "382--390" } @TECHREPORT{Chan:1988:ADP, OLDTAG = "4tch", AUTHOR = "Tony F. Chan and Diana C. Resasco", TITLE = "An analysis of domain decomposition preconditioners on L-shaped and C-shaped regions", INSTITUTION = "Yale University", YEAR = 1988, NUMBER = "{/DCS/RR-534}" } @PROCEEDINGS{Chan:1989:DDM, OLDTAG = "dom2", TITLE = "Domain Decomposition Methods", EDITOR = "Tony Chan and Roland Glowinski and Jacques P{\'e}riaux and Olof Widlund", YEAR = 1989, NOTE = "Proceedings of the {S}econd {I}nternational {S}ymposium on {D}omain {D}ecomposition {M}ethods, {L}os {A}ngeles, {C}alifornia, January 14 - 16, 1988.", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @INPROCEEDINGS{Chan:1990:IPD, OLDTAG = "7tch", AUTHOR = "Tony F. Chan and David F. Keyes", TITLE = "Interface Preconditioning for Domain-Decomposed Convection-Diffusion Operators", YEAR = 1990, EDITOR = "Tony Chan and Roland Glowinski and Jacques P{\'e}riaux and Olof Widlund", BOOKTITLE = "Third International Symposium on Domain Decomposition Methods for Partial Differential Equations", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", PAGES = "245--262" } @PROCEEDINGS{Chan:1990:TIS, OLDTAG = "dom3", TITLE = "Third International Symposium on Domain Decomposition Methods for Partial Differential Equations", EDITOR = "Tony Chan and Roland Glowinski and Jacques P{\'e}riaux and Olof Widlund", YEAR = 1990, PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @INPROCEEDINGS{Chan:1991:APT, OLDTAG = "1chma", AUTHOR = "Tony F. Chan and Tarek P. Mathew", TITLE = "An Application of the Probing Technique to the Vertex Space Method in Domain Decomposition", YEAR = 1991, BOOKTITLE = "Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations", EDITOR = "Roland Glowinski and Yuri A. Kuznetsov and G{\'e}rard A. Meurant and Jacques P{\'e}riaux and Olof Widlund", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", PAGES = "101--111" } @ARTICLE{Chan:1991:EDI, OLDTAG = "8tch", AUTHOR = "Tony F. Chan and Thomas Y. Hou", TITLE = "Eigendecomposition of Domain Decomposition Interface Operators for Constant Coefficient Elliptic Problems", JOURNAL = "SIAM J. Sci. Stat. Comput.", VOLUME = 12, YEAR = 1991, PAGES = "1471--1479" } @ARTICLE{Chan:1991:GRC, OLDTAG = "chholii", AUTHOR = "Tony Chan and Thomas Hou and P. L. Lions", TITLE = "Geometry Related Convergence Results for Domain Decomposition Algorithms", JOURNAL = "SIAM J. Numer. Anal.", VOLUME = 28, YEAR = 1991, PAGES = "378--391" } @ARTICLE{Chan:1992:IPT, OLDTAG = "4chma", AUTHOR = "Tony F. Chan and Tarek P. Mathew", TITLE = "The Interface Probing Technique in Domain Decomposition", NUMBER = 1, YEAR = 1992, VOLUME = 13, PAGES = "212--238", JOURNAL = "SIAM J. on Matrix Analysis and Applications" } @ARTICLE{Chan:1992:RON, OLDTAG = "6tch", AUTHOR = "Tony F. Chan and Danny Goovaerts", TITLE = "On the Relationship Between Overlapping and Nonoverlapping Domain Decomposition Methods", YEAR = 1992, JOURNAL = "SIAM J. Matrix Anal. Appl.", VOLUME = 13, PAGES = "663-670" } @ARTICLE{Chan:1994:ASD, OLDTAG = "1chan_zou", AUTHOR = "Tony F. Chan and Jun Zou", TITLE = "Additive {S}chwarz Domain Decomposition Methods for Elliptic Problems on Unstructured Meshes", JOURNAL = "Numer. Algorithms", VOLUME = 8, NUMBER = "2--4", YEAR = 1994, PAGES = "329--346" } @INCOLLECTION{Chan:1994:DOA, OLDTAG = "4chma", AUTHOR = "Tony F. Chan and Tarek P. Mathew", TITLE = "Domain Decomposition Algorithms", PAGES = "61--143", BOOKTITLE = "Acta Numerica 1994", PUBLISHER = "Cambridge University Press", YEAR = 1994 } @INPROCEEDINGS{Chan:1994:DPC, OLDTAG = "chma-dd6", AUTHOR = "Tony F. Chan and Tarek P. Mathew", TITLE = "Domain Decomposition Preconditioners for Convection Diffusion Problems", YEAR = 1994, pages = "157--175", BOOKTITLE = "Domain Decomposition Methods in Science and Engineering", EDITOR = "Alfio Quarteroni and Jacques P{\'e}riaux and Yuri A. Kuznetsov and Olof Widlund", PUBLISHER = "AMS", ADDRESS = "Providence, RI" } @ARTICLE{Chan:1994:EVV, OLDTAG = "3chma", AUTHOR = "Tony F. Chan and Tarek P. Mathew and Jian-Ping Shao", TITLE = "Efficient Variants of the Vertex Space Domain Decomposition Algorithm", YEAR = 1994, JOURNAL = "SIAM J. Sci. Comput.", NUMBER = 6, VOLUME = 15 } @ARTICLE{Chan:1994:OCG, OLDTAG = "9tch", AUTHOR = "Tony F. Chan and Jian-Ping Shao", TITLE = "Optimal Coarse Grid Size in Domain Decomposition", YEAR = 1994, JOURNAL = "J. Comp. Math.", VOLUME = "To appear" } @ARTICLE{Chan:1994:PCD, OLDTAG = "10tch", AUTHOR = "Tony F. Chan", TITLE = "Parallel Complexity of Domain Decomposition Methods and Optimal Coarse Grid Sizes", YEAR = 1994, JOURNAL = "Parallel Computing", VOLUME = "To appear" } @INPROCEEDINGS{Chan:1995:MDU, OLDTAG = "cs", AUTHOR = "Tony F. Chan and Barry F. Smith", TITLE = "Multigrid and Domain Decomposition on Unstructured Grids", YEAR = 1995, BOOKTITLE = "Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing", EDITOR = "David F. Keyes and and Jinchao Xu", PUBLISHER = "AMS", ADDRESS = "Providence, RI", NOTE = "Has also appeared in ETNA." } @ARTICLE{Chan:1996:OSM, OLDTAG = "csz", AUTHOR = "Tony F. Chan and Barry F. Smith and Jun Zou", TITLE = "Overlapping {S}chwarz Methods on Unstructured Meshes using Non-matching Coarse Grids", YEAR = 1996, JOURNAL = "Numer. Math.", VOLUME = 73, NUMBER = 2, PAGES = "149--167" } @PHDTHESIS{Cheng:1993:ISE, OLDTAG = "1cheng", AUTHOR = "Hsuanjen Cheng", TITLE = "Iterative Solution of Elliptic Finite Element Problems on Partially Refined Meshes and the Effect of Using Inexact Solvers", SCHOOL = "Courant Institute of Mathematical Sciences", YEAR = 1993, MONTH = "October", NOTE = "Tech. Rep. 649, Department of Computer Science, Courant Institute" } @TECHREPORT{Cheng:1994:MSM, OLDTAG = "2cheng", AUTHOR = "Hsuanjen Cheng", TITLE = "Multilevel {S}chwarz Methods with Partial Refinement", INSTITUTION = "Department of Computer Science, Courant Institute", NUMBER = 654, MONTH = "February", YEAR = 1994 } @BOOK{Ciarlet:1978:FEM, OLDTAG = "ciar", AUTHOR = "Philippe G. Ciarlet", TITLE = "The Finite Element Method for Elliptic Problems", PUBLISHER = "North-Holland", YEAR = 1978, ADDRESS = "Amsterdam" } @INPROCEEDINGS{Cognard:1995:AME, AUTHOR = "J.-Y. Cognard and D. Dureisseix and P. Ladev{\`e}ze and Ph. Lorong", TITLE = "Une approche multi-{\'e}chelles en calcul des structures pour ordinateur {\`a} architecture parall{\`e}le", BOOKTITLE = "Actes du 12{\`e}me Congr{\`e}s Fran\c{c}ais de M{\'e}canique", YEAR = 1995, PAGES = "101--104", ORGANIZATION = "Association Universitaire de M{\'e}canique", ADDRESS = "Strasbourg", MONTH = "September" } @ARTICLE{Cognard:1996:EAP, AUTHOR = "J.-Y. Cognard and D. Dureisseix and P. Ladev{\`e}ze and Ph. Lorong", TITLE = "Exp{\'e}rimentation d'une approche parall{\`e}le en calcul de structures", YEAR = 1996, JOURNAL = "Rev. Europ. {\'E}l{\'e}ments Finis", VOLUME = 5, PAGES = "197--220" } @INPROCEEDINGS{Concus:1976:GCG, OLDTAG = "cgol", AUTHOR = "Paul Concus and Gene H. Golub and Dianne P. O'Leary", TITLE = "A generalized conjugate gradient method for the numerical solution of elliptic {PDE}", BOOKTITLE = "Sparse Matrix Computations", YEAR = 1976, EDITOR = "James R. Bunch and Donald J. Rose", PAGES = "309--332", PUBLISHER = "Academic Press", ADDRESS = "New York" } @ARTICLE{Cottle:1974:MSC, OLDTAG = "cottle", AUTHOR = "R. W. Cottle", TITLE = "Manifestations of the {S}chur Complement", JOURNAL = "Lin. Alg. and Its Applic.", VOLUME = 8, YEAR = 1974, PAGES = "189--211" } @INPROCEEDINGS{Cowsar:1991:FIS, OLDTAG = "1cowwhe", AUTHOR = "Lawrence C. Cowsar and Mary F. Wheeler", TITLE = "Parallel Domain Decomposition Method for Mixed Finite Elements for Elliptic Partial Differential Equations", BOOKTITLE = "Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations", EDITOR = "Roland Glowinski and Yuri A. Kuznetsov and G{\'e}rard A. Meurant and Jacques P{\'e}riaux and Olof Widlund", YEAR = 1991, PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @INPROCEEDINGS{Cowsar:1992:PMD, OLDTAG = "1cowweiswhe", AUTHOR = "Lawrence C. Cowsar and Alan Weiser and Mary F. Wheeler", TITLE = "Parallel Multigrid and Domain Decomposition Algorithms for Elliptic Equations", BOOKTITLE = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations", EDITOR = "David E. Keyes and Tony F. Chan and G{\'e}rard A. Meurant and Jeffrey S. Scroggs and Robert G. Voigt", YEAR = 1992, PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", PAGES = "376--385" } @TECHREPORT{Cowsar:1993:DVS, OLDTAG = "1cow", AUTHOR = "Lawrence C. Cowsar", TITLE = "Dual Variable {S}chwarz Methods for Mixed Finite Elements", INSTITUTION = "Department of Mathematical Sciences, Rice University", YEAR = 1993, MONTH = "March", NUMBER = "TR93-09" } @ARTICLE{Cowsar:1995:BDM, OLDTAG = "1cowmawh", AUTHOR = "Lawrence C. Cowsar and Jan Mandel and Mary F. Wheeler", TITLE = "Balancing Domain Decomposition for Mixed Finite Elements", JOURNAL = "Math. Comp.", YEAR = 1995, MONTH = "July", VOLUME = 64, NUMBER = 211, PAGES = "989--1015" } @ARTICLE{Crane:1976:A5M, OLDTAG = "crane1", AUTHOR = "H. L. Crane Jr. and Norman E. Gibbs and William G. Poole Jr. and Paul K. Stockmeyer", TITLE = "Algorithm 508, Matrix bandwith and profile reduction", JOURNAL = "ACM Transactions on Mathematical Software", VOLUME = 2, NUMBER = 4, YEAR = 1976, MONTH = "December", KEY = "Bandwith reduction, diameter of a graph. profile reduction, sparse matrices" } @INPROCEEDINGS{Dawson:1991:DMP, OLDTAG = "dadu", AUTHOR = "Clint N. Dawson and Qiang Du", TITLE = "A Domain Decomposition Method for Parabolic Equations Based on Finite Elements", BOOKTITLE = "Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations", EDITOR = "Roland Glowinski and Yuri A. Kuznetsov and G{\'e}rard A. Meurant and Jacques P{\'e}riaux and Olof Widlund", YEAR = 1991, PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @ARTICLE{Deville:1990:FEP, OLDTAG = "devimun", AUTHOR = "M. O. Deville and E. H. Mund", TITLE = "Finite-Element Preconditioning for Pseudospectral Solutions of Elliptic Problems", YEAR = 1990, JOURNAL = "Siam J. Sci. Stat. Comput.", VOLUME = 11, PAGES = "311 -- 342", NUMBER = 2, MONTH = "March" } @INPROCEEDINGS{Dihn:1984:SEP, OLDTAG = "digp", AUTHOR = "Q.V. Dihn and Roland Glowinski and Jacques P{\'e}riaux", TITLE = "Solving elliptic problems by domain decomposition methods with applications", BOOKTITLE = "Elliptic Problem Solvers {II}", YEAR = 1984, EDITOR = "Garrett Birkhoff and Arthur Schoenstadt", PAGES = "395--426", PUBLISHER = "Academic Press", ADDRESS = "New York" } @PHDTHESIS{Donato:1991:IMS, OLDTAG = "1dona", AUTHOR = "June M. Donato", TITLE = "Iterative Methods for Scalar and Coupled Systems of Elliptic Equations", SCHOOL = "Department of Mathematics, UCLA", YEAR = 1991, MONTH = "September", NOTE = "CAM 91-20" } @INPROCEEDINGS{Dryja:1981:ACM, OLDTAG = "0dry", AUTHOR = "Maksymilian Dryja", TITLE = "An Algorithm with a Capacitance Matrix for a Variational-Difference Scheme", BOOKTITLE = "{V}ariational-{D}ifference {M}ethods in {M}athematical {P}hysics", YEAR = 1981, PAGES = "63--73", EDITOR = "G. I. Marchuk", PUBLISHER = "USSR {A}cademy of {S}ciences", ADDRESS = "Novosibirsk" } @ARTICLE{Dryja:1981:CMM, OLDTAG = "3dry", AUTHOR = "Maksymilian Dryja", TITLE = "A capacitance matrix method for {D}irichlet problem on polygon region", JOURNAL = "Numer. Math.", YEAR = 1982, VOLUME = 39, PAGES = "51--64" } @ARTICLE{Dryja:1984:FEC, OLDTAG = "4dry", AUTHOR = "Maksymilian Dryja", TITLE = "A finite element-capacitance method for elliptic problems on regions partitioned into subregions", JOURNAL = "Numer. Math.", YEAR = 1984, VOLUME = 44, PAGES = "153--168" } @INPROCEEDINGS{Dryja:1986:MDC, OLDTAG = "1dpw", AUTHOR = "Maksymilian Dryja and Wlodek Proskurowski and Olof Widlund", TITLE = "A Method of Domain Decomposition with Crosspoints for Elliptic Finite Element Problems", BOOKTITLE = "Optimal Algorithms", YEAR = 1986, EDITOR = "Bl. Sendov", PAGES = "97--111", PUBLISHER = "Bulgarian Academy of Sciences", ADDRESS = "Sofia, Bulgaria" } @TECHREPORT{Dryja:1987:AVS, OLDTAG = "6wid", AUTHOR = "Maksymilian Dryja and Olof B. Widlund", TITLE = "An Additive Variant of the {S}chwarz Alternating Method for the Case of Many Subregions", INSTITUTION = "Department of Computer Science, Courant Institute", YEAR = 1987, NUMBER = "339, also Ultracomputer Note 131" } @INPROCEEDINGS{Dryja:1988:MD3, OLDTAG = "1dry", AUTHOR = "Maksymilian Dryja", TITLE = "A Method of Domain Decomposition for 3-{D} Finite Element Problems", BOOKTITLE = "{F}irst {I}nternational {S}ymposium on {D}omain {D}ecomposition {M}ethods for {P}artial {D}ifferential {E}quations", YEAR = 1988, EDITOR = "Roland Glowinski and Gene H. Golub and G{\'e}rard A. Meurant and Jacques P{\'e}riaux", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", PAGES = "43--61" } @INPROCEEDINGS{Dryja:1989:ASA, OLDTAG = "2dry", AUTHOR = "Maksymilian Dryja", TITLE = "An Additive {S}chwarz Algorithm for Two- and Three-Dimensional Finite Element Elliptic Problems", BOOKTITLE = "Domain Decomposition Methods", YEAR = 1989, EDITOR = "Tony Chan and Roland Glowinski and Jacques P{\'e}riaux and Olof Widlund", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", PAGES = "168--172" } @INPROCEEDINGS{Dryja:1989:DAE, OLDTAG = "10wid", AUTHOR = "Maksymilian Dryja and Olof B. Widlund", TITLE = "Some Domain Decomposition Algorithms for Elliptic Problems", BOOKTITLE = "Iterative Methods for Large Linear Systems", PUBLISHER = "Academic Press", ADDRESS = "San Diego, California", EDITOR = "Linda Hayes and David Kincaid", PAGES = "273--291", YEAR = 1989, NOTE = "Proceeding of the Conference on Iterative Methods for Large Linear Systems held in {A}ustin, Texas, October 19 - 21, 1988, to celebrate the sixty-fifth birthday of {D}avid {M}. {Y}oung, {J}r." } @INPROCEEDINGS{Dryja:1989:OAI, OLDTAG = "11wid", AUTHOR = "Maksymilian Dryja and Olof B. Widlund", TITLE = "On the Optimality of an Additive Iterative Refinement Method", BOOKTITLE = "Proceedings of the {F}ourth {C}opper {M}ountain {C}onference on {M}ultigrid {M}ethods", YEAR = 1989, PAGES = "161--170", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @INPROCEEDINGS{Dryja:1990:TUT, OLDTAG = "12wid", AUTHOR = "Maksymilian Dryja and Olof B. Widlund", TITLE = "Towards a Unified Theory of Domain Decomposition Algorithms for Elliptic Problems", YEAR = 1990, EDITOR = "Tony Chan and Roland Glowinski and Jacques P{\'e}riaux and Olof Widlund", BOOKTITLE = "Third International Symposium on Domain Decomposition Methods for Partial Differential Equations", PUBLISHER = "SIAM, Philadelphia, PA", PAGES = "3--21" } @INPROCEEDINGS{Dryja:1991:MAM, OLDTAG = "13wid", AUTHOR = "Maksymilian Dryja and Olof B. Widlund", TITLE = "Multilevel Additive Methods for Elliptic Finite Element Problems", EDITOR = "Wolfgang Hackbusch", BOOKTITLE = "Parallel Algorithms for Partial Differential Equations, Proceedings of the Sixth GAMM-Seminar, Kiel, January 19--21, 1990", PAGES = "58--69", PUBLISHER = "Vieweg \& Son", ADDRESS = "Braunschweig, Germany", YEAR = 1991 } @INPROCEEDINGS{Dryja:1991:SMP, OLDTAG = "5dry", AUTHOR = "Maksymilian Dryja", TITLE = "Substructuring Methods for Parabolic Problems", YEAR = 1991, BOOKTITLE = "Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations", EDITOR = "Roland Glowinski and Yuri A. Kuznetsov and G{\'e}rard A. Meurant and Jacques P{\'e}riaux and Olof Widlund", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @INPROCEEDINGS{Dryja:1992:ASM, OLDTAG = "6dry", AUTHOR = "Maksymilian Dryja and Olof B. Widlund", TITLE = "Additive {S}chwarz Methods for Elliptic Finite Element Problems in Three Dimensions", BOOKTITLE = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations", EDITOR = "David E. Keyes and Tony F. Chan and G{\'e}rard A. Meurant and Jeffrey S. Scroggs and Robert G. Voigt", YEAR = 1992, PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", PAGES = "3--18" } @ARTICLE{Dryja:1994:DAS, OLDTAG = "16wid", AUTHOR = "Maksymilian Dryja and Olof B. Widlund", TITLE = "Domain Decomposition Algorithms with Small Overlap", JOURNAL = "SIAM J. Sci.Comput.", YEAR = 1994, MONTH = "May", VOLUME = 15, PAGES = "604--620", NUMBER = 3 } @INPROCEEDINGS{Dryja:1994:DMS, OLDTAG = "17wid", AUTHOR = "Maksymilian Dryja and Olof B. Widlund", TITLE = "Some Recent Results on {S}chwarz Type Domain Decomposition Algorithms", BOOKTITLE = "Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition", NOTE = "Held in Como, Italy, June 15--19,1992", VOLUME = 157, EDITOR = "Alfio Quarteroni and Yuri A. Kuznetsov and Jacques P{\'e}riaux and Olof B. Widlund", YEAR = 1994, SERIES = "Contemporary Mathematics", PUBLISHER = "AMS", PAGES = "53--62" } @INPROCEEDINGS{Dryja:1994:MME, OLDTAG = "7dry", AUTHOR = "Maksymilian Dryja", TITLE = "Multilevel Methods for Elliptic Problems with Discontinuous Coefficients in Three Dimensions", BOOKTITLE = "Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing", EDITOR = "David E. Keyes and Jinchao Xu", YEAR = 1994, PUBLISHER = "AMS", SERIES = "Contemporary Mathematics", VOLUME = 180, PAGES = "43--47", NOTE = "Held at Penn State University, October 27-30, 1993." } @ARTICLE{Dryja:1994:SAI, OLDTAG = "1dsw", AUTHOR = "Maksymilian Dryja and Barry F. Smith and Olof B. Widlund", TITLE = "{S}chwarz Analysis of Iterative Substructuring Algorithms for Elliptic Problems in Three Dimensions", MONTH = "December", YEAR = 1994, PAGES = "1662--1694", VOLUME = 31, NUMBER = 6, JOURNAL = "SIAM J. Numer. Anal." } @ARTICLE{Dryja:1995:SMN, OLDTAG = "14wid", AUTHOR = "Maksymilian Dryja and Olof B. Widlund", TITLE = "{S}chwarz Methods of {N}eumann-{N}eumann Type for Three-Dimensional Elliptic Finite Element Problems", YEAR = 1995, MONTH = "February", JOURNAL = "Comm. Pure Appl. Math.", VOLUME = 48, PAGES = "121--155", NUMBER = 2 } @INPROCEEDINGS{Dryja:1996:ASM, OLDTAG = "8dry", AUTHOR = "Maksymilian Dryja", TITLE = "Additive {S}chwarz Methods for Elliptic Mortar Finite Element Problems", BOOKTITLE = "Modeling and Optimization of Distributed Parameter Systems with Applications to Engineering", EDITOR = "K. Malanowski and Z. Nahorski and M. Peszynska", ORGANIZATION = "IFIP", PUBLISHER = "Chapman \& Hall, London", YEAR = 1996, NOTE = "To appear" } @ARTICLE{Dryja:1996:MSM, OLDTAG = "1drsawi", AUTHOR = "Maksymilian Dryja and Marcus V. Sarkis and Olof B. Widlund", TITLE = "Multilevel {S}chwarz Methods for Elliptic Problems with Discontinuous Coefficients in Three Dimensions", NUMBER = 3, JOURNAL = "Numer. Math.", VOLUME = 72, PAGES = "313--348", YEAR = 1996 } @INPROCEEDINGS{Dureisseix:1996:PML, AUTHOR = "D. Dureisseix and P. Ladev{\`e}ze", TITLE = "Parallel and multi-level strategies for structural analysis", BOOKTITLE = "Proceedings of the Second European Conference on Numerical Methods in Engineering", YEAR = 1996, EDITOR = "J.-A. Desideri", PAGES = "599--604", ORGANIZATION = "ECCOMAS", PUBLISHER = "Wiley", ADDRESS = "Paris", MONTH = "September" } @PHDTHESIS{Dureisseix:1997:AME, AUTHOR = "D. Dureisseix", TITLE = "Une approche multi-{\'e}chelles pour des calculs de structures sur ordinateurs {\`a} architecture parall{\`e}le", SCHOOL = "ENS de Cachan", YEAR = 1997, ADDRESS = "Cachan", MONTH = "January" } @ARTICLE{Eijkhout:1991:RSC, OLDTAG = "ev", AUTHOR = "Victor Eijkhout and Panayot Vassilevski", TITLE = "The Role of the Strengthened {C}auchy-{B}uniakowskii-{S}chwarz Inequality in Multilevel Methods", JOURNAL = "SIAM Review", VOLUME = 33, NUMBER = 3, YEAR = 1991, PAGES = "405--419" } @ARTICLE{Eisenstat:1983:VIM, OLDTAG = "eielsc", AUTHOR = "Stanley C. Eisenstat and Howard C. Elman and Martin H. Schultz", TITLE = "Variational Iterative Methods for Nonsymmetric Systems of Linear Equations", JOURNAL = "SIAM J. Numer. Anal.", YEAR = 1983, VOLUME = "20 (2)", PAGES = "345--357" } @ARTICLE{Elman:1995:AAH, OLDTAG = "ez", AUTHOR = "Howard C. Elman and Xuejun Zhang", TITLE = "Algebraic Analysis of the Hierarchical Basis Preconditioner", JOURNAL = "SIAM Matrix Analysis and Applications", YEAR = 1995, VOLUME = 16, MONTH = "January", PAGES = "192--205", NUMBER = 1 } @TECHREPORT{Ewing:1988:LRT, OLDTAG = "ewlv", AUTHOR = "R. E. Ewing and R. D. Lazarov and P. S. Vassilevski", TITLE = "Local refinement techniques for elliptic problems on cell-centered grids", INSTITUTION = "University of Wyoming", YEAR = 1988 } @INPROCEEDINGS{Ewing:1989:DTE, OLDTAG = "1ewi", AUTHOR = "Richard E. Ewing", TITLE = "Domain Decomposition Techniques for Efficient Adaptive Local Grid Refinement", BOOKTITLE = "Domain Decomposition Methods", YEAR = 1989, EDITOR = "Tony Chan and Roland Glowinski and Jacques P{\'e}riaux and Olof Widlund", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @ARTICLE{Ewing:1992:ASA, OLDTAG = "1ewwa", AUTHOR = "Richard E. Ewing and Junping Wang", TITLE = "Analysis of the {S}chwarz Algorithm for Mixed Finite Element Methods", JOURNAL = "RAIRO Mathematical Modelling and Numerical Analysis", VOLUME = 26, NUMBER = 6, YEAR = 1992, PAGES = "739--756" } @INCOLLECTION{Farhat:1994:CMA, OLDTAG = "1farhat", AUTHOR = "Charbel Farhat and Fran\c{c}ois-Xavier Roux", BOOKTITLE = "Computational Mechanics Advances", TITLE = "Implicit parallel processing in structural mechanics", PUBLISHER = "North-Holland", YEAR = 1994, VOLUME = "2 (1)", EDITOR = "Oden, J. Tinsley", PAGES = "1--124" } @ARTICLE{Fedorenko:1961:SCO, OLDTAG = "fed", AUTHOR = "R. P. Fedorenko", TITLE = "The Speed of Convergence of One Iterative Process", JOURNAL = "USSR Comput. Math. and Math. Phys.", VOLUME = 1, YEAR = 1961, PAGES = "1092--1096" } @INPROCEEDINGS{Feng:1983:FEM, OLDTAG = "feng", AUTHOR = "Feng, Kang", TITLE = "Finite Element Method and Natural Boundary Reduction", BOOKTITLE = "Proceeding of the International Congress of Mathematicians", YEAR = 1983, ADDRESS = "Warsaw, Poland" } @ARTICLE{Fischer:1994:SEM, OLDTAG = "1fischronq", AUTHOR = "Paul F. Fischer and Einar R{\o}nquist", TITLE = "Spectral Element Methods for Large Scale Parallel {N}avier-{S}tokes Calculations", JOURNAL = "Comput. Methods Appl. Mech. Engrg", YEAR = 1994, PAGES = "69--76", VOLUME = 