% % Last updated February 19, 1996 % % % NOTICE: This is the old list of BiBTeX references, please use the new one % at http://www.ddm.org/bibtex/ddm.bib if possible. % @ARTICLE{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" } @ARTICLE{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{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" } @TECHREPORT{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." } @INPROCEEDINGS{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{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{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{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{axel, AUTHOR="Owe Axelsson", TITLE="Iterative Solution Methods", YEAR="1994", PUBLISHER="Cambridge University Press", ADDRESS="New York" } @ARTICLE{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{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{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{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{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 " } @BOOK{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{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" } @BOOK{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" } @ARTICLE{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{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"} @ARTICLE{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" } @TECHREPORT{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{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{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" } @TECHREPORT{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{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{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" } @ARTICLE{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{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{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." } @TECHREPORT{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" } @INCOLLECTION{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." } @ARTICLE{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{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{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" } @INPROCEEDINGS{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{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 Olof Widlund", PUBLISHER="AMS", ADDRESS="Providence, RI" } @BOOK{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" } @PHDTHESIS{bjthesis, AUTHOR=" Petter E. Bj{\o}rstad", SCHOOL="Stanford University, Stanford, CA", TITLE=" Numerical solution of the biharmonic equation", YEAR="1980" } @INPROCEEDINGS{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" } @INPROCEEDINGS{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" } @ARTICLE{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{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{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{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{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{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{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", ADDRESS="", NOTE="To appear." } @ARTICLE{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" } @ARTICLE{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" } @ARTICLE{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" } @TECHREPORT{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{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" } @ARTICLE{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" } @TECHREPORT{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{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{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{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 " } @ARTICLE{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{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 " } @ARTICLE{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" } @ARTICLE{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{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{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{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." } @BOOK{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", } @INPROCEEDINGS{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{2brandt, AUTHOR="A. Brandt", TITLE="Multi-level Adaptive Solutions to Boundary Value Problems", JOURNAL="Numer. Math. ", YEAR=" 1977 ", VOLUME= "31", PAGES="333-390" } @BOOK{briggs, AUTHOR="William Briggs", TITLE="A Multigrid Tutorial", YEAR="1987", PUBLISHER="SIAM", ADDRESS="Philadelphia" } @INPROCEEDINGS{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 " } @ARTICLE{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{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 " } @PHDTHESIS{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{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{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" } @ARTICLE{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{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{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" } @INPROCEEDINGS{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{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{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", VOUME="1", NUMER="5", PAGES="477--504", YEAR="1994" } @ARTICLE{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" } @TECHREPORT{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)" } @INPROCEEDINGS{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 Navier-Stokes Equations, Notes in Numerical Fluid Mechanics", PUBLISHER="Vieweg Verlag, Braunschweig", YEAR="1994", NOTE="To appear." } @ARTICLE{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" } @INPROCEEDINGS{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", ADDRESS="", NOTE="To appear." } % This one seemed to be missing from data-base @ARTICLE{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" } @ARTICLE{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" } @ARTICLE{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{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" } @INPROCEEDINGS{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{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." } @TECHREPORT{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." } @PHDTHESIS{4casa, AUTHOR="Mario A. Casarin", TITLE="Schwarz 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" } @ARTICLE{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" } @ARTICLE{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{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{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} " } @TECHREPORT{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} " } @INPROCEEDINGS{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{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" } @INPROCEEDINGS{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" } @ARTICLE{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" } @INPROCEEDINGS{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{2chma, 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" } @INCOLLECTION{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{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 Olof Widlund", PUBLISHER="AMS", ADDRESS="Providence, RI" } @ARTICLE{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{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{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" } @ARTICLE{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{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{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{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" } @ARTICLE{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" } @PHDTHESIS{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{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{ciar, AUTHOR=" Philippe G. Ciarlet", TITLE=" The Finite Element Method for Elliptic Problems ", PUBLISHER=" North-Holland", YEAR=" 1978", ADDRESS="Amsterdam" } @INPROCEEDINGS{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, AUTHOR="R. W. Cottle", TITLE="Manifestations of the {S}chur Complement", JOURNAL="Lin. Alg. and Its Applic.", VOLUME="8", YEAR="1974", PAGES="189--211" } @TECHREPORT{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{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" } @INPROCEEDINGS{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{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" } @ARTICLE{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{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" } @PHDTHESIS{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" } @TECHREPORT{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{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" } @ARTICLE{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" } @ARTICLE{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{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{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" } @PROCEEDINGS{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" } @PROCEEDINGS{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" } @PROCEEDINGS{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" } @PROCEEDINGS{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" } @INPROCEEDINGS{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 " } @INPROCEEDINGS{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{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" } @ARTICLE{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{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{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{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" } @INPROCEEDINGS{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." } @INPROCEEDINGS{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" } @INPROCEEDINGS{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" } @ARTICLE{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" } @ARTICLE{1dsw, AUTHOR="Maksymilian Dryja and Barry F. Smith and Olof B. Widlund", TITLE="Schwarz 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{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{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{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" } @INPROCEEDINGS{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" } @TECHREPORT{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" } @ARTICLE{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{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{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, 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{1fischronq, AUTHOR="Paul F. Fischer and Einar R{\o}nquist", NOTE="Proceedings of ICOSAHOM 92, a conference held in Montpellier, France, June 22-26, 1992.", 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" } @INBOOK{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{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{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{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, AUTHOR="R. Glowinski and O. Pironneau", TITLE="Numerical Methods For The First Biharmonic Equation And For the Two-Dimensional Stokes Problem" , JOURNAL=" SIAM Review ", YEAR="1979 ", VOLUME="21", NUMBER="2 ", PAGES="167-- 212" } @INPROCEEDINGS{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" } @INPROCEEDINGS{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" } @INPROCEEDINGS{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{govl, AUTHOR="Gene H. Golub and Charles F. Van Loan ", TITLE=" Matrix Computations ", PUBLISHER=" Johns Hopkins Univ. Press ", YEAR=" 1989 ", NOTE=" Second