Send mail to: mgnet@cs.yale.edu for the digests or bakeoff mgnet-requests@cs.yale.edu for comments or help Current editor: Craig Douglas douglas-craig@cs.yale.edu Anonymous ftp repository: casper.cs.yale.edu (128.36.12.1) ftp.cerfacs.fr (138.63.200.33) World Wide Web: http://na.cs.yale.edu/mgnet/www/mgnet.html or http://www.cerfacs.fr/~douglas/mgnet.html Today's editor: Craig Douglas (douglas-craig@cs.yale.edu) Volume 5, Number 6 (approximately June 30, 1995) Today's topics: Best V-cycle Algorithm for 2D Poisson Equation Multigrid tutorial, with applications to molecular dynamics MGLab on MGNet Overhaul of 1993 Copper Mountain electronic proceedings Some of the new entries in the bibliography ------------------------------------------------------- Date: Fri, 30 June 1995 17:00:01 -0400 From: douglas-craig@CS.YALE.EDU (Craig Douglas) Subject: Best V-cycle Algorithm for 2D Poisson Equation The message in the last issue from Jun Zhangin the last issue sparked several interesting responses (one of which is still open). Due to a couple of unexpected trips that I took this month, I have not yet had a chance to edit these and see if the last open question can be answered. Stay tuned until next month. Craig ------------------------------------------------------- Date: Wed, 14 Jun 95 15:05:34 +0300 From: MABRANDT@WEIZMANN.weizmann.ac.il Subject: Multigrid tutorial, with applications to molecular dynamics MULTIGRID TUTORIAL, WITH APPLICATIONS TO MOLECULAR DYNAMICS October 10-12 Weizmann Institute of Science Rehovot, Israel Current molecular mechanics algorithms severely restrict the modelling efforts to relatively small molecular systems and/or tiny evolution intervals, since their computing cost rises very steeply with problem size. Model studies have shown that this steep rise can be substantially reduced by combining several types of multiscale methods. These are multigrid-like methods, based on designing a hierarchy of molecular motions on increasingly larger scales, with several kinds of inter-scale interactions. For large molecular structures, such methods might yield the following benefits: (1) fast energy minimization; (2) fast solution of the implicit systems of equations needed to perform large time steps in dynamics simulations; (3) fast calculation and compact description of a multitude of normal modes; (4) elimination of the slowing down and fast convergence of statistics in equilibrium Monte-Carlo calculations; (5) efficient combination of small-scale statistics with large-scale dynamics; and (6) direct computation of bulk material properties. The course will teach the elements of the multigrid methods for PDEs; algebraic multigrid (AMG), especially for non-PDE problems; multi-scale Monte-Carlo techniques; fast multi-scale summation of long-range forces; and global optimization by multi-level annealing. First steps in introducing such methods to molecular systems will be reported. Also, poster sessions on molecular mechanics and dynamics will be given by some of the course participants, exposing the audience to a large number of other topics and ideas. The course will assume an audience with a good working knowledge of numerical methods and a strong interest in molecular mechanics and dynamics simulations. Registration fee is $50.00. The number of participants will be limited. Some background reading material will be suggested and/or sent upon request. People interested in participating should contact the course secretary: Ms. Carol Weintraub Dept. of Applied Math. & Computer Science The Weizmann Institute of Science Rehovot 76100, Israel email: carol@wisdom.weizmann.ac.il tel: 972-8-343545 Organizers: Achi Brandt ---------- email: mabrandt@weizmann.weizmann.ac.il Tamar Schlick email: schlick@nyu.edu ------------------------------------------------------- Date: Tue, 20 Jun 1995 15:31:06 -0500 (CDT) From: bordner@ta18.cs.uiuc.edu Subject: MGLab on MGNet Craig, I have uploaded the files MGLab1.0.tar and MGLab.README to casper.cs.yale.edu in /mgnet/incoming. Note that MGLab.README is identical to the file README in the tar file. There are no constraints for using MGLab, it is public domain software. James Editor's Note: in mgnet/Codes/mglab/MGLab1.0.tgz. ------------- Here