116, NOTE = "Proceedings of ICOSAHOM 92, a conference held in Montpellier, France, June 22-26, 1992." } @INBOOK{Freund:1991:ISL, OLDTAG = "fgn", AUTHOR = "R. Freund and G. H. Golub and N. Nachtigal", TITLE = "Iterative Solution of Linear Systems", SERIES = "Acta Numerica 1992", YEAR = 1991, PUBLISHER = "Cambridge University Press", PAGES = "57--100" } @ARTICLE{George:1973:NDR, OLDTAG = "geor", AUTHOR = "Alan George", TITLE = "Nested Dissection of a Regular Finite Element Mesh", JOURNAL = "SIAM J. Numer. Anal.", YEAR = 1973, VOLUME = 10, PAGES = "345--363" } @BOOK{George:1981:CSL, OLDTAG = "2geor", AUTHOR = "Alan George and Joseph Liu", TITLE = "Computer Solution of Large Sparse Positive Definite Systems", PUBLISHER = "Prentice-Hall", ADDRESS = "Englewood Cliffs, NJ", YEAR = 1981 } @BOOK{Girault:1986:FEM, OLDTAG = "girrav", AUTHOR = "Vivette Girault and {P}ierre-{A}rnaud Raviart", TITLE = "Finite Element Methods for {N}avier-{S}tokes Equations", YEAR = 1986, PUBLISHER = "Springer-Verlag", ADDRESS = "New York" } @ARTICLE{Glowinski:1979:NMB, OLDTAG = "glowinski", AUTHOR = "R. Glowinski and O. Pironneau", TITLE = "Numerical Methods For The First Biharmonic Equation And For the Two-Dimensional {S}tokes Problem", JOURNAL = "SIAM Review", YEAR = 1979, VOLUME = 21, NUMBER = "2 ", PAGES = "167-- 212" } @TECHREPORT{Glowinski:1987:DMF, OLDTAG = "glwh", AUTHOR = "Roland Glowinski and Mary F. Wheeler", TITLE = "Domain decomposition and mixed finite element methods for elliptic problems", INSTITUTION = "Rice University", YEAR = 1987, NUMBER = "87-11" } @INPROCEEDINGS{Glowinski:1988:DMF, OLDTAG = "glowhe", AUTHOR = "Roland Glowinski and Mary F. Wheeler", TITLE = "Domain Decomposition and Mixed Finite Element Methods for Elliptic Problems", BOOKTITLE = "First International Symposium on Domain Decomposition Methods for Partial Differential Equations", YEAR = 1988, EDITOR = "Roland Glowinski and Gene H. Golub and G{\'e}rard A. Meurant and Jacques P{\'e}riaux", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @PROCEEDINGS{Glowinski:1988:DMP, OLDTAG = "dom1", TITLE = "Domain Decomposition Methods for Partial Differential Equations", EDITOR = "Roland Glowinski and Gene H. Golub and G{\'e}rard A. Meurant and Jacques P{\'e}riaux", YEAR = 1988, NOTE = "Proceedings of the {F}irst {I}nternational {S}ymposium on {D}omain {D}ecomposition {M}ethods for {P}artial {D}ifferential {E}quations, Paris, France, January 1987.", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @INPROCEEDINGS{Glowinski:1990:ADA, OLDTAG = "glkiwh", AUTHOR = "R. Glowinski and W. Kinton and M. F. Wheeler", TITLE = "Acceleration of Domain Decomposition Algorithms for Mixed Finite Elements by Multi-level Methods", YEAR = 1990, EDITOR = "Tony Chan and Roland Glowinski and Jacques P{\'e}riaux and Olof Widlund", BOOKTITLE = "Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, held in Houston, Texas, March 20-22, 1989", PUBLISHER = "SIAM, Philadelphia, PA" } @PROCEEDINGS{Glowinski:1991:FIS, OLDTAG = "dom4", TITLE = "Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations", EDITOR = "Roland Glowinski and Yuri A. Kuznetsov and G{\'e}rard A. Meurant and Jacques P{\'e}riaux and Olof Widlund", YEAR = 1991, PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", NOTE = "Held in Moscow, USSR, May 21--25, 1990." } @INPROCEEDINGS{Golub:1984:PIR, OLDTAG = "gome", AUTHOR = "Gene Golub and D. Mayers", TITLE = "The Use of Preconditioning Over Irregular Regions", BOOKTITLE = "Computing Methods in Applied Sciences and Engineering, VI", YEAR = 1984, EDITOR = "R. Glowinski and J. L. Lions", PAGES = "3--14", PUBLISHER = "North-Holland", ADDRESS = "Amsterdam, New York, Oxford", NOTE = "Proceedings of a conference held in Versailles, France, December 12-16,1983." } @BOOK{Golub:1989:MAC, OLDTAG = "govl", AUTHOR = "Gene H. Golub and Charles F. Van Loan", TITLE = "Matrix Computations", PUBLISHER = "Johns Hopkins Univ. Press", YEAR = 1989, NOTE = "Second Edition." } @BOOK{Goossens:1993:TLC, UPDATE = "Yes", AUTHOR = "Goossens, M., Mittelbach, F., Samarin, A.", TITLE = "The LaTeX Companion", YEAR = 1993, PUBLISHER = "Addison-Wesley", ADDRESS = "Reading, Massachusetts" } @ARTICLE{Greenbaum:1989:PPC, OLDTAG = "gree", AUTHOR = "Anne Greenbaum and Congming Li and Zheng Chao Han", TITLE = "Parallelizing Preconditioned Conjugate Gradient Algorithms", JOURNAL = "Computer Physics Communications", YEAR = 1989, VOLUME = 53, PAGES = "295--309" } @TECHREPORT{Griebel:1993:RAT, OLDTAG = "1go", AUTHOR = "Michael Griebel and Peter Oswald", TITLE = "Remarks on the Abstract Theory of Additive and Multiplicative {S}chwarz Algorithms", YEAR = 1993, INSTITUTION = "Technische Universit{\"{a}}t M{\"{u}}nchen" } @BOOK{Griebel:1994:MIE, OLDTAG = "2g", AUTHOR = "Michael Griebel", TITLE = "Multilevelmethoden als Iterationsverfahren {\"{u}}ber Erzeugendensystem", YEAR = 1994, PUBLISHER = "B.G.\ Teubner", SERIES = "Teubner {S}kripten zur {N}umerik", ADDRESS = "Stuttgart" } @BOOK{Grisvard:1985:EPN, OLDTAG = "gris", AUTHOR = "P. Grisvard", TITLE = "Elliptic problems in nonsmooth domains", PUBLISHER = "Pitman Publishing", ADDRESS = "Boston", YEAR = 1985 } @ARTICLE{Gropp:1989:DPC, OLDTAG = "5kegr", AUTHOR = "William D. Gropp and David E. Keyes", TITLE = "Domain Decomposition on Parallel Computers", JOURNAL = "Impact Comput. Sci. Eng.", VOLUME = 1, YEAR = 1989, PAGES = "421--439" } @INPROCEEDINGS{Gropp:1991:PDS, OLDTAG = "4kegr", AUTHOR = "William D. Gropp and David E. Keyes", TITLE = "Parallel Domain Decomposition and the Solution of Nonlinear Systems of Equations", BOOKTITLE = "Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations", EDITOR = "Roland Glowinski and Yuri A. Kuznetsov and G{\'e}rard A. Meurant and Jacques P{\'e}riaux and Olof Widlund", YEAR = 1991, PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", PAGES = "373--381" } @INPROCEEDINGS{Gropp:1992:PCD, OLDTAG = "1gropp", AUTHOR = "William D. Gropp", TITLE = "Parallel Computing and Domain Decomposition", BOOKTITLE = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations", EDITOR = "David E. Keyes and Tony F. Chan and G{\'e}rard A. Meurant and Jeffrey S. Scroggs and Robert G. Voigt", YEAR = 1992, PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", PAGES = "349--361" } @INPROCEEDINGS{Gropp:1994:EDT, OLDTAG = "1gs", AUTHOR = "William D. Gropp and Barry F. Smith", TITLE = "Experiences with Domain Decomposition in Three Dimensions: Overlapping {S}chwarz Methods", BOOKTITLE = "Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition", NOTE = "Held in Como, Italy, June 15--19,1992", VOLUME = 157, EDITOR = "Alfio Quarteroni and Yuri A. Kuznetsov and Jacques P{\'e}riaux and Olof B. Widlund", YEAR = 1994, SERIES = "Contemporary Mathematics", PUBLISHER = "AMS", PAGES = "323--334" } @INPROCEEDINGS{Gropp:1994:SEP, OLDTAG = "grsm", AUTHOR = "William D. Gropp and Barry F. Smith", TITLE = "Scalable, Extensible, and Portable Numerical Libraries", PUBLISHER = "IEEE", YEAR = 1994, BOOKTITLE = "Proceedings of Scalable Parallel Libraries Conference", PAGES = "87--93" } @inproceedings{Haase:1990:NAD, OLDTAG = "1hlm", AUTHOR = "Gundolf Haase and Ulrich Langer and Arnd Meyer", TITLE = "A New Approach to the {D}irichlet Domain Decomposition Method", BOOKTITLE = "Fifth Multigrid Seminar, Eberswalde 1990", EDITOR = "S. Hengst", ORGANIZATION = "Karl--Weierstrass--Institut", ADDRESS = "Berlin", YEAR = 1990, PAGES = "1--59", NOTE = "Report R--MATH--09/90" } @BOOK{Hackbusch:1985:MMA, OLDTAG = "2hack", AUTHOR = "Wolfgang Hackbusch", TITLE = "Multigrid Methods and Applications", YEAR = 1985, PUBLISHER = "Springer", ADDRESS = "Berlin" } @TECHREPORT{Hackbusch:1991:FDM, OLDTAG = "1hack", AUTHOR = "Wolfgang Hackbusch", TITLE = "The Frequency Decomposition Multi-Grid Method, Part {II}: Convergence Analysis Based on the Additive {S}chwarz Method", INSTITUTION = "Christian-Albrecht-Universit\H{a}t, Kiel, Germany", YEAR = 1991 } @BOOK{Hackbusch:1994:ISL, OLDTAG = "3hack", AUTHOR = "Wolfgang Hackbusch", TITLE = "Iterative Solution of Large Sparse Linear Systems of Equations", YEAR = 1994, PUBLISHER = "Springer-Verlag", ADDRESS = "Berlin" } @BOOK{Hardy:1934:INE, OLDTAG = "hardy", AUTHOR = "G. H. Hardy and J. E. Littlewood and G. P\'{o}lya", TITLE = "Inequalities", YEAR = 1934, PUBLISHER = "Cambridge University Press", ADDRESS = "Cambridge" } @ARTICLE{Hart:1989:AMA, OLDTAG = "3mcc", AUTHOR = "Leslie Hart and Steve McCormick", TITLE = "Asynchronous Multilevel Adaptive Methods for Solving Partial Differential Equations on Multiprocessors: Computational Analysis", JOURNAL = "Parallel Computing", YEAR = 1989, VOLUME = 12, PAGES = "131-144" } @INPROCEEDINGS{Hestenes:1956:CGM, OLDTAG = "hest", AUTHOR = "Magnus R. Hestenes", TITLE = "The Conjugate Gradient Method for Solving Linear Systems", BOOKTITLE = "Proc. Symp. Appl. Math VI, American Mathematical Society", YEAR = 1956, PAGES = "83--102", PUBLISHER = "McGraw-Hill", ADDRESS = "New York" } @TECHREPORT{Hsiao:1992:DBE, OLDTAG = "3wend", AUTHOR = "G. C. Hsiao and W. L. Wendland", TITLE = "Domain Decomposition via Boundary Element Methods", YEAR = 1992, INSTITUTION = "Mathematics Institut A, Universit{\"a}t Stuttgart", NUMBER = "92-14" } @INPROCEEDINGS{Hughes:1988:FVE, OLDTAG = "hufe", AUTHOR = "Thomas R. Hughes and Robert M. Ferencz", TITLE = "Fully Vectorized EBE Preconditioners for Nonlinear Solid Mechanics: Applications to Large-Scale Three-Dimensional Continuum, Shell and Contact/Impact Problems", BOOKTITLE = "First International Symposium on Domain Decomposition Methods for Partial Differential Equations ", YEAR = 1988, EDITOR = "Roland Glowinski and Gene H. Golub and G{\'e}rard A. Meurant and Jacques P{\'e}riaux", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @PHDTHESIS{Hvidsten:1990:PFE, OLDTAG = "hvid", AUTHOR = "Anders Hvidsten", TITLE = "On the Parallelization of a Finite Element Structural Analysis Program", YEAR = 1990, SCHOOL = "Computer Science Department, University of Bergen, Norway" } @INBOOK{Ilin:1969:PCD, OLDTAG = "ilin", AUTHOR = "V. P. Il'in", TITLE = "The Properties of Some Classes of Differentiable Functions of Several Variables Defined in an n-dimensional Region", VOLUME = 81, PAGES = "91--256", SERIES = 2, NOTE = "Originally in Trudy Mat. Inst. Steklov. 66 (1962), 227--363", PUBLISHER = "American Mathematical Society", YEAR = 1969 } @BOOK{Johnson:1987:NSP, OLDTAG = "johnson", AUTHOR = "Claes Johnson", TITLE = "Numerical Solutions of Partial Differential Equations by the Finite Element Method", PUBLISHER = "Cambridge University Press", ADDRESS = "Cambridge", YEAR = 1987 } @TECHREPORT{Kaporin:XXXX:BSP, OLDTAG = "1kapkolyer", AUTHOR = "I. E. Kaporin and L. Yu. Kolotilina and A. Yu. Yeremin", TITLE = "Block {SSOR} preconditionings for high order {3D} {FE} systems {II}: incomplete {BSSOR} preconditionings", YEAR = "XXXX", INSTITUTION = "The {D}epartment of {N}umerical {M}athematics and {C}ybernetics of the {M}oscow {S}tate {U}niversity, {L}eninskije {G}ory, 119899, {M}oscow B-234, {USSR} and the {L}eningrad {B}ranch of {V. A.