Subject: NA Digest, V. 95, # 12 NA Digest Sunday, March 19, 1995 Volume 95 : Issue 12 Today's Editor: Cleve Moler The MathWorks, Inc. moler@mathworks.com Today's Topics: Nonlinear Schrodinger Equation Iterative Solvers Iterative Methods for Cache Base System VECFEM, VECtorized Finite Element Method News from ILAS Information Center 1995 MATLAB Conference Summer School on Optimization and Identification in Prague PARA95, Workshop on Applied Parallel Computing IBM High Performance Computing Conference Industrial Mathematics Modeling Workshop Method of Lines Workshop Postdoc Position at Argonne National Laboratory Contents, Computational Fluid Dynamics Contents, Interval Computations Contents, Surveys on Mathematics for Industry Submissions for NA Digest: Mail to na.digest@na-net.ornl.gov. Information about NA-NET: Mail to na.help@na-net.ornl.gov. URL for the World Wide Web: http://www.netlib.org/na-net/na_home.html ------------------------------------------------------- From: Giovanni Filippo Naldi Date: Mon, 13 Mar 1995 16:27:09 +0100 Subject: Nonlinear Schrodinger Equation We are concerned with approximating the cubic nonlinear Schrodinger equation in two dimension. In particular we would like to follow the evolution of a single soliton solution. The initial datum (the so called ground state) is the positive solution u of the following nonlinear equation -\Delta u + u - u^3 =0 subjected to a fast decay condition at infinity. The numerical experiments that we have tried for the determination of u were non successfull due to the instability of such a solution. We are aware of some results of M. Weinstein, although we were not able to find them. A shape of the ground state function is given in: Sulem, Sulem and Patera (Comm. Pure and Appl. Math, Vol. 37, 1984), but there are not indications for the computation. Does anybody know about this topic? Thanks, Daniele Funaro and Giovanni Naldi Dipartimento di Matematica, Universita' di Pavia, via Abbiategrasso 209, 27100 Pavia Italy. E-mail: naldi@dragon.ian.pv.cnr.it ------------------------------ From: Paresh Pattani Date: Mon, 13 Mar 95 9:28:49 CST Subject: Iterative Solvers Dear NA-netters: I would greatly appreciate if you could provide me pointers to public domain packages which include highly vectorized iterative solvers such as preconditioned conjugate gradient. Thanks in advance for your help. Best regards. Paresh Pattani pattani@hstc.necsyl.com ------------------------------ From: Jerzy Wasniewski Date: Thu, 16 Mar 1995 22:41:40 +0100 (MET) Subject: Iterative Methods for Cache Base System Is there any work done on "Iterative methods for cache base system". Could you send me some references. Jerzy Wasniewski Fax: + (45)45 930 220 Email: jerzy.wasniewski@uni-c.dk ------------------------------ From: Lutz Grosz Date: Wed, 15 Mar 95 11:44:00 MEZ Subject: VECFEM, VECtorized Finite Element Method VECFEM Version 2.0 VECtorized Finite Element Method designed by the research group for numerical algorithms on supercomputers at the Computing Center of the University of Karlsruhe VECFEM is a FORTRAN77 library of subroutines for the solution of systems of steady or nonsteady nonlinear partial differential equations (PDE). The domain is an arbitrary 1-dimensional, 2-dimensional or 3-dimensional set. For the discretization in space direction finite elements are used. The time direction is discretized by finite differences with variable order and step size, where the optimal order an step size is independently found. To check the quality of the calculated solution an error indicator is computed. For the solution of the resulting large scaled and sparse linear systems iterative methods of the conjugate gradient type (CG-methods) are used. For the mesh generation and graphical representation of the solution interfaces to the pre- and postprocessor programs I-DEAS and PATRAN are available. The data structures and algorithms are optimal for a vectorization on a vector computer. Therefore VECFEM is especially suitable for the solution of large scaled problems. The licence fee for noncommerical application is 250 DM (=170US$). More informations are available in WWW on http://www.uni-karlsruhe.de/~vecfem. Contact: Lutz Grosz Universitaet Karlsruhe Rechenzentrum Zirkel 2 D-76128 Karlsruhe Germany e-mail: vecfem@rz.uni-karlsruhe.de ------------------------------ From: Danny Hershkowitz Date: Mon, 13 Mar 1995 18:04:48 +0200 (EET) Subject: News from ILAS Information Center News from ILAS INFORMATION CENTER (IIC) IIC is happy to announce new services: I. Links to Electronic journals II. Links to institutional home pages so far we have links to 1. American Mathematical Society 2. Mathematics Information Servers (Penn. State Univ.) 3. The World-Wide Web Virtual Library: Math. (Florida State Univ.) 4. Centre for Experimental & Constructive Math. (Simon Fraser Univ.) 5. SIAM's undergraduate WWW pages 6. Journal of Approximation Theory 7. MacTutor History of Mathematics Archives 8. Center for Scientific Computing (Finland) 9. Mathematics Archives - Mathematics Departments 10. Home pages of various mathematics departments 11. NA-NET home page III. Links to members' home pages (Those who wish to have links from our database center to their home page should e-mail their home page address to hershkow@techunix.technion.ac.il) There are three ways to use the services of IIC: MOSAIC, XMOSAIC, NETSCAPE or LYNX - by issuing the command "command http://math.technion.ac.il/iic" where command stands for mosaic, xmosaic, netscape or lynx. FTP - by anonymous FTP to "math.technion.ac.il" (for the IIC database change directory to "iic"). E-mail - by including the command "SEND http://math.technion.ac.il/iic/filename" (where "filename" is the file you request) in the mail body of a message sent to agora@mail.w3.org . The list of files that can be obtained from IIC is included in the file index.html . Detailed instructions as to how to use IIC are included in the file IIC.GUIDE. CONFERENCES: The IIC Database contains information about 166 conferences. JOURNALS: The information available from our paper JOURNALS Section consists of Contents and further information for: Linear Algebra and its Applications (LAA): Linear and Multilinear Algebra (LAMA): Journal of Numerical Linear Algebra with Applications (JNLAA): SIAM Journal on Matrix Analysis and Applications (SIMAX): Mathematics of Control, Signals, and Systems (MCSS): ------------------------------ From: Karen Tuttle Date: Wed, 15 Mar 1995 12:05:50 -0500 Subject: 1995 MATLAB Conference 1995 MATLAB Conference Every two years The MathWorks hosts a MATLAB Conference for its user community. Our 1993 Conference was well received and attendance was over 400. The 1995 Conference will be held October 16-18, 1995 at the Hyatt Regency in Cambridge, Massachusetts. Program The Conference is a combination of special sessions, expository talks by The MathWorks development staff and toolbox authors, user-contributed papers, and product minicourses. The Conference is focused on providing a forum for discussion and learning not only on MATLAB, SIMULINK and toolboxes, but also on the state of research and development in the fields of mathematics, education and engineering. This year's Conference will feature special sessions by Cleve Moler, Jack Little, fuzzy logic expert Lotfi Zadeh, signal processing expert Ron Schafer, and several industry leaders in the field of control design. Call for Papers We are issuing a Call for Papers for the Conference. The process for acceptance will be more formal for the 1995 Conference than it was for the 1993 Conference and proceedings will be generated for the 1995 MATLAB Conference. If you are interested in the Call for Papers, send mail to: conference@mathworks.com For More Information We have an interactive multimedia diskette that contains details on the 1995 Conference. It is available for PC or Macintosh and also through our Home Page (http://www.mathworks.com). If you would like to receive a disk, which includes both a registration form and Call for Papers details, please send your name, shipping address, phone number and choice of PC or Macintosh to: conference@mathworks.com Thanks, and we hope to see many of you in October. Karen Tuttle MathWorks ------------------------------ From: Alexander Kuznetsov Date: Mon, 13 Mar 1995 15:47:28 Subject: Summer School on Optimization and Identification in Prague Announcement about a summer school on: IDENTIFICATION AND OPTIMIZATION Prague, 17-18 July 1995 The school is organised within the framework of the project "Adaptive and predictive control with physical constraints" (PREDCON) funded by the Commission of the European Communities (grant CP941174) under COPERNICUS