is the MGLab.README file: What is MGLab? MGLab is a set of public domain Matlab functions that defines an interactive environment for experimenting with multigrid algorithms. The package solves two-dimensional elliptic partial differential equations using finite differences and includes several built-in problems (Poisson Helmholtz, discontinuous coefficient problems and non-self adjoint problems). A number of parameters controlling the V-cycle can be set using a point and click mechanism. The menu-based user interface also allows a choice of several Krylov subspace accelerators (PCG, GMRES(k), BiCG/STAB). The package exploits Matlabs visualization and sparse matrix features and has been structured to be extensible. MGLab Files The Graphical User Interface MGLab.m show_params.m set_defaults.m run.m multigrid_setup.m menu_header.m menu_item.m version_info.m Contents.m Global Variables include_globals.m extract_globals.m include_flags.m include_figs.m Linear Systems get_matrix.m sp_laplace.m sp_cutsq2d.m sp_convdiff.m get_rhs.m Solvers solve.m converged.m vmg.m fmg.m pcg.m pcgs.m pbicgstab.m pgmres.m sor.m get_SOR_omega.m Preconditioners precondition.m precond_mg.m Results update_results.m Multigrid Routines: High Level mg_cycle.m vmg_cycle.m fmg_cycle.m wmg_cycle.m halfvmg_cycle.m Multigrid Routines: Middle Level smooth.m residual.m restrict.m coarse_grid_solve.m interpolate.m sp_prolong.m Multigrid Routines: Low Level coarsest.m max_level.m Demos demo_globals.m demo1.m demo1_run.m demo2.m demo2_run.m demo2_Vcycle.m demo3.m demo3_run.m demo3_vmg.m sint.m sint2.m Documentation Thanks to Craig Douglas, a PostScript version of a short paper describing MGLab is available from mgnet. The paper can be retrieved by anonymous ftp to ftp.cerfacs.fr or casper.cs.yale.edu in the directory pub/mgnet/Conferences/CopperMtn95 The name of the file is bordner_saied.ps.gz To run MGLab, simply start up Matlab (Version 4.0 or later) and type `MGLab'. You may wish to include this directory in your Matlab path by typing `path (path,pwd)' while in your MGLab directory. Future Releases Comments about and suggestions for improvements of the code are welcome: we plan to have future versions of MGLab that incorporate enhancements and bug fixes. To be put on a mailing list to be informed of new versions, send email to James Bordner (bordner@cs.uiuc.edu). Revision History 10 June 1995 V1.00beta: Initial release 20 June 1995 V1.0: SOR solver added James Bordner (bordner@cs.uiuc.edu) Faisal Saied (saied@cs.uiuc.edu) University of Illinois at Urbana-Champaign Department of Computer Science 20 June 1995 ------------------------------------------------------- Date: Fri, 30 June 1995 16:47:18 -0400 From: douglas@mlat.watson.ibm.com (Craig Douglas) Subject: Overhaul of 1993 Copper Mountain electronic proceedings Those of you who access MGNet through the World Wide Web can now view the electronic version of the 1993 Copper Mountain proceedings in what I think is a much nicer manner. You can see the papers or abstracts conveniently (particularly if your web browser understands HTML 3.0 tags like ). You can point and click on just what you want. What was done here will also be done to the 1995 proceedings over the next month or so. Hence, any feedback would be appreciated. Thanks, Craig ------------------------------------------------------- Date: Wed, 31 May 1995 14:19:28 -0400 From: douglas-craig@CS.YALE.EDU (Craig Douglas) Subject: Some of the new entries in the bibliography This is a bit repetitious, but next month's entries will be from all over the place. Sorry about this... Craig \begin{thebibliography}{100} \bibitem{MIsraeli_LVozovoi_AAverbuch_1994a} {\sc M.~Israeli, L.~Vozovoi, and A.~Averbuch}, {\em Domain decomposition methods with local {F}ourer basis for parabolic problems}, in Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~223--230. \bibitem{PGJacobs_VAMousseau_PRMcHugh_DAKnoll_1994a} {\sc P.~G. Jacobs, V.~A. Mousseau, P.~R. McHugh, and D.~A. Knoll}, {\em Newton--{K}rylov--{S}chwarz techniques applied to the two--dimensional imcompressible {N}avier--{S}tokes and energy equations}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~503--507. \bibitem{EKatzer_1994a} {\sc E.