} {S}teklov {M}athematical {I}institute of the {USSR} {A}cademy of {S}ciences, {F}ontanka 27, {L}eningrad 191011, {USSR} and the {D}epartment of {N}umerical {M}athematics of the {USSR} {A}cademy of {S}ciences, {R}yleev str. 29, 119034, {M}oscow, {USSR}" } @TECHREPORT{Karypis:1995:MUG, AUTHOR = "George Karypis and Vipin Kumar", TITLE = "METIS, Unstructured Graph Partitioning and Sparse Matrix Ordering System. Version 2.0", INSTITUTION = "University of Minnesota, Department of Computer Science", YEAR = 1995, ADDRESS = "Minneapolis, MN 55455", MONTH = "August" } @ARTICLE{Keyes:1987:CDT, OLDTAG = "kegr", AUTHOR = "David E. Keyes and William D. Gropp", TITLE = "A comparison of domain decomposition techniques for elliptic partial differential equations and their parallel implementation", JOURNAL = "SIAM J. Sci. Stat. Comput.", YEAR = 1987, VOLUME = 8, NUMBER = 2, PAGES = "s166--s202" } @ARTICLE{Keyes:1990:DTP, OLDTAG = "2kegr", AUTHOR = "David E. Keyes and William D. Gropp", TITLE = "Domain Decomposition Techniques for the Parallel Solution of Nonsymmetric Systems of Elliptic {BVP}s", JOURNAL = "Appl. Num. Math.", VOLUME = 6, YEAR = 1990, PAGES = "281--301" } @ARTICLE{Keyes:1992:DLM, OLDTAG = "3kegr", AUTHOR = "David E. Keyes and William D. Gropp", TITLE = "Domain Decomposition with Local Mesh refinement", YEAR = 1992, VOLUME = 13, PAGES = "967--993", JOURNAL = "SIAM J. Sci. Stat. Comp." } @PROCEEDINGS{Keyes:1992:FIS, OLDTAG = "dom5", TITLE = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations", EDITOR = "David E. Keyes and Tony F. Chan and G{\'e}rard A. Meurant and Jeffrey S. Scroggs and Robert G. Voigt", YEAR = 1992, PUBLISHER = "SIAM", NOTE = "Held in Norfolk, VA, May 6--8, 1991", ADDRESS = "Philadelphia, PA" } @PROCEEDINGS{Keyes:1994:PSI, OLDTAG = "dom7", TITLE = "Domain Decomposition Methods in Science and Engineering", EDITOR = "David E. Keyes and Jinchao Xu", YEAR = 1994, SERIES = "Contemporary Mathematics", PUBLISHER = "AMS", VOLUME = 180, ADDRESS = "Providence, R.I.", NOTE = "Proceedings of the Seventh International Conference on Domain Decomposition, October 27-30, 1993, The Pennsylvania State University" } @ARTICLE{Khoromskij:1992:SEP, OLDTAG = "2wend", AUTHOR = "B. N. Khoromskij and W. L. Wendland", TITLE = "Spectrally Equivalent Preconditioners for Boundary Equations in Substructuring Techniques", JOURNAL = "East-West J. Numer. Anal.", VOLUME = 1, YEAR = 1992, PAGES = "1--27" } @TECHREPORT{Klawonn:1994:OPC, OLDTAG = "klaw1", AUTHOR = "Axel Klawonn", TITLE = "An optimal preconditioner for a class of saddle point problems with a penalty term", INSTITUTION = "Courant Institute of Mathematical Sciences, New York University", YEAR = 1994, MONTH = "December", NUMBER = 676 } @TECHREPORT{Klawonn:1995:OPC, OLDTAG = "klaw2", AUTHOR = "Axel Klawonn", TITLE = "An optimal preconditioner for a class of saddle point problems with a penalty term, {P}art {II}: General Theory", YEAR = 1995, MONTH = "April", INSTITUTION = "Westf{\"{a}}lische Wilhelms-Universit{\"{a}}t M{\"{u}}nster, Germany", NUMBER = "14/95", NOTE = "Also available as Technical Report 683 of the Courant Institute of Mathematical Sciences, New York University" } @PHDTHESIS{Klawonn:1996:PIP, OLDTAG = "klaw3", AUTHOR = "Axel Klawonn", TITLE = "Preconditioners for Indefinite Problems", YEAR = 1996, MONTH = "February", SCHOOL = "Westf{\"{a}}lische Wilhelms-Universit{\"{a}}t M{\"{u}}nster", NOTE = "Technical Report 716, Department of Computer Science, Courant Institute of Mathematical Sciences, New York University" } @ARTICLE{Kolotilina:1989:BSP, OLDTAG = "1kolyer", AUTHOR = "L. Yu. Kolotilina and A. Yu. Yermin", TITLE = "Block {SSOR} preconditionings for high order {3D} {FE} systems", JOURNAL = "BIT", YEAR = 1989, VOLUME = 29, PAGES = "805--823" } @TECHREPORT{Kolotilina:XXXX:FSA, OLDTAG = "2kolyer", AUTHOR = "L. Yu. Kolotilina and A. Yu. Yermin", TITLE = "Factorized sparse approximate inverse preconditioners", YEAR = "XXXX", INSTITUTION = "The {L}eningrad {B}ranch of {V. A.} {S}teklov {M}athematical {I}institute of the {USSR} {A}cademy of {S}ciences, {F}ontanka 27, {L}eningrad 191011, {USSR} and the {D}epartment of {N}umerical {M}athematics of the {USSR} {A}cademy of {S}ciences, {R}yleev str. 29, 119034, {M}oscow, {USSR}" } @ARTICLE{Kuznetsov:1989:MDM, OLDTAG = "1kuzn", AUTHOR = "Yuri A. Kuznetsov", TITLE = "Multilevel Domain Decomposition Methods", JOURNAL = "Appl. Numer. Math.", YEAR = 1989, VOLUME = 5 } @INPROCEEDINGS{Kuznetsov:1991:ODM, OLDTAG = "2kuzn", AUTHOR = "Yuri A. Kuznetsov", TITLE = "Overlapping Domain Decomposition Methods for FE-Problems with Elliptic Singular Perturbed Operators", BOOKTITLE = "Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations", EDITOR = "Roland Glowinski and Yuri A. Kuznetsov and G{\'e}rard A. Meurant and Jacques P{\'e}riaux and Olof Widlund", YEAR = 1991, PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @TECHREPORT{Kuznetsov:1993:NEN, OLDTAG = "KuMaVa", AUTHOR = "Yuri Kuznetsov and Petri Manninen and Yuri Vassilevski", TITLE = "On numerical experiments with {N}eumann-{N}eumann and {N}eumann-{D}irichlet domain decomposition preconditioners", INSTITUTION = "University of Jyv{\"{a}}skyl{\"{a}}", YEAR = 1993 } @ARTICLE{Kuznetsov:1995:EIS, OLDTAG = "kuznet1", AUTHOR = "Yuri A.\ Kuznetsov", TITLE = "Efficient Iterative Solvers for Elliptic Problems on Nonmatching Grids", JOURNAL = "Russ. J. Numer. Anal. Math. Modelling", YEAR = 1995, VOLUME = 10, NUMBER = 3, PAGES = "187--211" } @ARTICLE{Kuznetsov:1995:OOS, OLDTAG = "kuznet_wheeler", AUTHOR = "Yuri A.\ Kuznetsov and Mary F.\ Wheeler", TITLE = "Optimal Order Substructuring Preconditioners for Mixed Finite Element Methods on Nonmatching Grids", JOURNAL = "East-West J. Numer. Math.", YEAR = 1995, VOLUME = 3, NUMBER = 2, PAGES = "127--143" } @ARTICLE{Lanczos:1938:TIE, OLDTAG = "2lanczos", AUTHOR = "Cornelius Lanczos", TITLE = "Trigonometric Interpolation of Empirical and Analytical Functions", JOURNAL = "J. Math. Phys.", YEAR = 1938, PAGES = "123--199", VOLUME = 17 } @ARTICLE{Lanczos:1950:IMS, OLDTAG = "1lanczos", AUTHOR = "Cornelius Lanczos", TITLE = "An Iterative Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators", JOURNAL = "J. Res. Nat. Bur. Standards, Sect. B.", YEAR = 1950, PAGES = "225--280", VOLUME = 45 } @ARTICLE{LeTallec:1993:DNG, OLDTAG = "1letallec_sassi", AUTHOR = "Le Tallec, Patrick and Taoufik Sassi", JOURNAL = "Mathematics of Computation", TITLE = "Domain Decomposition with Nonmatching Grids: Augmented {L}agrangian Approach", YEAR = 1993, NOTE = "To appear." } @ARTICLE{LeTallec:1993:NDA, OLDTAG = "2letallec", AUTHOR = "Le Tallec, Patrick", JOURNAL = "East-West J. Numer. Math.", TITLE = "Neumann-{N}eumann domain decomposition algorithms for solving 2{D} elliptic problems with nonmatching grids", YEAR = 1993, PAGES = "129--146", VOLUME = 1, NUMBER = 2 } @INCOLLECTION{LeTallec:1994:DMC, OLDTAG = "1letallec", AUTHOR = "Le Tallec, Patrick", BOOKTITLE = "Computational Mechanics Advances", TITLE = "Domain decomposition methods in computational mechanics", PUBLISHER = "North-Holland", YEAR = 1994, VOLUME = "1 (2)", EDITOR = "Oden, J. Tinsley", PAGES = "121--220" } @BOOK{Lebedev:1986:COM, OLDTAG = "lebe", AUTHOR = "V. I. Lebedev", TITLE = "Composition methods", PUBLISHER = "USSR {A}cademy of {S}ciences", YEAR = 1986, ADDRESS = "Moscow", NOTE = "In {R}ussian" } @BOOK{Lions:1972:NBV, OLDTAG = "1lima", AUTHOR = "Jacques-Louis Lions and Enrico Magenes", TITLE = "Nonhomogeneous Boundary Value Problems and Applications", VOLUME = "I", PUBLISHER = "Springer, New York, Heidelberg, Berlin", YEAR = 1972 } @ARTICLE{Lions:1978:ISM, OLDTAG = "3lion", TITLE = "Interpr\'{e}tation stochastique de la m\'{e}thode altern\'{e}e de {S}chwarz", AUTHOR = "Pierre Louis Lions", JOURNAL = "C. R. Acad. Sci. Paris", VOLUME = 268, YEAR = 1978, PAGES = "325--328" } @INPROCEEDINGS{Lions:1988:SAM, OLDTAG = "lion", TITLE = "On the {S}chwarz alternating method. {I.}", AUTHOR = "Pierre-Louis Lions", BOOKTITLE = "First International Symposium on Domain Decomposition Methods for Partial Differential Equations", YEAR = 1988, EDITOR = "Roland Glowinski and Gene H. Golub and G{\'e}rard A. Meurant and Jacques P{\'e}riaux", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", PAGES = "1--42" } @INPROCEEDINGS{Lions:1989:SAM, OLDTAG = "2lion", AUTHOR = "Pierre Louis Lions", TITLE = "On the {S}chwarz alternating method. {II.}", BOOKTITLE = "Domain Decomposition Methods", YEAR = 1989, EDITOR = "Tony Chan and Roland Glowinski and Jacques P{\'e}riaux and Olof Widlund", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", PAGES = "47--70" } @INPROCEEDINGS{Lions:1990:SAM, OLDTAG = "4lion", AUTHOR = "Pierre Louis Lions", TITLE = "On the {S}chwarz alternating method. {III:} A variant for nonoverlapping subdomains", BOOKTITLE = "Third International Symposium on Domain Decomposition Methods for Partial Differential Equations , held in Houston, Texas, March 20-22, 1989", EDITOR = "Tony F. Chan and Roland Glowinski and Jacques P{\'e}riaux and Olof Widlund", YEAR = 1990, PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @ARTICLE{Maday:1989:RTP, OLDTAG = "1maday", AUTHOR = "Yvon Maday", TITLE = "Rel\`{e}vement de traces polynomiales et interpolations hilbertiennes entre espaces de polyn\^{o}mes", JOURNAL = "C. R. Acad. Sci. Paris", VOLUME = "309, S\'{e}rie I", PAGES = "463--468", YEAR = 1989 } @INPROCEEDINGS{Maday:1989:SEM, OLDTAG = "madpa", AUTHOR = "Yvon Maday and Anthony T. Patera", TITLE = "Spectral Element Methods for the {N}avier-{S}tokes Equations", BOOKTITLE = "State of the Art Surveys in Computational Mechanics", YEAR = 1989, EDITOR = "A.K. Noor and J.T. Oden", PUBLISHER = "ASME", ADDRESS = "New York" } @ARTICLE{Maday:1993:AIM, OLDTAG = "mameparo", AUTHOR = "Yvon Maday and Dan Meiron and Anthony T.\ Patera and Einar M.