Edition." } @TECHREPORT{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" } @PROCEEDINGS{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." } @ARTICLE{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" } @INPROCEEDINGS{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" } @TECHREPORT{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{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{gris, AUTHOR="P. Grisvard", TITLE="Elliptic problems in nonsmooth domains", PUBLISHER="Pitman Publishing", ADDRESS="Boston", YEAR="1985" } @inproceedings{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", } @TECHREPORT{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{2hack, AUTHOR="Wolfgang Hackbusch", TITLE="Multigrid Methods and Applications", YEAR="1985", PUBLISHER="Springer", ADDRESS="Berlin" } @BOOK{3hack, AUTHOR="Wolfgang Hackbusch", TITLE="Iterative Solution of Large Sparse Linear Systems of Equations", YEAR="1994", PUBLISHER="Springer-Verlag", ADDRESS="Berlin" } @BOOK{hardy, AUTHOR="G. H. Hardy and J. E. Littlewood and G. P\'{o}lya", TITLE="Inequalities", YEAR="1934", PUBLISHER="Cambridge University Press", ADDRESS="Cambridge" } @INPROCEEDINGS{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{hvid, AUTHOR="Anders Hvidsten", TITLE="On the Parallelization of a Finite Element Structural Analysis Program ", YEAR="1990", INSTITUTION="University of Bergen, Norway", NOTE="Ph.D. Thesis. Computer Science Department" } @INPROCEEDINGS{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 " } @INBOOK{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, AUTHOR="Claes Johnson", TITLE="Numerical Solutions of Partial Differential Equations by the Finite Element Method", PUBLISHER="Cambridge University Press", ADDRESS="Cambridge", YEAR="1987" } @TECHREPORT{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 = "", 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}" } @PROCEEDINGS{dom7, TITLE="Domain Decomposition Methods in Science and Engineering" , NOTE="Proceedings of the Seventh International Conference on Domain Decomposition, October 27-30, 1993, The Pennsylvania State University", EDITOR="David E. Keyes and Jinchao Xu", YEAR="1994", SERIES="Contemporary Mathematics", PUBLISHER="AMS", VOLUME="180", ADDRESS="Providence, R.I." } @ARTICLE{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{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{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." } @INPROCEEDINGS{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" } @ARTICLE{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{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{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" } @TECHREPORT{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{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{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{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{2kolyer, AUTHOR = "L. Yu. Kolotilina and A. Yu. Yermin", TITLE = "Factorized sparse approximate inverse preconditioners", YEAR = "", 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{1kuzn, AUTHOR="Yuri A. Kuznetsov", TITLE="Multilevel Domain Decomposition Methods", JOURNAL="Appl. Numer. Math.", YEAR="1989", VOLUME="5" } @INPROCEEDINGS{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{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{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{2lanczos, AUTHOR="Cornelius Lanczos", TITLE="Trigonometric Interpolation of Empirical and Analytical Functions", JOURNAL="J. Math. Phys.", YEAR="1938", PAGES="123--199", VOLUME="17" } @BOOK{lebe, AUTHOR="V. I. Lebedev", TITLE="Composition methods " , PUBLISHER="USSR {A}cademy of {S}ciences", YEAR=1986, ADDRESS="Moscow", NOTE="In {R}ussian" } @INCOLLECTION{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" } @ARTICLE{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" } @ARTICLE{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", PAGES="", VOLUME="", NUMBER="", NOTE="To appear." } @INPROCEEDINGS{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{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" } @ARTICLE{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{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" } @BOOK{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{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" } @TECHREPORT{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{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" } @INPROCEEDINGS{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{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{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" } @INPROCEEDINGS{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{4jama, AUTHOR="Jan Mandel", TITLE="On Block Diagonal and {S}chur Complement Preconditioning", journal = "Numer. Math.", volume = "58", year = "1990", pages = "79--93" } @TECHREPORT{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"} @INCOLLECTION{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" } @ARTICLE{7jama, AUTHOR="Jan Mandel", TITLE="Balancing Domain Decomposition", journal = "Comm. Numer. Meth. Engrg.", volume = "9", year = "1993", pages = "233--241" } @ARTICLE{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 " } @TECHREPORT{MandelB-bal92, AUTHOR="Jan Mandel and Marian Brezina", INSTITUTION="Center for Computational Mathematics, University of Colorado at Denver", YEAR="1993", TITLE="Balancing Domain Decomposition: Theory and Computations in Two and Three Dimensions", NUMBER="UCD/CCM 2" } @unpublished{MandelB-bal92-94, author="Jan Mandel and Marian Brezina", title="Balancing Domain Decomposition for Problems with Large Jumps in Coefficients", filename="balance-j.ps", note="Math. Comp., to appear" } @INPROCEEDINGS{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-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" } @INPROCEEDINGS{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" } @unpublished{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" } @INPROCEEDINGS{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{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 " } @PHDTHESIS{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{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{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" } @INPROCEEDINGS{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{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{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" } @ARTICLE{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{kuznet_wheeler, AUTHOR="Yuri A.