~Katzer}, {\em A parallel subspace decomposition method for hyperbolic equations}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~239--244. \bibitem{DEKeyes_JXu_1994a} {\sc D.~E. Keyes and J.~Xu}, {\em Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition}, vol.~180 of Contemporary Mathematics, American Mathematical Society, Providence, Rhode Island, 1994. \bibitem{SKim_1994a} {\sc S.~Kim}, {\em Numerical treatments for the {H}elmholtz problem by domain decomposition techniques}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~245--250. \bibitem{RKornhuber_HYserentant_1994a} {\sc R.~Kornhuber and H.~Yserentant}, {\em Multilevel methods for elliptic problems on domains not resolved by the coarse grid}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~49--60. \bibitem{HCKu_HEGilreath_RRaul_JCSommerer_1994a} {\sc H.~C. Ku, H.~E. Gilreath, R.~Raul, and J.~C. Sommerer}, {\em Direct numerical simulation of jet flow via a multi--block technique}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~509--514. \bibitem{YAKuznetsov_1994a} {\sc Yu.~A. Kuznetsov}, {\em Overlapping domain decomposition methods for parabolic problems}, in Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~63--69. \bibitem{YAKuznetsov_PNeittaanmaki_PTarvainen_1994a} {\sc Yu.~A. Kuznetsov, P.~Neittaanm{\"a}ki, and P.~Tarvainen}, {\em Overlapping domain decomposition methods for the obstacle problem}, in Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~271--277. \bibitem{YAKuznetsov_PNeittaanmaki_PTarvainen_1994b} \leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em Schwarz methods for obstacle problems with convection-- diffusion operators}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~251--256. \bibitem{CHLai_1994a} {\sc C.~H. Lai}, {\em An iterative scheme for non--symmetric interface operator}, in Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~279--285. \bibitem{CHLai_1994b} {\sc C.-H. Lai}, {\em On domain decomposition and shooting methods for two--point boundary value problems}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~257--263. \bibitem{ULanger_1994a} {\sc U.~Langer}, {\em Parallel iterative solution of symmetric coupled {FE}/{BE}--equations via domain decomposition}, in Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~335--344. \bibitem{WLayton_JMaubach_PRabier_1994a} {\sc W.~Layton, J.~Maubach, and P.~Rabier}, {\em Robust methods for highly nonsymmetric problems}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~265--270. \bibitem{PLeTallec_JMandel_MVidrascu_1994a} {\sc P.~LeTallec, J.~Mandel, and M.~Vidrascu}, {\em Balancing domain decomposition for plates}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~515--524. \bibitem{PLeTallec_TSassi_MVidrascu_1994a} {\sc P.~LeTallec, T.~Sassi, and M.~Vidrascu}, {\em Three--dimensional domain decomposition methods with nonmatching grids and unstructured coarse solvers}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~61--74. \bibitem{ILie_1994a} {\sc I.~Lie}, {\em Interface conditions for heterogeneous domain decomposition: {C}oupling of different hyperbolic systems}, in Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~469--476. \bibitem{HXLin_1994a} {\sc H.~X. Lin}, {\em Analysis and implementation of {DD} methods for parallel {FE} computations}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~407--412. \bibitem{NJLybeck_KLBowers_1994a} {\sc N.~J. Lybeck and K.~L. Bowers}, {\em Domain decomposition via the {S}inc--{G}alerkin method for second order differential equations}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~271--276. \bibitem{JMandel_1994a} {\sc J.~Mandel}, {\em Hybrid domain decomposition with unstructured subdomains}, in Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~103--112. \bibitem{DMansutti_FPitolli_1994a} {\sc D.~Mansutti and F.~Pitolli}, {\em Simultation of 3{D} {N}avier--{S}tokes flows via domain decomposition by the modified discrete vector potential model}, in Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~477--482. \bibitem{MRMehrabi_RABrown_1994a} {\sc M.~R. Mehrabi and R.~A. Brown}, {\em Finite--element/{N}ewton method for solution of nonlinear problems in transport processes using domain decomposition and nested dissection on {MIMD} parallel computers}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~413--425. \bibitem{PMejzlik_1994a} {\sc P.