\ R{\o}nquist", TITLE = "Analysis of Iterative Methods for the Steady and Unsteady {S}tokes Problem: Application to Spectral Element Discretizations", JOURNAL = "SIAM J. Sci. Comp.", VOLUME = 14, NUMBER = 2, YEAR = 1993, PAGES = "310--337" } @TECHREPORT{Maday:1996:ISM, OLDTAG = "madwid1", AUTHOR = "Yvon Maday and Olof B. Widlund", TITLE = "Some Iterative Substructuring Methods for Mortar Finite Elements: The Lower Order Case", INSTITUTION = "Courant Institute of Mathematical Sciences", YEAR = 1996, NOTE = "In preparation." } @ARTICLE{Mande:1990:BDS, OLDTAG = "4jama", AUTHOR = "Jan Mandel", TITLE = "On Block Diagonal and {S}chur Complement Preconditioning", JOURNAL = "Numer. Math.", VOLUME = 58, YEAR = 1990, PAGES = "79--93" } @TECHREPORT{Mandel:1989:EDP, OLDTAG = "5jama", AUTHOR = "Jan Mandel", TITLE = "Efficient Domain Decomposition Preconditioning for the p-version Finite Element Method in Three Dimensions", YEAR = 1989, INSTITUTION = "Computational Mathematics Group, University of Colorado at Denver"} @INPROCEEDINGS{Mandel:1989:ISEa, OLDTAG = "mamc1", AUTHOR = "Jan Mandel and Steve McCormick", TITLE = "Iterative Solution of Elliptic Equations with Refinement: {T}he Two-Level Case", BOOKTITLE = "Domain Decomposition Methods", YEAR = 1989, EDITOR = "Tony Chan and Roland Glowinski and Jacques P{\'e}riaux and Olof Widlund", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @INPROCEEDINGS{Mandel:1989:ISEb, OLDTAG = "mamc2", AUTHOR = "Jan Mandel and Steve McCormick", TITLE = "Iterative Solution of Elliptic Equations with Refinement: The Model Multi-Level Case", BOOKTITLE = "Domain Decomposition Methods", YEAR = 1989, EDITOR = "Tony Chan and Roland Glowinski and Jacques P{\'e}riaux and Olof Widlund", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @INPROCEEDINGS{Mandel:1990:HPP, OLDTAG = "3jama", AUTHOR = "Jan Mandel", TITLE = "Hierarchical preconditioning and partial orthogonalization for the p-version finite element method", BOOKTITLE = "Third International Symposium on Domain Decomposition Methods for Partial Differential Equations", EDITOR = "Tony F. Chan and Roland Glowinski and Jacques P{\'e}riaux and Olof Widlund", YEAR = 1990, PUBLISHER = "SIAM", NOTE = "Held in Houston, Texas, March 20-22, 1989.", ADDRESS = "Philadelphia, PA" } @ARTICLE{Mandel:1990:ISS, OLDTAG = "2jama", AUTHOR = "Jan Mandel", TITLE = "Iterative solvers by substructuring for the p-version finite element method", JOURNAL = "Comp. Methods Appl. Mech. Eng.", VOLUME = 80, YEAR = 1990, PAGES = "117--128" } @ARTICLE{Mandel:1990:TDP, OLDTAG = "1jama", AUTHOR = "Jan Mandel", TITLE = "Two-level domain decomposition preconditioning for the p-version finite element version in three dimensions", JOURNAL = "Int. J. Numer. Meth. Eng.", VOLUME = 29, PAGES = "1095--1108", YEAR = 1990 } @ARTICLE{Mandel:1991:DPP, OLDTAG = "8jama", AUTHOR = "Jan Mandel and G. Scott Lett", TITLE = "Domain Decomposition Preconditioning for p-version Finite Elements with High Aspect Ratios", VOLUME = 8, PAGES = "411--425", YEAR = 1991, JOURNAL = "Applied Numerical Analysis" } @unpublished{Mandel:1992:BDM, OLDTAG = "MandelCowsarWheeler", AUTHOR = "Lawrence Cowsar and Jan Mandel and Mary F. Wheeler", TITLE = "Balancing Domain Decomposition for Mixed Problems in Oil Reservoir Simulation", NOTE = "Presented at the 6th International Symposium on Domain Decomposition Methods, Como, Italy, 1992" } @ARTICLE{Mandel:1993:BDD, OLDTAG = "7jama", AUTHOR = "Jan Mandel", TITLE = "Balancing Domain Decomposition", JOURNAL = "Comm. Numer. Meth. Engrg.", VOLUME = 9, YEAR = 1993, PAGES = "233--241" } @TECHREPORT{Mandel:1993:BDT, OLDTAG = "MandelB-bal92", AUTHOR = "Jan Mandel and Marian Brezina", TITLE = "Balancing Domain Decomposition: Theory and Computations in Two and Three Dimensions", INSTITUTION = "Center for Computational Mathematics, University of Colorado at Denver", YEAR = 1993, NUMBER = "UCD/CCM 2" } @INPROCEEDINGS{Mandel:1993:IBI, OLDTAG = "10jama", AUTHOR = "Jan Mandel", TITLE = "Intelligent Block Iterative Methods", BOOKTITLE = "Proceedings of the 7th World Congress on Finite Elements, Monte Carlo, November 1993", EDITOR = "J. Robinson", YEAR = 1993, PAGES = "471--477", ISBN = "0 9507172 8 2", PUBLISHER = "Robinson Associates, Ltd., Okehampton, Devon EX20 4NT, England" } @INCOLLECTION{Mandel:1993:SLS, OLDTAG = "6jama", AUTHOR = "Jan Mandel", BOOKTITLE = "Solving Large Scale Problems in Mechanics. The Development and Application of Computational Solution Methods", EDITOR = "M. Papadrakakis", TITLE = "Adaptive Iterative Solvers in Finite Elements", YEAR = 1993, ADDRESS = "London", PUBLISHER = "John Wiley {\&} Sons", PAGES = "65--88" } @unpublished{Mandel:1994:BDP, OLDTAG = "MandelB-bal92-94", AUTHOR = "Jan Mandel and Marian Brezina", TITLE = "Balancing Domain Decomposition for Problems with Large Jumps in Coefficients", YEAR = 1994, FILENAME = "balance-j.ps", NOTE = "Math. Comp., to appear" } @INPROCEEDINGS{Mandel:1994:HDU, OLDTAG = "9jama", AUTHOR = "Jan Mandel", TITLE = "Hybrid Domain Decomposition with Unstructured Subdomains", BOOKTITLE = "Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition", EDITOR = "Alfio Quarteroni and Yuri A. Kuznetsov and Jacques P{\'e}riaux and Olof B. Widlund", YEAR = 1994, PUBLISHER = "AMS", SERIES = "Contemporary Mathematics", VOLUME = 157, NOTE = "Held in Como, Italy, June 15--19,1992.", PAGES = "103--112" } @ARTICLE{Mandel:1994:ISP, OLDTAG = "Mandel-pversion92", AUTHOR = "Jan Mandel", TITLE = "Iterative Solvers for p-Version Finite Element Method in Three Dimensions", NOTE = "Proceedings of ICOSAHOM 92, a conference held in Montpellier, France, June 1992.", JOURNAL = "Comput. Methods Appl. Mech. Engrg", YEAR = 1994, PAGES = "175--183", VOLUME = 116 } @ARTICLE{Marchuk:1986:FDM, OLDTAG = "makuma", AUTHOR = "G. I. Marchuk and Yu. A. Kuznetsov and A. M. Matsokin", TITLE = "Fictitious domain and domain decomposition methods", YEAR = 1986, VOLUME = 1, JOURNAL = "Soviet J. of Numer. Anal. Math. Modelling", PAGES = "3--61" } @PHDTHESIS{Mathew:1989:DIR, OLDTAG = "1mat", AUTHOR = "Tarek P. Mathew", TITLE = "Domain Decomposition and Iterative Refinement Methods for Mixed Finite Element Discretizations of Elliptic Problems", YEAR = 1989, MONTH = "September", SCHOOL = "Courant Institute of Mathematical Sciences", NOTE = "Tech. Rep. 463, Department of Computer Science, Courant Institute" } @ARTICLE{Mathew:1993:SAIa, OLDTAG = "2mat", AUTHOR = "Tarek P. Mathew", TITLE = "{S}chwarz alternating and iterative refinement methods for mixed formulations of elliptic Problems, Part {I}: {A}lgorithms and {N}umerical Results", YEAR = 1993, JOURNAL = "Numer. Math.", PAGES = "445--468", VOLUME = 65, NUMBER = 4 } @ARTICLE{Mathew:1993:SAIb, OLDTAG = "3mat", AUTHOR = "Tarek P. Mathew", TITLE = "{S}chwarz alternating and iterative refinement methods for mixed formulations of elliptic Problems, Part {II}: {T}heory", YEAR = 1993, JOURNAL = "Numer. Math.", PAGES = "469--492", VOLUME = 65, NUMBER = 4 } @ARTICLE{Matsokin:1985:SAM, OLDTAG = "mane", AUTHOR = "A. M. Matsokin and S. V. Nepomnyaschikh", TITLE = "A {S}chwarz alternating method in a subspace", YEAR = 1985, VOLUME = "29(10)", JOURNAL = "Soviet Mathematics", PAGES = "78--84" } @ARTICLE{Matsokin:1988:NST, OLDTAG = "mane2", AUTHOR = "A. M. Matsokin and S. V. Nepomnyaschikh", TITLE = "Norms on the space of traces of mesh functions", JOURNAL = "Sov. J. Numer. Anal. Math. Modeling", VOLUME = 3, YEAR = 1988, PAGES = "199-216" } @ARTICLE{Matsokin:1989:UBM, OLDTAG = "mane3", AUTHOR = "A. M. Matsokin and Sergey V. Nepomnyaschikh", TITLE = "On using the bordering method for solving systems of mesh equations", JOURNAL = "Sov. J. Numer. Anal. Math. Modeling", VOLUME = 4, YEAR = 1989, PAGES = "487-492" } @INPROCEEDINGS{McCormick:1984:FAC, OLDTAG = "1mcc", AUTHOR = "Steve McCormick", TITLE = "Fast adaptive composite grid ({FAC}) methods", BOOKTITLE = "Defect Correction Methods: Theory and Applications", YEAR = 1984, EDITOR = "K. B{\"{o}}hmer and H. J. Stetter", ORGANIZATION = "Computing Supplementum 5", PUBLISHER = "Springer-Verlag, Wien", PAGES = "115--121" } @ARTICLE{McCormick:1986:FAC, OLDTAG = "2mcc", AUTHOR = "Steve McCormick and Jim Thomas", TITLE = "The Fast Adaptive Composite Grid ({FAC}) Method for Elliptic Equations", JOURNAL = "Math. Comp.", YEAR = 1986, VOLUME = 46, NUMBER = 174, PAGES = "439--456" } @ARTICLE{McCormick:1986:UMS, OLDTAG = "mcru", AUTHOR = "S. McCormick and J. Ruge", TITLE = "Unigrid for multigrid simulation", JOURNAL = "Math. Comp.", YEAR = 1986, VOLUME = 41, PAGES = "43-62" } @BOOK{McCormick:1987:MUM, OLDTAG = "5mcc", EDITOR = "Stephen F. McCormick", TITLE = "Multigrid Methods", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", NOTE = "Frontiers in Appl. Math. Vol. 6", YEAR = 1987 } @BOOK{McCormick:1989:MAM, OLDTAG = "4mcc", AUTHOR = "Stephen F. McCormick", TITLE = "Multilevel Adaptive Methods for Partial Differential Equations", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", YEAR = 1989 } @INPROCEEDINGS{Meurant:1991:NED, OLDTAG = "1meur", AUTHOR = "G{\'e}rard A. Meurant", TITLE = "Numerical Experiments with a Domain Decomposition Method for Parabolic Problems on Parallel Computers", BOOKTITLE = "Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations", EDITOR = "Roland Glowinski and Yuri A. Kuznetsov and G{\'e}rard A. Meurant and Jacques P{\'e}riaux and Olof Widlund", YEAR = 1991, PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @ARTICLE{Miller:1965:NAS, OLDTAG = "1miller", AUTHOR = "Keith Miller", TITLE = "Numerical Analogs to the {S}chwarz Alternating Procedure", JOURNAL = "Numer. Math.", VOLUME = 7, YEAR = 1965, PAGES = "91--103" } @ARTICLE{Morgenstern:1956:BAV, OLDTAG = "morg", AUTHOR = "D. Morgenstern", TITLE = "Begr{\"u}ndung des alternierenden {V}erfahrens durch {O}rthogonalprojektion", JOURNAL = "ZAMM", YEAR = 1956, VOLUME = 36, PAGES = "7--8" } @BOOK{Necas:1967:MDT, OLDTAG = "nech", AUTHOR = "Jind\v{r}ich Ne\v{c}as", TITLE = "Les m{\'e}thodes directes en th{\'e}orie des {\'e}quations elliptiques", PUBLISHER = "Academia", YEAR = 1967, ADDRESS = "Prague" } @TECHREPORT{Nepomnyaschikh:1984:AMB, OLDTAG = "nepo", AUTHOR = "Sergey V. Nepomnyaschikh", TITLE = "On the application of the method of bordering for elliptic mixed boundary value problems and on the difference norms of $ {W}^{1/2}_{2}({S}) $", INSTITUTION = "Computing Center of the Siberian Branch of the {USSR} Academy of Sciences", YEAR = 1984, NUMBER = 106, ADDRESS = "Novosibirsk", NOTE = "In Russian" } @PHDTHESIS{Nepomnyaschikh:1986:DSM, OLDTAG = "nepo2", AUTHOR = "Sergey V. Nepomnyaschikh", TITLE = "Domain Decomposition and {S}chwarz Methods in a Subspace for the Approximate Solution of Elliptic Boundary Value Problems", SCHOOL = "Computing Center of the Siberian Branch of the USSR Academy of Sciences", ADDRESS = "Novosibirsk, USSR", YEAR = 1986 } @ARTICLE{Nepomnyaschikh:1989:ABM, OLDTAG = "nep1", AUTHOR = "Sergey V. Nepomnyaschikh", TITLE = "On the application of the bordering method to the mixed boundary value problem for elliptic equations and on the mesh norms in $ W_{2}^{1/2}(S)$", JOURNAL = "Sov. J. Numer. Anal. Math. Modeling", VOLUME = 4, YEAR = 1989, PAGES = "493-506" } @INPROCEEDINGS{Nepomnyaschikh:1991:ADE, OLDTAG = "nepo3", AUTHOR = "Sergey V. Nepomnyaschikh", TITLE = "Application of Domain Decomposition to Elliptic Problems on with Discontinuous Coefficients", BOOKTITLE = "Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations", EDITOR = "Roland Glowinski and Yuri A. Kuznetsov and G{\'e}rard A. Meurant and Jacques P{\'e}riaux and Olof Widlund", YEAR = 1991, PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", PAGES = "242--251" } @TECHREPORT{Nepomnyaschikh:1991:ETC, OLDTAG = "nepo4", AUTHOR = "Sergey V. Nepomnyaschikh and Olof B. Widlund", TITLE = "Extension Theorems for the Case of Locally Refined Meshes", YEAR = 1991, INSTITUTION = "Dept. of Computer Science, Courant Institute of Mathematical Sciences", NOTE = "To appear" } @ARTICLE{Nepomnyaschikh:1991:MTT, OLDTAG = "nep2", AUTHOR = "Sergey V. Nepomnyaschikh", TITLE = "Mesh theorems of