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) 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 1 (approximately January 31, 1995) Today's topics: MGNet WWW Access Change at Yale GMD - Multigrid Course 1995 Copper Mountain Abstracts and Schedule Available Soon Preprints from Z. Chen and D. Y. Kwak or T. Arbogast Paper on Compressible Euler Equations (Sidilkover) Interpolation/Projection/Restriction in Multigrid Additions to mgnet.bib (Brenner) Some bibliography additions in mgnet/bib/mgnet.bib ------------------------------------------------------- Date: Thu, 2 Feb 1995 13:47:22 -0500 From: douglas-craig@cs.yale.edu (Craig Douglas) Subject: MGNet WWW Access Change at Yale We now have a http daemon running on the NA server at Yale. The new URL is http://na.cs.yale.edu/mgnet/www/mgnet.html For those of you with the old URL in HTML files, please update your files to either this one or, in Europe, http://www.cerfacs.fr/~douglas/mgnet.html ------------------------------------------------------- Date: Thu, 12 Jan 1995 12:36:52 +0100 From: mgkurs@gmd.de (Barbara Steckel) Subject: GMD - Multigrid Course 1995 **************************************** * * * GMD - Multigrid Course 1995 * * * * April 24 - 28, 1995 * * * * Bad Honnef near Bonn, Germany * * * **************************************** The GMD (The German National Research Center for Computer Science) will give a multigrid course on April 24 - 28, 1995 at Bad Honnef near Bonn, Germany. The principal lecturer is Professor Achi Brandt from the Weizmann Institute, Rehovot, Israel, one of the pioneers of multigrid. The other lecturers are members of the GMD multigrid research group. The topics of this course will cover the basic principles of multigrid, recent developments and applications. The main scope of the course is to provide with an understanding of multigrid. The visitor will, at the end of the course, be able to write a multigrid program for model problems. Additionally, the course will supply with an overview of multigrid application and recent research activities. The course is especially designed for all those which have to solve partial differential equations in practice. For scalar linear elliptic model problems the efficiency of multigrid algorithms was established at the very beginning of multigrid research. These methods turned out to be the most efficient techniques for solving elliptic partial differential equations. The theory states that a multigrid solution is generally obtained in a time directly proportional to the number of unknowns on serial computers. The inherent locality of the multigrid components allows a very efficient parallelization with nearly optimal speed up. Multigrid, or more general multilevel computational methods have evolved into an independent discipline by itself, interacting with numerous engineering application areas and impacting fundamental developments in several sciences. The recent past shows an increased development of multilevel solvers for various areas, including: aerodynamics, atmospheric and oceanic research, structural mechanics, quantum mechanics and VLSI-Design. For further information, please contact: Barbara Steckel, Wolfgang Joppich Gesellschaft fuer Mathematik und Datenverarbeitung (GMD) Institute for Algorithms and Scientific Computing Schloss Birlinghoven 53754 Sankt Augustin, Germany Phone: (0)2241 14 2768 or - 2748 Fax: (0)2241 14 2460 E-mail: mgkurs@gmd.de ------------------------------------------------------- Date: Thu, 2 Feb 1995 13:35:12 -0500 From: douglas-craig@cs.yale.edu (Craig Douglas) Subject: Copper Mountain Abstracts and Schedule Available Soon All of the abstracts that were received electronically will be available in the next few days in the directory mgnet/Conferences/CopperMtn95 These will be accessible through WWW or anonymous ftp. The schedule will appear sometime in February (hopefully in the middle of the month). It will be in the same directory under the name Schedule. Papers