~Mejzl{\'i}k}, {\em A bisection method to find all solutions of a system of nonlinear equations}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~277--282. \bibitem{SMicheletti_AQuarteroni_RSacco_1994a} {\sc S.~Micheletti, A.~Quarteroni, and R.~Sacco}, {\em Nonlinear block iterative solution of semiconductor device equations by a domain decomposition method}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~525--531. \bibitem{IDMishev_1994a} {\sc I.~D. Mishev}, {\em Preconditioning cell--centered finite difference equations on grids with local refinement}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~283--288. \bibitem{MMu_JRRice_1994a} {\sc M.~Mu and J.~R. Rice}, {\em Modeling with collaborating {PDE} solvers: Theory and practice}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~427--438. \bibitem{FNataf_FRogier_1994a} {\sc F.~Nataf and F.~Rogier}, {\em Factorization of the convection--diffusion operator and a (possibly) non overlapping {S}chwarz method}, in Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~287--292. \bibitem{FNataf_FRogier_1994b} \leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em Outflow boundary conditions and domain decomposition method}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~289--293. \bibitem{SVNepomnyaschikh_1994a} {\sc S.~V. Nepomnyaschikh}, {\em Domain decomposition for elliptic problems with large condition numbers}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~75--85. \bibitem{JTOden_APatra_YFeng_1994a} {\sc J.~T. Oden, A.~Patra, and Y.~Feng}, {\em Domain decomposition for adaptive hp finite element methods}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~295--301. \bibitem{POswald_1994a} {\sc P.~Oswald}, {\em Stable subspace splittings for {S}obolev spaces and domain decomposition algorithms}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~87--98. \bibitem{SVParter_1988a} {\sc S.~V. Parter}, {\em Estimates for multigrid methods based on red--black {G}auss--{S}eidel smoothings}, Numer. Math., 52 (1988), pp.~701--723. \bibitem{LFPavarino_1994c} {\sc L.~F. Pavarino}, {\em Some {S}chwarz algorithms for the {P}--version finite element method}, in Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~113--119. \bibitem{LFPavarino_1994d} \leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em A wire basket based method for spectral elements in three dimensions}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~99--104. \bibitem{MPernice_1994a} {\sc M.~Pernice}, {\em Domain decomposed preconditioners with {K}rylov methods as subdomain solvers}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~303--309. \bibitem{APothen_1994a} {\sc A.~Pothen}, {\em An analysis of spectral graph partitioning via quadratic assignment problems}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~105--110. \bibitem{AQuarteroni_JPeriaux_YAKuznetsov_OBWidund_1994a} {\sc A.~Quarteroni, J.~P{\'e}riaux, Yu.~A. Kuznetsov, and O.~B. Widund}, {\em Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition}, vol.~157 of Contemporary Mathematics, American Mathematical Society, Providence, Rhode Island, 1994. \bibitem{AQuarteroni_AValli_1994a} {\sc A.~Quarteroni and A.~Valli}, {\em Numerical Approximation of Partial Differential Equations}, Springer--Verlag, Berlin, 1994. \bibitem{IRaspo_JOuazzani_RPeyret_1994a} {\sc I.~Raspo, J.~Ouazzani, and R.~Peyret}, {\em A direct {C}hebyshev multidomain method for flow computation with application to rotating systems}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~533--538. \bibitem{FXRoux_DTromeurDervout_1994a} {\sc F.-X. Roux and D.~Tromeur-Dervout}, {\em Parallelization of a multigrid solver via a domain decomposition method}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~439--444. \bibitem{URude_1994b} {\sc U.~R{\"u}de}, {\em Error estimators based on stable splittings}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~111--118. \bibitem{URude_1994a} \leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em On the robustness and efficiency of the fully adaptive multigrid method}, in Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~121--126. \bibitem{MSarkis_1994a} {\sc M.