traces, normalizations of function traces and their inversions", JOURNAL = "Sov. J. Numer. Anal. Math. Modeling", VOLUME = 6, YEAR = 1991, PAGES = "1-25" } @INPROCEEDINGS{Nepomnyaschikh:1992:DFD, OLDTAG = "nepo5", AUTHOR = "Sergey V. Nepomnyaschikh", TITLE = "Decomposition and Fictious Domains for Elliptic Boundary Value Problems", BOOKTITLE = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations", EDITOR = "David E. Keyes and Tony F. Chan and G{\'e}rard A. Meurant and Jeffrey S. Scroggs and Robert G. Voigt", YEAR = 1992, PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", PAGES = "62--72" } @BOOK{Oden:1982:IMT, OLDTAG = "odred", AUTHOR = "J. T. Oden and J. N. Reddy", TITLE = "An Introduction to the Mathematical Theory of Finite Elements", PUBLISHER = "John Wiley and Sons", ADDRESS = "New York", YEAR = 1982 } @TECHREPORT{Ong:1989:HBP, OLDTAG = "ong", AUTHOR = "M.E.G. Ong", TITLE = "Hierarchical Basis Preconditioners for Second Order Elliptic Problems in Three Dimensions", YEAR = 1989, NUMBER = "89--3", INSTITUTION = "Dept. of Applied Math. University of Washington, Seattle" } @TECHREPORT{Oswald:1989:CIH, OLDTAG = "2osw", AUTHOR = "Peter Oswald", TITLE = "On $C^1$ interpolating hierarchical spline bases", YEAR = 1989, NUMBER = "N/89/16", INSTITUTION = "Friedrich Schiller Universit\H{a}t, Jena, Germany" } @TECHREPORT{Oswald:1989:EHB, OLDTAG = "5osw", AUTHOR = "Peter Oswald", TITLE = "On estimates for hierarchic basis representations of finite element functions", YEAR = 1989, NUMBER = "N/89/16", INSTITUTION = "Friedrich Schiller Universit\H{a}t, Jena, Germany" } @ARTICLE{Oswald:1990:DNS, OLDTAG = "3osw", AUTHOR = "Peter Oswald", TITLE = "On the degree of nonlinear spline approximation in Besov-Sobolev spaces", JOURNAL = "J. Appr. Theory", NUMBER = 61, YEAR = 1990, PAGES = "131-157" } @ARTICLE{Oswald:1990:FSR, OLDTAG = "4osw", AUTHOR = "Peter Oswald", TITLE = "On function spaces related to finite element approximation theory", JOURNAL = "Z. Anal. Anwendungen", VOLUME = "9(1)", YEAR = 1990, PAGES = "43-64" } @TECHREPORT{Oswald:1991:BPP, OLDTAG = "10osw", AUTHOR = "Peter Oswald", TITLE = "On a {BPX}-Preconditioner For {P}1 Elements", NUMBER = "Math./91/2", NOTE = "(part 2)", YEAR = 1991, INSTITUTION = "Friedrich Schiller Universit\H{a}t, Jena, Germany" } @TECHREPORT{Oswald:1991:MPA, OLDTAG = "7osw", AUTHOR = "Peter Oswald", TITLE = "On multilevel preconditioners adapted to a variable coefficient problem", NUMBER = "Math./91/1", YEAR = 1991, INSTITUTION = "Friedrich Schiller Universit\H{a}t, Jena, Germany" } @TECHREPORT{Oswald:1991:PDB, OLDTAG = "11osw", AUTHOR = "Peter Oswald", TITLE = "Preconditioners for discretizations of the biharmonic equation by rectangular finite elements", YEAR = 1991, INSTITUTION = "Friedrich Schiller Universit\H{a}t, Jena, Germany" } @TECHREPORT{Oswald:1991:RMP, OLDTAG = "8osw", AUTHOR = "Peter Oswald", TITLE = "Two remarks on multilevel preconditioners", NUMBER = "Math./91/2", NOTE = "(part 2)", YEAR = 1991, INSTITUTION = "Friedrich Schiller Universit\H{a}t, Jena, Germany" } @INPROCEEDINGS{Oswald:1992:DNE, OLDTAG = "1osw", AUTHOR = "Peter Oswald", TITLE = "On Discrete Norm Estimates Related to Multilevel Preconditioners in the Finite Element Method", YEAR = 1992, PAGES = "203--241", EDITOR = "K. Ivanov and B. Sendov", BOOKTITLE = "Proc. Int. Conf. Constructive Theory of Functions, Varna 91" } @ARTICLE{Oswald:1992:HBM, OLDTAG = "9osw", AUTHOR = "Peter Oswald", TITLE = "On a hierarchical basis multilevel method with nonconforming {P}1 elements", JOURNAL = "Numer. Math.", YEAR = 1992, VOLUME = 62, NUMBER = 2, PAGES = "189--212" } @ARTICLE{Oswald:1992:HCF, OLDTAG = "6osw", AUTHOR = "Peter Oswald", TITLE = "On Hierarchical conforming finite element methods for the biharmonic equation", YEAR = 1992, JOURNAL = "SIAM J. Numer. Anal.", NOTE = "To appear" } @BOOK{Oswald:1994:MFE, OLDTAG = "12osw", AUTHOR = "Peter Oswald", TITLE = "Multilevel Finite Element Approximation, Theory and Applications", PUBLISHER = "B.G.\ Teubner", YEAR = 1994, SERIES = "Teubner {S}kripten zur {N}umerik", ADDRESS = "Stuttgart" } @ARTICLE{Overton:1988:MME, OLDTAG = "over", AUTHOR = "Michael L. Overton", TITLE = "On minimizing the maximum eigenvalue of a symmetric matrix", JOURNAL = "SIAM J. Matrix Anal. Appl.", YEAR = 1988, VOLUME = 9, NUMBER = 2, PAGES = "256--268" } @MASTERSTHESIS{Pahl:1993:STD, OLDTAG = "1pahl", AUTHOR = "Shannon S. Pahl", SCHOOL = "Department of Computational and Applied Mathematics, University of the Witwatersrand", ADDRESS = "Johannesburg, South Africa", TITLE = "{S}chwarz Type Domain Decomposition Methods for Spectral Element Discretizations", YEAR = 1993, MONTH = "December" } @ARTICLE{Parter:1995:PLS, OLDTAG = "parrot", AUTHOR = "Seymour V. Parter and Ernest E. Rothman", TITLE = "Preconditioning {L}egendre Spectral Collocation Approximations to Elliptic Problems", YEAR = 1995, VOLUME = 32, NUMBER = 2, JOURNAL = "SIAM J. Numer. Anal.", MONTH = "April", PAGES = "333--385" } @INPROCEEDINGS{Pasciak:1988:DPE, OLDTAG = "6bps", AUTHOR = "Joseph E. Pasciak", TITLE = "Domain Decomposition Preconditioners for Elliptic Problems in Two and Three Dimensions: {F}irst Approach", BOOKTITLE = "First International Symposium on Domain Decomposition Methods for Partial Differential Equations", YEAR = 1988, EDITOR = "Roland Glowinski and Gene H. Golub and G{\'e}rard A. Meurant and Jacques P{\'e}riaux", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @PHDTHESIS{Pavarino:1992:DAP, OLDTAG = "3pava", AUTHOR = "Luca F. Pavarino", SCHOOL = "Courant Institute, New York University", TITLE = "Domain Decomposition Algorithms for the p-version Finite Element Method for Elliptic Problems", INSTITUTION = "Courant Institute of Mathematical Sciences, Department of Mathematics", YEAR = 1992, MONTH = "September", NUMBER = 616 } @ARTICLE{Pavarino:1994:ASM, OLDTAG = "1pava", AUTHOR = "Luca F. Pavarino", TITLE = "Additive {S}chwarz Methods for the p-version Finite Element Method", YEAR = 1994, VOLUME = 66, NUMBER = 4, PAGES = "493--515", JOURNAL = "Numer. Math." } @INPROCEEDINGS{Pavarino:1994:ISMa, OLDTAG = "1pavwid", AUTHOR = "Luca F. Pavarino and Olof B. Widlund", TITLE = "Iterative Substructuring Methods for Spectral Elements in Three Dimensions", YEAR = 1994, PAGES = "345-355", BOOKTITLE = "The Finite Element Method: Fifty Years of the Courant Element", PUBLISHER = "Marcel Dekker", EDITOR = "M. K\v{r}i\v{z}ek and P. Neittaanm{\"{a}}ki and R. Stenberg", ADDRESS = "New York, Basel, Hong Kong" } @TECHREPORT{Pavarino:1994:ISMb, OLDTAG = "3pavwid", AUTHOR = "Luca F. Pavarino and Olof B. Widlund", TITLE = "Iterative Substructuring Methods for Spectral Elements: Problems in Three Dimensions Based on Numerical Quadrature", YEAR = 1994, MONTH = "May", NUMBER = 663, NOTE = "To appear in Computers Math. Applic.", INSTITUTION = "Courant Institute of Mathematical Sciences, Department of Computer Science" } @INPROCEEDINGS{Pavarino:1994:SAP, OLDTAG = "2pava", AUTHOR = "Luca F. Pavarino", TITLE = "Some {S}chwarz Algorithms for the p-version Finite Element Method", BOOKTITLE = "Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition", EDITOR = "Alfio Quarteroni and Yuri A. Kuznetsov and Jacques P{\'e}riaux and Olof B. Widlund", YEAR = 1994, SERIES = "Contemporary Mathematics", PUBLISHER = "AMS", VOLUME = 157, NOTE = "Held in Como, Italy, June 15--19,1992." } @ARTICLE{Pavarino:1994:SML, OLDTAG = "4pava", AUTHOR = "Luca F. Pavarino", TITLE = "{S}chwarz Methods with Local Refinement for the p-version Finite Element Method", YEAR = 1994, VOLUME = 69, NUMBER = 2, PAGES = "185--211", JOURNAL = "Numer. Math." } @INPROCEEDINGS{Pavarino:1994:WBB, OLDTAG = "5pava", AUTHOR = "Luca F. Pavarino", TITLE = "A Wire Basket Based Method for Spectral Elements in Three Dimensions", BOOKTITLE = "Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing", EDITOR = "David E. Keyes and Jinchao Xu", YEAR = 1994, VOLUME = 180, PAGES = "99--104", PUBLISHER = "AMS", SERIES = "Contemporary Mathematics", NOTE = "Held at Penn State University, October 27-30, 1993." } @INPROCEEDINGS{Pavarino:1995:PCG, OLDTAG = "4pavwid", AUTHOR = "Luca F. Pavarino and Olof B. Widlund", TITLE = "Preconditioned Conjugate Gradient Solvers for Spectral Elements in 3{D}", BOOKTITLE = "Solution Techniques for Large-Scale {CFD} Problems", YEAR = 1995, EDITOR = "W. G. Habashi", PAGES = "249--270", PUBLISHER = "John Wiley \& Sons", NOTE = "Proceedings of the International Workshop on Solution Techniques for Large-Scale {CFD} Problems held at {CERCA}, Montr\'{e}al, Canada, September 26--28, 1994" } @ARTICLE{Pavarino:1996:PBI, OLDTAG = "2pavwid", AUTHOR = "Luca F. Pavarino and Olof B. Widlund", TITLE = "A Polylogarithmic Bound for an Iterative Substructuring Method for Spectral Elements in Three Dimensions", YEAR = 1996, MONTH = "August", VOLUME = 33, NUMBER = 4, JOURNAL = "SIAM J. Numer. Anal.", PAGES = "1303--1335" } @ARTICLE{Peisker:1988:NSF, OLDTAG = "peisker", AUTHOR = "P. Peisker", TITLE = "On the Numerical Solution of the First Biharmonic Equation", JOURNAL = "RAIRO Mathematical Modelling and Numerical Analysis", YEAR = 1988, VOLUME = 22, NUMBER = 4, PAGES = "655--676" } @ARTICLE{Poincare:1896:MNP, OLDTAG = "poin", AUTHOR = "Henri Poincar{\'e}", TITLE = "La m{\'e}thode de {N}eumann et le probl{\`e}me de {D}irichlet", JOURNAL = "Acta Mathematica", YEAR = 1896, VOLUME = 20, PAGES = "59--??" } @PHDTHESIS{Pourquier:1994:MEF, OLDTAG = "pourquier_thesis", AUTHOR = "Olivier Pourquier", TITLE = "M\'ethode des \'el\'ements finis de haut degr\'e (p-version): estimation du conditionnement des matrices et construction de pr\'econditionneurs", SCHOOL = "L'{E}cole {C}entrale de {L}yon, {F}rance", YEAR = 1994, MONTH = "July" } @ARTICLE{Przemieniecki:1963:MSA, OLDTAG = "prze", AUTHOR = "Przemieniecki, J. S.", TITLE = "Matrix structural analysis of substructures.", JOURNAL = "Am. Inst. Aero. Astro. J.", VOLUME = 1, PAGES = "138--147", YEAR = 1963 } @BOOK{Przemieniecki:1985:TMS, OLDTAG = "2prz", AUTHOR = "J. S. Przemieniecki", TITLE = "Theory of Matrix Structural Analysis", PUBLISHER = "Dover Publications, Inc.", ADDRESS = "New York", NOTE = "Reprint of McGraw Hill, 1968", YEAR = 1985 } @INPROCEEDINGS{Quarteroni:1989:DAS, OLDTAG = "quar", AUTHOR = "Alfio Quarteroni", TITLE = "Domain Decomposition Algorithms for the {S}tokes Equations", BOOKTITLE = "Domain Decomposition Methods", YEAR = 1989, EDITOR = "Tony Chan and Roland Glowinski and Jacques P{\'e}riaux and Olof Widlund", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @ARTICLE{Quarteroni:1992:FEP, OLDTAG = "quarzamp", AUTHOR = "Alfio Quarteroni and Elena Zampieri", TITLE = "Finite Element Preconditioning for {L}egendre Spectral Collocation Approximations to Elliptic Problems and Systems", YEAR = 1992, VOLUME = 29, NUMBER = 4, PAGES = "917--936", JOURNAL = "SIAM J. Numer. Anal." } @PROCEEDINGS{Quarteroni:1994:DMS, OLDTAG = "dom6", TITLE = "Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition", EDITOR = "Alfio