\ Kuznetsov and Mary F.\ Wheeler", TITLE="Optimal Order Suubstructuring Preconditioners for Mixed Finite Element Methods on Nonmatching Grids", JOURNAL="East-West J. Numer. Math.", YEAR="1995", VOLUME="3", NUMBER="2", PAGES="127--143" } @BOOK{4mcc, AUTHOR="Stephen F. McCormick", TITLE="Multilevel Adaptive Methods for Partial Differential Equations", PUBLISHER="SIAM", ADDRESS="Philadelphia, PA", YEAR="1989" } @BOOK{5mcc, EDITOR="Stephen F. McCormick", TITLE="Multigrid Methods", PUBLISHER="SIAM", ADDRESS="Philadelphia, PA", NOTE="Frontiers in Appl. Math. Vol. 6", YEAR="1987" } @ARTICLE{mcru, AUTHOR="S. McCormick and J. Ruge", TITLE="Unigrid for multigrid simulation", JOURNAL="Math. Comp.", YEAR="1986", VOLUME= "41", PAGES="43-62" } @ARTICLE{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" } @ARTICLE{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" } @INPROCEEDINGS{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{1miller, AUTHOR="Keith Miller", TITLE="Numerical Analogs to the {S}chwarz Alternating Procedure", JOURNAL="Numer. Math.", VOLUME="7", YEAR="1965", PAGES="91--103" } @ARTICLE{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{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{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" } @ARTICLE{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" } @PHDTHESIS{nepo2, AUTHOR="Sergey V. Nepomnyaschikh", TITLE="Domain Decomposition and Schwarz 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" } @INPROCEEDINGS{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{nepo4, AUTHOR="Sergey V. Nepomnyaschikh and Olof B. Widlund", TITLE="Extension Theorems for the Case of Locally Refined Meshes", YEAR="1991", NUMBER="", INSTITUTION="Dept. of Computer Science, Courant Institute of Mathematical Sciences", NOTE="To appear" } @INPROCEEDINGS{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" } @ARTICLE{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{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" } @ARTICLE{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" } @BOOK{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, 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" } @INPROCEEDINGS{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" } @TECHREPORT{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" } @ARTICLE{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{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{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{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" } @TECHREPORT{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{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" } @ARTICLE{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" } @TECHREPORT{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{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" } @BOOK{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{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{1pahl, AUTHOR="Shannon S. Pahl", SCHOOL="Department of Computational and Applied Mathematics, University of the Witwatersrand", ADDRESS="Johannesburg, South Africa", TITLE="Schwarz Type Domain Decomposition Methods for Spectral Element Discretizations", YEAR="1993", MONTH="December" } @ARTICLE{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" } @ARTICLE{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{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." } @PHDTHESIS{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{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{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{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" } @ARTICLE{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" } @TECHREPORT{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{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{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{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_thesis, AUTHOR="Pourquier, Olivier", 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{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{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{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{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{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{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, AUTHOR="Theodore J. Rivlin ", TITLE="The Chebyshev Polynomials", PUBLISHER="Wiley Interscience", YEAR="1990 " } @INPROCEEDINGS{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{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{1rude, AUTHOR="Ulrich R{\"{u}}de", TITLE="Mathematical and Computational Techniques for Multilevel Adaptive Methods", YEAR="1993", ADDRESS="Philadelphia, PA", PUBLISHER="SIAM" } @ARTICLE{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{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{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{3sarkis, AUTHOR="Marcus V. Sarkis ", SCHOOL="Courant Institute, New York University", TITLE="Schwarz 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{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{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." } @ARTICLE{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" } @PHDTHESIS{1skogen, AUTHOR="Morten D. Skogen", TITLE=" Schwarz Methods and Parallelism", SCHOOL=" Department of Informatics, University of