scheme (Cooperation in Science and Technology with Central and Eastern European Countries). Its main aims are: - to give an overview of on-line identification; - to present new results in the field of identification methods used for predictor-based self-tuning controllers; - to introduce current and perspective optimization methods for controller design. The proceedings will contain full papers of presented lectures. Registration fee is 40 GB pounds, including lunches, refreshments and proceedings. Venue: Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic. LECTURES 1. Identification in adaptive control. (J.Bohm -UTIA) 2. Bayesian Structure Estimation: State and Progress (M. Karny- UTIA) 3. Simultaneous estimation of models with different order (D.Clarke - OU) 4. Identification of distributed parameter systems. (B. Rohal - STU) 5. Optimization in constrained predictive control. (A.Kuznetsov - OU) 6. Direct search optimization. (A.Rykov -- MISIS) 7. Adaptive and Predictive Control of Lumped Input and Distributed Output Systems. (G. Hulko -- STU) 8. Problem formulations in multiobjective optimization.(A.Rykov --MISIS) 9. Methods for solving problems of multiobjective optimization.(A.Rykov --MISIS) 10. Regularization methods --- introduction. (T.Hruz -- STU) 11. Regularization methods in identification. (J. Kadlec --UTIA) 12. Applications: (STU, RB, UTIA) -- information about selected practical applications -- demonstration on laboratory models -- exhibition of software 13. Discussion. PREDCON participating institutions: OU -- Oxford University, Department of Engineering Science (United Kingdom) UTIA -- Institute of Information Theory and Automation (Czech Republic) STU -- Slovak Technical University, Faculty of Mechanical Engineering (Slovakia) MISIS -- Moscow Institute for Steel and Alloys (Russia) RB -- RB Ltd. company (Slovakia) Registration and additional information at: Josef Bohm, Institute of Information Theory and Automation, AV CR Pod vodarenskou vezi 4, 182 08 Prague 8, Czech Republic tel. 42-2-66052337, fax. 42-2-66414903, E--mail : bohm@utia.cas.cz The deadline for application (and reservation) is the May, 5. The registration fee after the deadline could be higher. E-mail communication should be preferred ------------------------------ From: Jerzy Wasniewski Date: Tue, 14 Mar 1995 18:41:58 +0100 (MET) Subject: PARA95, Workshop on Applied Parallel Computing PARA95, WORKSHOP ON APPLIED PARALLEL COMPUTING IN PHYSICS, CHEMISTRY AND ENGINEERING SCIENCE Organized by: UNI*C (The Danish Computing Centre for Research and Education) and IMM (The Institute for Mathematical Modelling of the Technical University of Denmark) in collaboration with Professor Jack Dongarra from the University of Tennessee and Oak Ridge National Laboratory. Dates: August 21, 1995 - Tutorial: ScaLAPACK and Parallel NAG Library on IBM SP2 and SGI Power Challenge in Multiprocessing Environment August 22 - 24, 1994 - Workshop sessions Place: UNI*C, The Danish Computing Centre for Research and Education, The Technical University of Denmark, 2800 Lyngby, DENMARK The PARA95 workshop information (program, hotel details, maps, etc) successively will be available by anonymous ftp: ftp ftp.denet.dk (or 129.142.6.74) anonymous cd uni-c/unijw/para95 Some of the PARA95 information is also distributed by the mailing list para95-l@listserv.uni-c.dk To subscribe send a message to listserv@listserv.uni-c.dk containing sub para95-l yourname For more PARA95 information contact: PARA95, UNI*C, DTU, Bldg. 304 2800 Lyngby, Denmark Attn: Jerzy Wasniewski Email: workshop@uni-c.dk Fax: (+45) 45 93 02 20 Tel: (+45) 45 88 39 99 after the tone 2426 ------------------------------ From: Robert Gallagher Date: Wed, 15 Mar 95 16:21:34 EST Subject: IBM High Performance Computing Conference SUPER!95 IBM High Performance Computing SUPER! 