Quarteroni and Yuri A. Kuznetsov and Jacques P{\'e}riaux and Olof B. Widlund", YEAR = 1994, PUBLISHER = "AMS", SERIES = "Contemporary Mathematics", VOLUME = 157, NOTE = "Held in Como, Italy, June 15--19,1992." } @INPROCEEDINGS{Raviart:1975:MFE, OLDTAG = "rath", AUTHOR = "P. A. Raviart and J. M. Thomas", TITLE = "A Mixed Finite Element Method for 2-nd Order Elliptic Problems", BOOKTITLE = "Mathematical Aspects of Finite Element Methods", NOTE = "Lecture Notes of Mathematics, Volume 606", YEAR = 1975, EDITOR = "A. Dold and B. Eckmann", PUBLISHER = "Springer" } @BOOK{Rivlin:1990:CHP, OLDTAG = "rivlin", AUTHOR = "Theodore J. Rivlin", TITLE = "The Chebyshev Polynomials", PUBLISHER = "Wiley Interscience", YEAR = 1990 } @TECHREPORT{Roeck:1989:LPD, OLDTAG = "1deroeck", AUTHOR = "De {R}oeck, Yann-Herv{\'e}", TITLE = "A local preconditioner in a domain-decomposed method", YEAR = 1989, INSTITUTION = "Centre Europ{\'e}en de Recherche et de Formation Avanc{\'e}e en Calcul Scientifique", NUMBER = "TR89/10", ADDRESS = "Toulouse, France" } @INPROCEEDINGS{Roeck:1991:FIS, OLDTAG = "2deroeck", AUTHOR = "De {R}oeck, Yann-Herv{\'e} and Le Tallec, Patrick", TITLE = "Analysis and Test of a Local Domain Decomposition Preconditioner", BOOKTITLE = "Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations", YEAR = 1991, EDITOR = "Roland Glowinski and Yuri Kuznetsov and G{\'e}rard Meurant and Jacques P{\'e}riaux and Olof Widlund", PUBLISHER = "SIAM, Philadelphia, PA", PAGES = "112--128" } @PHDTHESIS{Roeck:1991:ROM, OLDTAG = "deroeckthes", AUTHOR = "De {R}oeck, Yann-Herv{\'e}", TITLE = "R\'{e}solution sur Ordinateurs Multi-Processeurs de Probl\`{e}me d'Elasticit\'{e} par D\'{e}composition de Domaines", SCHOOL = "Universit\'{e} Paris IX Daupine", YEAR = 1991 } @INPROCEEDINGS{Ronquist:1992:DME, OLDTAG = "1ronquist", AUTHOR = "Einar M. R{\o}nquist", TITLE = "A Domain Decomposition Method for Elliptic Boundary Value Problems: Application to Unsteady Incompressible Fluid Flow", BOOKTITLE = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations", YEAR = 1992, EDITOR = "David E. Keyes and Tony F. Chan and G{\'e}rard A. Meurant and Jeffrey S. Scroggs and Robert G. Voigt", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", PAGES = "545--557" } @TECHREPORT{Ronquist:1993:ESB, OLDTAG = "2ronquist", AUTHOR = "Einar M. R{\o}nquist", TITLE = "An Elliptic Solver Based on Conjugate Gradients, Domain Decomposition and Deflation", YEAR = 1993, INSTITUTION = "Nektonics Inc.", ADDRESS = "875 Main Street, Cambridge, MA 02139, USA" } @BOOK{Rude:1993:MCT, OLDTAG = "1rude", AUTHOR = "Ulrich R{\"{u}}de", TITLE = "Mathematical and Computational Techniques for Multilevel Adaptive Methods", YEAR = 1993, ADDRESS = "Philadelphia, PA", PUBLISHER = "SIAM" } @ARTICLE{Saad:1986:GGM, OLDTAG = "sasch", AUTHOR = "Y. Saad and M. H. Schultz", TITLE = "{GMRES}: A generalized minimal residual algorithm for solving nonsymmetric linear systems", JOURNAL = "SIAM J. Sci. Stat. Comp.", YEAR = 1986, VOLUME = 7, PAGES = "856--869" } @INPROCEEDINGS{Sarkis:1993:TSM, OLDTAG = "1sarkis", AUTHOR = "Marcus V. Sarkis", TITLE = "Two-Level {S}chwarz Methods for Nonconforming Finite Elements and Discontinuous Coefficients", YEAR = 1993, BOOKTITLE = "Proceedings of the Sixth Copper Mountain Conference on Multigrid Methods, Volume 2", EDITOR = "N. Duane Melson and Thomas A. Manteuffel and Steve F. McCormick", NUMBER = 3224, PAGES = "543--566", PUBLISHER = "NASA", ADDRESS = "Hampton VA" } @INPROCEEDINGS{Sarkis:1994:MMP, OLDTAG = "2sarkis", AUTHOR = "Marcus V. Sarkis", TITLE = "Multilevel Methods for ${P}_1$ Nonconforming Finite Elements and Discontinuous Coefficients in Three Dimensions", BOOKTITLE = "Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing", EDITOR = "David E. Keyes and Jinchao Xu", YEAR = 1994, PUBLISHER = "AMS", SERIES = "Contemporary Mathematics", VOLUME = 180, PAGES = "119--124", NOTE = "Held at Penn State University, October 27-30, 1993." } @PHDTHESIS{Sarkis:1994:SPE, OLDTAG = "3sarkis", AUTHOR = "Marcus V. Sarkis", SCHOOL = "Courant Institute, New York University", TITLE = "{S}chwarz Preconditioners for Elliptic Problems with Discontinuous Coefficients Using Conforming and Non-Conforming Elements", INSTITUTION = "Courant Institute of Mathematical Sciences, Department of Mathematics", YEAR = 1994, MONTH = "September", NUMBER = 671 } @ARTICLE{Schatz:1974:OCR, OLDTAG = "schatz", AUTHOR = "Alfred H. Schatz", TITLE = "An Observation Concerning {R}itz-{G}alerkin Methods with Indefinite Bilinear Forms", JOURNAL = "Math. Comp.", YEAR = 1974, VOLUME = 28, NUMBER = 128, PAGES = "959--962" } @ARTICLE{Schultz:1971:LEB, OLDTAG = "schultz1", AUTHOR = "Martin H. Schultz", TITLE = "$L^{2}$ error bounds for the {R}ayleigh-{R}itz-{G}alerkin method", JOURNAL = "SIAM J. Numer. Anal.", YEAR = 1971, VOLUME = 8, PAGES = "737--748" } @INBOOK{Schwarz:1890:GMA, OLDTAG = "schw", AUTHOR = "H. A. Schwarz", TITLE = "Gesammelte {M}athematische {A}bhandlungen", PAGES = "133-143", PUBLISHER = "Springer", YEAR = 1890, VOLUME = 2, ADDRESS = "Berlin", NOTE = "First published in {V}ierteljahrsschrift der {N}aturforschenden {G}esellschaft in {Z}{\"u}rich, volume 15, 1870, pp. 272--286." } @PHDTHESIS{Skogen:1992:SMP, OLDTAG = "1skogen", AUTHOR = "Morten D. Skogen", TITLE = "{S}chwarz Methods and Parallelism", SCHOOL = "Department of Informatics, University of Bergen, Norway", YEAR = 1992, MONTH = "February" } @ARTICLE{Smith:1990:DAH, OLDTAG = "1smwi", AUTHOR = "Barry F. Smith and Olof B. Widlund", TITLE = "A Domain Decomposition Algorithm Using a Hierarchical Basis", JOURNAL = "SIAM J. Sci. Stat. Comput.", VOLUME = 11, NUMBER = 6, YEAR = 1990, PAGES = "1212--1220" } @PHDTHESIS{Smith:1990:DAP, OLDTAG = "2smith", AUTHOR = "Barry F. Smith", TITLE = "Domain Decomposition Algorithms for the Partial Differential Equations of Linear Elasticity", SCHOOL = "Courant Institute of Mathematical Sciences", YEAR = 1990, MONTH = "September", NOTE = "Tech. Rep. 517, Department of Computer Science, Courant Institute" } @ARTICLE{Smith:1991:DAE, OLDTAG = "3smith", AUTHOR = "Barry F. Smith", TITLE = "A Domain Decomposition Algorithm for Elliptic Problems in Three Dimensions", JOURNAL = "Numer. Math.", VOLUME = 60, YEAR = 1991, PAGES = "219--234", NUMBER = 2 } @INPROCEEDINGS{Smith:1992:ISA, OLDTAG = "5smith", AUTHOR = "Barry F. Smith", TITLE = "An Iterative Substructuring Algorithm for Problems in Three Dimensions", BOOKTITLE = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations", YEAR = 1992, EDITOR = "David E. Keyes and Tony F. Chan and G{\'e}rard A. Meurant and Jeffrey S. Scroggs and Robert G. Voigt", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", PAGES = "91--98" } @ARTICLE{Smith:1992:ODP, OLDTAG = "1smith", AUTHOR = "Barry F. Smith", TITLE = "An Optimal Domain Decomposition Preconditioner for the Finite Element Solution of Linear Elasticity Problems", JOURNAL = "SIAM J. Sci. Stat. Comput.", YEAR = 1992, MONTH = "January", VOLUME = 13, NUMBER = 1, PAGES = "364--378" } @ARTICLE{Smith:1993:PII, OLDTAG = "4smith", AUTHOR = "Barry F. Smith", TITLE = "A Parallel Implementation of an Iterative Substructuring Algorithm for Problems in Three Dimensions", JOURNAL = "SIAM J. Sci. Comput.", VOLUME = 14, NUMBER = 2, MONTH = "March", YEAR = 1993, PAGES = "406--423" } @TECHREPORT{Smith:1994:EPS, OLDTAG = "smi3", AUTHOR = "Barry F. Smith", TITLE = "Extensible {PDE} Solvers Package Users Manual", YEAR = 1994, INSTITUTION = "Argonne National Laboratory", MONTH = "September", NUMBER = "ANL-94/40" } @BOOK{Smith:1996:DPM, OLDTAG = "1sbg", AUTHOR = "Barry F. Smith and Petter E. Bj{\o}rstad and William Gropp", TITLE = "Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations", YEAR = 1996, PUBLISHER = "Cambridge University Press" } @ARTICLE{Sobolev:1936:AST, OLDTAG = "sobo", AUTHOR = "S. L. Sobolev", TITLE = "L'{A}lgorithme de {S}chwarz dans la {T}h\'{e}orie de l'{E}lasticit\'{e}", JOURNAL = "Comptes {R}endus ({D}oklady) de l'{A}cad\'{e}mie des {S}ciences de l'{URSS}", YEAR = 1936, VOLUME = "IV", NUMBER = "(XIII) 6", PAGES = "243--246" } @ARTICLE{Southwell:1935:SCFa, OLDTAG = "1south", AUTHOR = "R. V. Southwell", TITLE = "Stress-Calculation in Frameworks by the Method of ``Systematic Relaxation of Constraints''", JOURNAL = "Proc. Roy. Soc. Edinburgh Sect. A", VOLUME = 151, YEAR = 1935, PAGES = "57-91", NOTE = "parts I and II" } @ARTICLE{Southwell:1935:SCFb, OLDTAG = "2south", AUTHOR = "R. V. Southwell", TITLE = "Stress-Calculation in Frameworks by the Method of ``Systematic Relaxation of Constraints''", JOURNAL = "Proc. Roy. Soc. Edinburgh Sect. A", VOLUME = 153, YEAR = 1935, PAGES = "41-76", NOTE = "part III" } @ARTICLE{Starius:1977:CMD, OLDTAG = "1starus", AUTHOR = "G. Starius", TITLE = "Composite Mesh Difference Methods for Elliptic Boundary Value Problems", JOURNAL = "Numer. Math.", VOLUME = 28, PAGES = "243--258", YEAR = 1977 } @BOOK{Steklov:1901:GMS, OLDTAG = "stek", AUTHOR = "V.A. Steklov", TITLE = "General Methods for Solving Basic Problems of Mathematical Physics", PUBLISHER = "Mathematical Society of Charkov", ADDRESS = "Charkov", YEAR = 1901 } @ARTICLE{Strang:1972:AFE, OLDTAG = "strang", AUTHOR = "Gilbert Strang", TITLE = "Approximation in the finite element method", JOURNAL = "Numer. Math.", YEAR = 1972, VOLUME = 19, PAGES = "81--98" } @BOOK{Strang:1973:AFE, OLDTAG = "strfix", AUTHOR = "Gilbert Strang and George J. Fix", TITLE = "An Analysis of the Finite Element Method", PUBLISHER = "Prentice-{H}all", ADDRESS = "Englewood Cliffs, N.J.", YEAR = 1973 } @ARTICLE{Sun:1996:OSA, AUTHOR = "H. Sun and W.