~Sarkis}, {\em Multilevel methods for p1 nonconforming finite elements and discontinuous coefficients in three dimensions}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~119--124. \bibitem{CRSchneidesch_MODeville_EHMund_1994a} {\sc C.~R. Schneidesch, M.~O. Deville, and E.~H. Mund}, {\em Domain decomposition method coupling finite elements and preconditioned {C}hebyshev collocation to solve elliptic problems}, in Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~293--298. \bibitem{LRScott_1994a} {\sc L.~R. Scott}, {\em Elliptic preconditioners using fast summation techniques}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~311--323. \bibitem{JPShao_1994a} {\sc J.~P. Shao}, {\em The modified vertex space domain decomposition method for {N}eumann boundary value problems}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~325--336. \bibitem{JRShewchuk_OGhattas_1994a} {\sc J.~R. Shewchuk and O.~Ghattas}, {\em A compiler for parallel finite element methods with domain--decomposed unstructured meshes}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~445--450. \bibitem{TMShih_CBLiem_TLu_1994a} {\sc T.-M. Shih, C.-B. Liem, and T.~Lu}, {\em Additive {S}chwarz methods and acceleration with variable weights}, in Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~299--309. \bibitem{TMShih_CBLiem_TLu_AZhou_1994a} {\sc T.-M. Shih, C.-B. Liem, T.~Lu, and A.~Zhou}, {\em A multi--color splitting method and convergence analysis for local grid refinement}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~337--342. \bibitem{OSteinbach_1994a} {\sc O.~Steinbach}, {\em Boundary elements in domain decomposition methods}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~343--348. \bibitem{EDeSturler_1994a} {\sc E.~De {S}turler}, {\em {IBLU} preconditioners for massively parallel computers}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~395--400. \bibitem{JSSun_1994a} {\sc J.-S. Sun}, {\em Domain decomposition and multilevel {PCG} method for solving 3--{D} fourth order problems}, in Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~71--78. \bibitem{VHSun_WPTang_1994a} {\sc V.~H. Sun and W.-P. Tang}, {\em An overdetermined {S}chwarz alternating method}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~349--354. \bibitem{XCTai_1994a} {\sc X.-C. Tai}, {\em Domain decomposition for linear and nonlinear elliptic problems via function or space decomposition}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~355--360. \bibitem{KHTan_JABorsboom_1994a} {\sc K.~H. Tan and J.~A. Borsboom}, {\em On generalized {S}chwarz coupling applied to advection-- dominated problems}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~125--130. \bibitem{TETezduyar_MBehr_SKAliabadi_SMittal_SERay_1994a} {\sc T.~E. Tezduyar, M.~Behr, S.~K. Aliabadi, S.~Mittal, and S.~E. Ray}, {\em A new mixed preconditionaing method based on the clustered element--by--element preconditioners}, in Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~215--222. \bibitem{JMThomas_DTrujillo_1994a} {\sc J.-M. Thomas and D.~Trujillo}, {\em Finite volume variational formulation. {A}pplication to domain decomposition methods}, in Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~127--132. \bibitem{LVozovoi_MIsraeli_AAverbuch_1994a} {\sc L.~Vozovoi, M.~Israeli, and A.~Averbuch}, {\em Multi--domain {F}ourier algorithms for parallel solution of the {N}avier--{S}tokes equations}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~539--546. \bibitem{HWang_HKDahle_REEwing_TLin_JEVag_1994a} {\sc H.~Wang, H.~K. Dahle, R.~E. Ewing, T.~Lin, and J.~E. V{/o}ag}, {\em {ELLAM}--based domain decomposition and local refinement techniques for advection--diffusion equations with interfaces}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~361--366. \bibitem{OBWidlund_1994a} {\sc O.~B. Widlund}, {\em Exotic coarse spaces for {S}chwarz methods for lower order and spectral finite elements}, in Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~131--138. \bibitem{JXu_1994a} {\sc J.~Xu}, {\em Some two--grid finite element methods}, in Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994, American Mathematical Society, pp.~79--87. \end{thebibliography} ------------------------------ End of MGNet Digest **************************