contributed to the pre-proceedings will also appear in that directory. A few are there already (contributed so far by Maliassov, Pflaum, Xie, and Xu). Hopefully, all will be there by the time of the conference or shortly thereafter. ------------------------------------------------------- Date: Thu, 19 Jan 1995 20:12:14 -0600 From: zhangxin ChenSubject: Preprints from Z. Chen and D. Y. Kwak or T. Arbogast THE ANALYSIS OF MULTIGRID ALGORITHMS FOR NONCONFORMING AND MIXED METHODS FOR SECOND ORDER ELLIPTIC PROBLEMS Zhangxin Chen Department of Mathematics and Institute for Scientific Computation, Texas A&M University College Station, TX 77843--3404 Do Y. Kwak Department of Mathematics, Korea Advanced Institute cience and Technology, Taejon, Korea 305--701 Abstract. In this paper we consider multigrid algorithms for nonconforming and mixed finite element methods for second order elliptic problems on triangular and rectangular finite elements. We prove optimal convergence properties of the W-cycle multigrid algorithm and uniform condition number estimates for the variable V-cycle preconditioner. Lower order terms are treated, so our results also apply to parabolic equations. Editor's Note: in mgnet/papers/ChenZ-et-al/MGnon.{abs,ps}. ------------- ON THE IMPLEMENTATION OF MIXED METHODS AS NONCONFORMING METHODS FOR SECOND ORDER ELLIPTIC PROBLEMS Todd Arbogast Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77251 Zhangxin Chen Department of Mathematics and the Institute for Scientific Computation, Texas A&M University, College Station, Texas 77843 Abstract. In this paper we show that mixed finite element methods for a fairly general second order elliptic problem with variable coefficients can be given a nonmixed formulation. (Lower order terms are treated, so our results apply also to parabolic equations.) We define an approximation method by incorporating some projection operators within a standard Galerkin method, which we call a projection finite element method. It is shown that for a given mixed method, if the projection method's finite element space $M_h$ satisfies three conditions, then the two approximation methods are equivalent. These three conditions can be simplified for a single element in the case of mixed spaces possessing the usual vector projection operator. We then construct appropriate nonconforming spaces $M_h$ for the known triangular and rectangular elements. The lowest-order Raviart-Thomas mixed solution on rectangular finite elements in $\Re^2$ and $\Re^3$, on simplices, or on prisms, is then implemented as a nonconforming method modified in a simple and computationally trivial manner. This new nonconforming solution is actually equivalent to a postprocessed version of the mixed solution. A rearrangement of the computation of the mixed method solution through this equivalence allows us to design simple and optimal order multigrid methods for the solution of the linear system. Editor's Note: in mgnet/papers/ChenZ-et-al/mix.{abs,ps}. ------------- ------------------------------------------------------- Date: Wed, 1 Feb 1995 11:57:55 -0500 From: Sidilkover David Subject: Paper on Compressible Euler Equations A GENUINELY MULTIDIMENSIONAL UPWIND SCHEME AND EFFICIENT MULTIGRID SOLVER FOR THE COMPRESSIBLE EULER EQUATIONS David Sidilkover ICASE, Mail Stop 132C NASA Langley Research Center Hampton, VA 23681 ABSTRACT We present a new approach towards the construction of a genuinely multidimensional high-resolution scheme for computing steady-state solutions of the Euler equations of gas dynamics. The unique advantage of this approach is that the Gauss-Seidel relaxation is stable when applied directly to the high-resolution discrete equations, thus allowing us to construct a very efficient and simple multigrid steady-state solver. This is the only high-resolution scheme known to us that has this property. The two-dimensional scheme is presented in detail. It is formulated on triangular (structured and unstructured) meshes and can be interpreted as a genuinely two-dimensional extension of the Roe scheme. The quality of the solutions obtained using this scheme and the performance of the multigrid algorithm are illustrated by the numerical experiments. Construction of the three-dimensional scheme is outlined briefly as well. The quality of the solutions obtained using this scheme and the performance of the multigrid algorithm are illustrated by the numerical experiments. Construction of the three-dimensional scheme is outlined briefly as well. Editor's Note: in mgnet/papers/Sidilkover/euler.