-P. Tang", TITLE = "An overdetermined {S}chwarz alternating method", YEAR = 1996, JOURNAL = "SIAM Journal on Scientific Computing", VOLUME = 17, NUMBER = 4, PAGES = "884-905", MONTH = "Jul." } @BOOK{Szabo:1991:FEA, OLDTAG = "babsza", AUTHOR = "Barna Szab\'{o} and Ivo Babu\v{s}ka", TITLE = "Finite Element Analysis", YEAR = 1991, PUBLISHER = "John Wiley \& Sons", ADDRESS = "New York" } @ARTICLE{Szyld:1993:VAC, OLDTAG = "szwid", AUTHOR = "Daniel B. Szyld and Olof B. Widlund", TITLE = "Variational Analysis of Some Conjugate Gradient Methods.", JOURNAL = "East-West J. Numer. Math.", YEAR = 1993, PAGES = "51--74", VOLUME = 1, NUMBER = 1 } @ARTICLE{Tallec:1991:DML, OLDTAG = "3deroeck", AUTHOR = "Le {T}allec, Patrick and De {R}oeck, Yann-Herv{\'e} and Vidrascu, Marina", TITLE = "Domain-decomposition methods for large linearly elliptic three dimensional problems", YEAR = 1991, JOURNAL = "J. of Computational and Applied Mathematics", VOLUME = 34 } @INPROCEEDINGS{Tallec:1997:GNN, AUTHOR = "Patrick Le Tallec and Marina Vidrascu", TITLE = "Generalized {N}eumann-{N}eumann preconditioners for Iterative Substructuring", BOOKTITLE = "Domain Decomposition Methods in Sciences and Engineering", YEAR = 1997, EDITOR = "Petter E. Bj{\o}rstad and Magne Espedal and David Keyes", PUBLISHER = "John Wiley \& Sons", NOTE = "Proceedings from the Ninth International Conference, June 1996, Bergen, Norway" } @ARTICLE{Tang:1992:GSS, OLDTAG = "tang", AUTHOR = "Wei Pai Tang", TITLE = "Generalized {S}chwarz Splittings", JOURNAL = "SIAM J. Sci. Stat. Comp.", VOLUME = 13, NUMBER = 2, YEAR = 1992, PAGES = "573--595" } @INPROCEEDINGS{Tezduyar:1988:EEI, OLDTAG = "teli", AUTHOR = "T. E. Tezduyar and J. Liou", TITLE = "Element-by-element and implicit-explicit finite element formulations for computational fluid dynamics", BOOKTITLE = "First International Symposium on Domain Decomposition Methods for Partial Differential Equations", YEAR = 1988, EDITOR = "Roland Glowinski and Gene H. Golub and G{\'e}rard A. Meurant and Jacques P{\'e}riaux", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @ARTICLE{Tong:1991:DPB, OLDTAG = "tochku", AUTHOR = "Charles H. Tong and Tony F. Chan and C. C. Jay Kuo", TITLE = "A Domain Decomposition Preconditioner Based on a Change to a Multilevel Nodal Basis", YEAR = 1991, JOURNAL = "SIAM J. Sci. Stat. Comput.", VOLUME = 12, NUMBER = 6, PAGES = "1486--1495" } @BOOK{Varga:1962:MIA, OLDTAG = "varga", AUTHOR = "Richard S. Varga", TITLE = "Matrix Iterative Analysis", PUBLISHER = "Prentice-Hall", ADDRESS = "Englewood Cliffs, New Jersey", YEAR = 1962 } @TECHREPORT{Venkatakrishnan:1991:MIP, AUTHOR = "V. Venkatakrishnan and H. D. Simon and Timothy J. Barth", TITLE = "A MIMD Implementation of a Parallel Euler Solver for Unstructured Grids", INSTITUTION = "NASA Ames", YEAR = 1991, ADDRESS = "Mail stop 202A NASA Ames Research Center, Moffett Field, CA 94305", MONTH = "September", NOTE = "RNR Technical Report RNR-91-024", URL = "http://www.nas.nasa.gov/NAS/TechReports/RNRreports/hsimon/RNR-91-024/RNR-91-024.ps" } @INBOOK{Wendland:1988:FEB, OLDTAG = "1wend", AUTHOR = "W. L. Wendland", TITLE = "Finite Element and Boundary Element Techniques from an Engineering and Mathematical Point of View", BOOKEDITOR = "E. Stein and W. Wendland", YEAR = 1988, PUBLISHER = "Springer-Verlag", PAGES = "273--333" } @BOOK{Wesseling:1992:IMM, OLDTAG = "wess", AUTHOR = "Peter Wesseling", TITLE = "An Introduction To Multigrid Methods", PUBLISHER = "Wiley", ADDRESS = "New York", YEAR = 1992 } @INPROCEEDINGS{Widlund:1984:IME, OLDTAG = "1wid", AUTHOR = "Olof B. Widlund", TITLE = "Iterative Methods for Elliptic Problems on Regions Partitioned into Substructures and the Biharmonic {D}irichlet Problem", BOOKTITLE = "Computing Methods in Applied Sciences and Engineering, VI", YEAR = 1984, EDITOR = "R. Glowinski and J. L. Lions", PAGES = "33--45", PUBLISHER = "North-Holland", ADDRESS = "Amsterdam, New York, Oxford" } @INPROCEEDINGS{Widlund:1987:ETF, OLDTAG = "2wid", AUTHOR = "Olof B. Widlund", TITLE = "An Extension Theorem for Finite Element Spaces with Three Applications", BOOKTITLE = "Numerical Techniques in Continuum Mechanics", YEAR = 1987, EDITOR = "Wolfgang Hackbusch and Kristian Witsch", PAGES = "110--122", PUBLISHER = "Notes on Numerical Fluid Mechanics, v. 16, Friedr. Vieweg und Sohn", ADDRESS = "Braunschweig/Wiesbaden", NOTE = "Proceedings of the Second {GAMM}-{S}eminar, {K}iel, {J}anuary, 1986" } @TECHREPORT{Widlund:1988:CDI, OLDTAG = "5wid", AUTHOR = "Olof B. Widlund", TITLE = "A Comparison of Some Domain Decomposition and Iterative Refinement Algorithms for Elliptic Finite Element Problems", INSTITUTION = "IBM Bergen Scientific Centre", YEAR = 1988, NUMBER = "BSC 88/15", ADDRESS = "Thorm{\o}hlensgaten 55, N-5006 Bergen, Norway" } @INPROCEEDINGS{Widlund:1988:ISMa, OLDTAG = "3wid", AUTHOR = "Olof B. Widlund", TITLE = "Iterative Substructuring Methods: {T}he General Elliptic Case", BOOKTITLE = "Computational Processes and Systems, 6", YEAR = 1988, PUBLISHER = "Nauka", ADDRESS = "Moscow", NOTE = "Proceedings of Modern Problems in Numerical Analysis, a conference held in Moscow, USSR, September 1986. In Russian, also available from the author, in English." } @INPROCEEDINGS{Widlund:1988:ISMb, OLDTAG = "4wid", AUTHOR = "Olof B. Widlund", TITLE = "Iterative Substructuring Methods: {A}lgorithms and Theory for Elliptic Problems in the Plane", BOOKTITLE = "First International Symposium on Domain Decomposition Methods for Partial Differential Equations", YEAR = 1988, EDITOR = "Roland Glowinski and Gene H. Golub and G{\'e}rard A. Meurant and Jacques P{\'e}riaux", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @ARTICLE{Widlund:1989:DIR, OLDTAG = "8wid", AUTHOR = "Olof B. Widlund", TITLE = "Some Domain Decomposition and Iterative Refinement Algorithms for Elliptic Finite Element Problems", JOURNAL = "Journal of Computational Mathematics", YEAR = 1989, VOLUME = 7, NUMBER = 2, PAGES = "200--208", NOTE = "Proceedings of the China - U. S. Seminar on Boundary Integral Equations and Boundary Element Methods in Physics and Engineering, held at the Xi'an Jiaotong University, Xi'an, The People's Republic of China, December 27, 1987 - January 1, 1988." } @INPROCEEDINGS{Widlund:1989:ISE, OLDTAG = "9awid", AUTHOR = "Olof B. Widlund", TITLE = "Iterative Solution of Elliptic Finite Element Problems on Locally Refined Meshes", BOOKTITLE = "Finite Element Analysis in Fluids", PUBLISHER = "University of Alabama in Huntsville Press", ADDRESS = "Huntsville, Alabama", EDITOR = "T. J. Chung and G. R. Karr", PAGES = "462--467", YEAR = 1989, NOTE = "Proceeding of the 7th International Conference on Finite Element Methods in Flow Problems held in {H}untsville, {A}labama, April 3 -- 7, 1989." } @INPROCEEDINGS{Widlund:1989:OIR, OLDTAG = "7wid", AUTHOR = "Olof B. Widlund", TITLE = "Optimal Iterative Refinement Methods", BOOKTITLE = "Domain Decomposition Methods", YEAR = 1989, EDITOR = "Tony Chan and Roland Glowinski and Jacques P{\'e}riaux and Olof Widlund", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA" } @TECHREPORT{Widlund:1989:RCC, OLDTAG = "9wid", AUTHOR = "Olof B. Widlund", TITLE = "On the Rate of Convergence of the Classical {S}chwarz Alternating Method in the Case of more than Two Subregions", INSTITUTION = "Department of Computer Science, Courant Institute", YEAR = 1989, NOTE = "A revised version in preparation" } @INPROCEEDINGS{Widlund:1992:SMS, OLDTAG = "15wid", AUTHOR = "Olof B. Widlund", TITLE = "Some {S}chwarz Methods for Symmetric and Nonsymmetric Elliptic Problems", BOOKTITLE = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations", EDITOR = "David E. Keyes and Tony F. Chan and G{\'e}rard A. Meurant and Jeffrey S. Scroggs and Robert G. Voigt", YEAR = 1992, PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", PAGES = "19--36" } @INPROCEEDINGS{Widlund:1994:ECS, OLDTAG = "18wid", AUTHOR = "Olof B. Widlund", TITLE = "Exotic Coarse Spaces for {S}chwarz Methods for Lower Order and Spectral Finite Elements", BOOKTITLE = "Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing", EDITOR = "David E. Keyes and Jinchao Xu", YEAR = 1994, SERIES = "Contemporary Mathematics", VOLUME = 180, PAGES = "131--136", PUBLISHER = "AMS", NOTE = "Held at Penn State University, October 27-30, 1993." } @INPROCEEDINGS{Widlund:1996:DMS, OLDTAG = "19wid", AUTHOR = "Olof B. Widlund", TITLE = "Domain Decomposition Methods for Spectral and Mortar Finite Element Approximations of Elliptic Problems", YEAR = 1996, SERIES = "ZAMM", PUBLISHER = "Akademie Verlag, Berlin", NOTE = "Proceedings of ICIAM 95" } @INPROCEEDINGS{Widlund:1996:PSM, OLDTAG = "20wid", AUTHOR = "Olof B. Widlund", TITLE = "Preconditioners for Spectral and Mortar Finite Element Methods", BOOKTITLE = "Eighth International Conference of Domain Decomposition Methods", EDITOR = "Roland Glowinski and Jacques P{\'e}riaux and Zhong-Ci Shi and Olof B. 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Voigt", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, PA", YEAR = 1992, PAGES = "119--126" } @ARTICLE{Zhang:1992:MSM, OLDTAG = "1zha", AUTHOR = "Xuejun Zhang", TITLE = "Multilevel {S}chwarz Methods", JOURNAL = "Numer. Math.", YEAR = 1992, VOLUME = 63, NUMBER = 4, PAGES = "521--539" } @ARTICLE{Zhang:1994:MSM, OLDTAG = "4zha", AUTHOR = "Xuejun Zhang", TITLE = "Multilevel {S}chwarz Methods for the Biharmonic {D}irichlet Problem", JOURNAL = "SIAM J. Sci. Comput.", YEAR = 1994, VOLUME = 15, NUMBER = 3, PAGES = "621--644" } @ARTICLE{Zhang:1996:TSM, OLDTAG = "5zha", AUTHOR = "Xuejun Zhang", TITLE = "Two-level {S}chwarz methods for the biharmonic problem discretized by ${C}^1$ elements", YEAR = 1996, VOLUME = 33, NUMBER = 2, JOURNAL = "SIAM J. Numer. 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E. Bj{\o}rstad and M. Espedal and D. Keyes", PAGES = "434--440", PUBLISHER = "ddm.org" } @INPROCEEDINGS{Ghanemi:1997:DDh, AUTHOR = "S. Ghanemi", TITLE = "A domain decomposition method for {H}elmholtz scattering problems", BOOKTITLE = "Ninth International Conference on Domain Decomposition Methods", YEAR = 1997, EDITOR = "P. E. Bj{\o}rstad and M. Espedal and D. Keyes", PAGES = "105--112", PUBLISHER = "ddm.org" } @INPROCEEDINGS{Feng:1997:NDE, AUTHOR = "X. Feng", TITLE = "A non-overlapping domain decomposition method for solving elliptic problems by finite element methods", BOOKTITLE = "Ninth International Conference on Domain Decomposition Methods", YEAR = 1997, EDITOR = "P. E. Bj{\o}rstad and M. Espedal and D. Keyes", PAGES = "222--229", PUBLISHER = "ddm.org" } @ARTICLE{Douglas:1999:NCG, AUTHOR = "J. {Douglas, Jr.} and J. E. Santos and D. Sheen and X. Ye", TITLE = "Nonconforming {G}alerkin methods based on quadrilateral elements for second order elliptic problems", JOURNAL = "Mathematical Modelling and Numerical Analysis, M$^2$AN", YEAR = 1999, VOLUME = 33, PAGES = "747--770" } @UNPUBLISHED{Douglas:1997:NCM, AUTHOR = "J. {Douglas, Jr.} and J. E. Santos and D. Sheen", TITLE = "A nonconforming mixed finite element method for {M}axwell's equations", NOTE = "to appear in Math. Models Meth. Appl. Sci.", YEAR = 1997, URL = "http://www.math.snu.ac.kr/~sheen" } @UNPUBLISHED{Ha:1999:NCM, AUTHOR = "T. Ha and O. Kwon and D. Sheen", TITLE = "Seidel-type nonconforming domain decomposition methods for {M}axwell's equations", NOTE = "to appear", YEAR = 1999, URL = "http://www.math.snu.ac.kr/~sheen" } @UNPUBLISHED{Kwon:1999:SDD, AUTHOR = "O. Kwon and D. Sheen", TITLE = "Seidel-type nonoverlapping domain decomposition iterative methods", NOTE = "to appear", YEAR = 1999, URL = "http://www.math.snu.ac.kr/~sheen" } @UNPUBLISHED{Kwon:1999:SNC, AUTHOR = "O. Kwon", TITLE = "Spectral radius of red-black {G}auss-{S}eidel nonconforming domain decomposition methods for second order elliptic problems", NOTE = "to appear", YEAR = 1999 } @ARTICLE{Benamou:1997:DDH, AUTHOR = "J. D. Benamou and B. Despr\'{e}s", TITLE = "A domain decomposition method for the {H}elmholtz equation and related optimal control", JOURNAL = "J. Comp. Phys.", YEAR = 1997, VOLUME = 136, PAGES = "68--82" } @ARTICLE{Collino:1997:NIM, AUTHOR = "P. Collino and G. Delbue and P. Joly and A. Piacentini", TITLE = "A new interface condition in the non-overlapping domain decomposition for the {M}axwell equations {H}elmholtz equation and related optimal control", JOURNAL = "Comput. Methods Appl. Mech. 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