Bergen, Norway", YEAR="1992", MONTH="February" } @ARTICLE{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" } @ARTICLE{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" } @PHDTHESIS{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{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" } @ARTICLE{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" } @INPROCEEDINGS{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" } @TECHREPORT{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{1sbg, AUTHOR="Barry F. Smith and Petter Bj{\o}rstad and William Gropp", TITLE="Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations", YEAR="1996", PUBLISHER="Cambridge University Press" } @ARTICLE{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{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{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{1starus, AUTHOR="G. Starius", TITLE="Composite Mesh Difference Methods for Elliptic Boundary Value Problems", JOURNAL="Numer. Math.", VOLUME="28", YEAR="1977", PAGES="243--258" } @BOOK{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, AUTHOR=" Gilbert Strang", TITLE=" Approximation in the finite element method", JOURNAL= " Numer. Math. ", YEAR=" 1972", VOLUME="19", PAGES="81--98" } @BOOK{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{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{tang, AUTHOR="Wei Pai Tang", TITLE="Generalized Schwarz Splittings", JOURNAL="SIAM J. Sci. Stat. Comput.", VOLUME="13", YEAR="1992", PAGES="573--595" } @INPROCEEDINGS{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" } @BOOK{varga, AUTHOR="Richard S. Varga", TITLE="Matrix Iterative Analysis", PUBLISHER="Prentice-Hall", ADDRESS="Englewood Cliffs, New Jersey", YEAR="1962" } @INBOOK{1wend, AUTHOR="W. L. Wendland", BOOKEDITOR="E. Stein and W. Wendland", TITLE="Finite Element and Boundary Element Techniques from an Engineering and Mathematical Point of View", YEAR="1988", PUBLISHER="Springer-Verlag", PAGES="273--333" } @ARTICLE{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{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" } @BOOK{wess, AUTHOR="Peter Wesseling", TITLE="An Introduction To Multigrid Methods", PUBLISHER="Wiley", ADDRESS="New York", YEAR="1992" } @INPROCEEDINGS{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{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" } @INPROCEEDINGS{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{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" } @TECHREPORT{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" } @TECHREPORT{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{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 " } @ARTICLE{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. " } @TECHREPORT{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{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{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{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{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{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" } @ARTICLE{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{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" } @ARTICLE{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{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{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{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{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. Widlund", YEAR="1996", PAGES=" ", PUBLISHER="John Wiley \& Sons, Ltd, Strasbourg, France", NOTE="Held in Beijing, PRC, May 15-19, 1995." } @PHDTHESIS{1xu, AUTHOR="Jinchao Xu", TITLE="Theory of Multilevel Methods", SCHOOL="Cornell University", YEAR="1989", MONTH="May" } @ARTICLE{2xu, AUTHOR="Jinchao Xu", TITLE="Iterative methods by space decomposition and subspace correction", JOURNAL="SIAM Review", YEAR="1992", MONTH="December", VOLUME="34", NUMBER="4", PAGES="581--613" } @ARTICLE{3xu, AUTHOR="Jinchao Xu", TITLE="A New Class of Iterative Methods for Nonselfadjoint or Indefinite Problems", JOURNAL="SIAM J. Numer. Anal.", VOLUME="29", NUMBER="2", YEAR="1992", PAGES="303--319" } @ARTICLE{4xu, AUTHOR="Jinchao Xu", TITLE="Counter Examples Concerning a Weighted ${L}^{2}$ Projection", YEAR="1991", PAGES="563--568", VOLUME="57", JOURNAL= "Math. Comp." } @ARTICLE{yser, AUTHOR="Harry Yserentant", TITLE="On the Multi-Level Splitting of Finite Element Spaces ", JOURNAL="Numer. Math. ", YEAR="1986", VOLUME="49", PAGES="379--412" } @ARTICLE{2yser, AUTHOR="Harry Yserentant", TITLE="Hierarchical Bases Give Conjugate Gradient Type Methods a Multigrid Speed of Convergence ", JOURNAL="Appl. Math. Comp.", YEAR="1986", VOLUME="19", PAGES="347--358 " } @ARTICLE{3yser, AUTHOR="Harry Yserentant", TITLE=" On the Multi-Level Splitting of Finite Element Spaces for Indefinite Elliptic Boundary Value Problems", JOURNAL=" SIAM J. Numer. Anal.", YEAR="1986", VOLUME="23", PAGES="581--595" } @ARTICLE{4yser, AUTHOR="Harry Yserentant", TITLE="Hierarchical Bases of Finite-Element Spaces in the Discretization of Nonsymmetric Elliptic Boundary Value Problems", JOURNAL="Computing ", YEAR="1985", VOLUME="35", PAGES="39--49" } @ARTICLE{5yser, AUTHOR="Harry Yserentant", TITLE="Two preconditioners based on the multi-level splitting of finite element spaces ", JOURNAL="Numer. Math.", VOLUME="58", NUMBER="2", PAGES=" 163--184", YEAR="1990" } @ARTICLE{1zha, AUTHOR="Xuejun Zhang", TITLE="Multilevel {S}chwarz Methods", JOURNAL="Numer. Math.", YEAR="1992", VOLUME="63", NUMBER="4", PAGES="521--539" } @PHDTHESIS{2zha, AUTHOR="Xuejun Zhang", SCHOOL="Courant Institute, New York University", TITLE="Studies in Domain Decomposition: Multilevel Methods and the Biharmonic {D}irichlet Problem", INSTITUTION="Courant Institute of Mathematical Sciences, Department of Mathematics", YEAR="1991", MONTH="September", NUMBER="584 " } @INPROCEEDINGS{3zha, AUTHOR="Xuejun Zhang", TITLE="Domain Decomposition Algorithms for the Biharmonic {D}irichlet Problem", 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 ", PUBLISHER="SIAM", ADDRESS="Philadelphia, PA", YEAR="1992", PAGES="119--126" } @ARTICLE{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{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. Anal", PAGES="555--570" }