{abs,ps}. ------------- ------------------------------------------------------- Date: Thu, 2 Feb 95 13:56:23 GMT From: George Cardew Subject: Interpolation/Projection/Restriction in Multigrid Dear Sirs I have just got started with a multigrid style application in Finite elements on imbedded subgrids. So far I've been unable to find an explanantion of how I might perform an accurate interpolation (Projection) to a higher level grid. Currently , A simple interpolation is performed at element level (using the Shape functions of that element) in either direction (Projecting or Restricting/Injecting) . I beleive it is important to enhance the accuracy when projecting Up. I therefore need to perform interpolation over a patch of elements - therein lies the difficulty . Interpolation over a patch within a curvilinear grid implies that a transformation of coordinates X-Y-Z to R-S-T (0 < R,S,T < 1) will be needed with an inversion of X,Y,Z of the node involed in the interpolation/ projection . I generate my grids using either Transfinite interpolation or Elliptic equations (Thompson et al) - Do I need to invert (say) the Transfinite equation at the node in question (by iteration , naturally) ?? If you have any info on MGNET which could cast light on this problem I would welcome it . Many thanks , George Cardew Univ of Sheffield , UK Editor's Note: Please Cc mgnet@cs.yale.edu if you can help him. ------------- ------------------------------------------------------- Date: Thu, 12 Jan 95 18:35:40 EST From: Susanne Brenner Subject: Additions to mgnet.bib @article{SCBrenner_1994a, author = "S. C. Brenner", title = "A nonconforming mixed multigrid method for the pure traction problem in planar linear elasticity", journal = "Math. Comp.", volume = "63", year = "1994", pages = "435--460 and S1--S5", } @book{SCBrenner_LRScott_1994a, author = "S. C. Brenner and L. R. Scott", title = "The Mathematical Theory of Finite Element Methods", series = "Texts in Applied Mathematics", vol = "15", publisher = "Springer--Verlag", address = "New York", year = "1994", } ------------------------------------------------------- Date: Sat, 29 Jan 1995 17:42:56 -0500 From: douglas@watson.ibm.com (Craig Douglas) Subject: Some bibliography additions in mgnet/bib/mgnet.bib Here are some recent additions to mgnet/bib/mgnet.bib. Please send corrections and additions to mgnet@cs.yale.edu. Thanks. @article{HNishida_NSatofuka_1994a, author = "H. Nishida and N. Satofuka", title = "Numerical solution of unsteady incompressible {N}avier {S}tokes equations using high order method of lines", journal = "Finite Elem. Anal. Des.", volume = "16", year = "1994", pages = "P285--297", } @article{SWOtto_1993a, author = "SWOtto", title = "Parallel array classes and lightweight sharing mechanisms", journal = "Sci. Prog.", volume = "2", year = "1993", pages = "203--216", } @article{JPadovan_SMSansgiri_LKrishna_1994a, author = "J. Padovan and S. M. Sansgiri and L. Krishna", title = "Multiply gauged solution initialization with steepest descent smoothing", journal = "Int. J. Comput. Math.", volume = "50", year = "1994", pages = "165--182", } @article{OPatzold_ASchuller_HSchwichtenberg_1994a, author = "O. Patzold and A. Schuller and H. Schwichtenberg", title = "Parallel applications and performance measurements on {SUPRENUM}", journal = "Parallel Comput.", volume = "20", year = "1994", pages = "1571--1582", } @article{MRannacher_GZhou_1994a, author = "M. Rannacher and G. Zhou", title = "Analysis of a domain-splitting method for nonstationary convection-diffusion problems", journal = "E. W. J. Numer. Math.", volume = "2", year = "1994", pages = "151--172", } @article{ARMRao_KLoganathan_NVRaman_1994a, author = "A. R. M. Rao and K. Loganathan and N. V. Raman", title = "Multi frontal based approach for concurrent finite element analysis", journal = "Comput. Struct.", volume = "52", year = "1994", pages = "841--846", } @article{ARieder_ROWellsJr_XZhou_1994a, author = "A. Rieder and R. O. Wel{ls,~Jr.} and X. Zhou", title = "A wavelet approach to robust multilevel solvers for anisotropic elliptic problems", journal = "Appl. Comput. Harmon. Anal.", volume = "1", year = "1994", pages = "355--367", } @article{ARieder_XZhou_1994a, author = "A. Rieder and X. Zhou", title = "On the robustness of the damped {V} cycle of the wavelet frequency decomposition multigrid method", journal = "Comput.", volume = "53", year = "1994", pages = "155--171", } @article{HRitzdorf_ASchuller_ABSteckel_KStuben_1994a, author = "H. Ritzdorf and A. Sch{\"u}ller and A. B. Steckel and K. St{\"u}ben", title = "$L_iSS$ -- {A}n environment for the parallel multigrid solution of partial differential equations on general {2D} domains", journal = "Parallel Comput.", volume = "20", year = "1994", pages = "1559--1570", } @inproceedings{JSingh_CHolt_JHennessy_AGupta_1993a, author = "J. Singh and C. Holt and J. Hennessy and A. Gupta", title = "Parallel adaptive fast multipole method", booktitle = "Proceedings of the Supercomputing Conference 1993", editors = "", series = "", volume = "", publisher = "IEEE, Computer Society Press", address = "Los Alamitos", year = "1993", pages = "54--65", } @article{LCStone_SBShukla_BNeta_1994a, author = "L. C. Stone and S. B. Shukla and B. Neta", title = "Parallel satellite orbit prediction using a workstation cluster", journal = "Comput. Math. Appl.", volume = "28", year = "1994", pages = "1--8", } @article{TStreit_1994a, author = "T. Streit", title = "Euler and {N}avier-{S}tokes solutions for supersonic flow around a complex missile", journal = "J. Spacecraft Rockets", volume = "31", year = "1994", pages = "600--608", } @article{ASydow_1994a, author = "A. Sydow", title = "Parallel simulation of air pollution", journal = "IFIP Trans. A, Comput. Sci. Technol.", volume = "52", year = "1994", pages = "605--612", } @inproceedings{RFVanderWinjngaaart_1993a, author = "R. F. Van{~der~W}injngaaart", title = "Efficient implementation of a 3-dimensional {ADI} method on the {iPSC}/860", booktitle = "Proceedings of the Supercomputing Conference 1993", editors = "", series = "", volume = "", publisher = "IEEE, Computer Society Press", address = "Los Alamitos", year = "1993", pages = "102--111", } @article{AWiedermann_JIwamoto_1994a, author = "A. Wiedermann and J. Iwamoto", title = "Multigrid {TVD}-type scheme for computing inviscid and viscous flows", journal = "Comput. Fluids", volume = "23", year = "1994", pages = "711--735", } @article{YZang_RLStreet_JRKoseff_1994a, author = "Y. Zang and R. L. Street and J. R. Koseff", title = "A non staggered grid, fractional step method for time dependent incompressible {N}avier {S}tokes equations in curvilinear coordinates", journal = "J. Comput. Phys.", volume = "114", year = "1994", pages = "18--33", } @article{LBZhang_1994a, author = "L. B. Zhang", title = "A multigrid solver for the steady incompressible {N}avier {S}tokes equations on curvilinear coordinate systems", journal = "J. Comput. Phys.", volume = "113", year = "1994", pages = "26--34", } @article{SZhao_MJYedlin_1994a, author = "S. Zhao and M. J. Yedlin", title = "A new iterative {C}hebyshev spectral method for solving the elliptic equation $\bigtriangledown(\sigma\bigtriangledown u)=f$", journal = "J. Comput. Phys.", volume = "113", year = "1994", pages = "215--223", } ------------------------------ End of MGNet Digest **************************