95, the eighth annual conference for users of IBM-based high performance computing systems, will be hosted by the University of Arizona in Tucson, Arizona. Reserve April 23 - 26, 1995 to attend this excellent technical program and enjoy the wonderful weather and cuisine of the great Southwest. Attendees are people who use or manage high performance computing facilities. This includes faculty, research scientists, technical and user support staff, computing center managers, and others interested in IBM's newest high performance computing technology. Some of the topics and speakers include: * "The Impact of Impacts in the Solar System" Professor Willy Benz, University of Arizona * "What's in a Name? NII and NREN" Stephen Wolff (former Director of the Network Programs, National Science Foundation), Cisco Systems, Inc. * "High Performance Computing in Diagnostic and Therapeutic Radiology" Professor Timothy Solberg, University of California at Los Angeles * "Interactive Access to Massive Social Science Data Sets" Professor Albert Anderson, University of Michigan * "IBM Directions in High Performance Computing" Irving Wladawsky-Berger, General Manager, POWER Parallel Division, IBM * "Configuring and Managing Large SP2 Parallel Environments" Douglas Carlson, Cornell Theory Center, and John Sobolewski, Maui HPC Center and University of New Mexico * "A High-Altitude View of the Computational Trends in the Automotive Industry" Myron Ginsberg, EDS/General Motors One of the highlights of SUPER! is the Open Forum. This is when the attendees "get the floor" for 90 minutes to interact with a panel of the IBM managers responsible for the POWER Parallel Division, RS/6000 development, AIX development, and POWER parallel application software development about issues and concerns, new directions, or anything attendees wish to ask. Last year the IBM panelists were very open and forthcoming! Many of the same panelists will return this year. The complete program and information about registration is on the SUPER!95 World Wide Web server at the address below. For more information, contact: Research Computing Group Center for Computing and Information Technology The University of Arizona Tucson, AZ 85721 e-mail: super95@aruba.ccit.arizona.edu phone: (602) 621-4245 fax: (602) 621-8668 WWW/Mosaic, Lynx: URL-HTTP://aruba.ccit.arizona.edu/super95.html ------------------------------ From: H. T. Tran Date: Thu, 16 Mar 95 12:27:16 EST Subject: Industrial Mathematics Modeling Workshop Announcing the INDUSTRIAL MATHEMATICS MODELING WORKSHOP FOR GRADUATE STUDENTS August 7 - 16, 1995 Center for Research in Scientific Computation North Carolina State University Raleigh, North Carolina FOREWORD The Industrial Mathematics Modeling Workshop for Graduate Students, which is the fourth in the series, will take place at the Center for Research in Scientific Computation at North Carolina State University in Raleigh, North Carolina, 7-16 August 1995. This workshop is being held annually, the previous highly successful meetings was held at the University of Minnesota in 1992 and at the Claremont Colleges in 1993 and 1994. A description of the 1993 Claremont workshop can be found in SIAM NEWS, November, 1993 issue. In line with the previous workshops the goals of this workshop are: * to expose 30 graduate students in mathematics and statistics to the challenging and exciting real-world problems from industry and government laboratories; * to introduce students to the team approach to problem solving. Funding for this workshop has been requested with the National Security Agency and the Army Research Office. Additional support is anticipated from the Center for Research in Scientific Computation. FORMAT In the workshop the students will be divided into six teams to work on "industrial mathematics" problems brought on by experienced applied mathematicians. These problems are challenging, real-world problems from industry or applied science and require fresh, new insight for their formulation and solution. The problem presenters, primarily from industry and government laboratories, are being recruited and their names will be announced subsequently. APPLICATION PROCEDURE Graduate students in mathematics, applied mathematics, statistics or operations research can be nominated for this program by a faculty member by sending a letter of recommendation. In addition, the student is required to send in a copy of a recent transcript. THE DEADLINE FOR APPLICATION IS JUNE, 30. Students will be expected to finance their travel. The workshop will cover local living expenses for U.S. citizens and permanent residents. ORGANIZERS Ben Fitzpatrick (Center for Research in Scientific Computation) Hien T. Tran (Center for Research in Scientific Computation) CONTACT PERSON Submit your complete applications or any inquiries you may have concerning this workshop to: Hien T. Tran Center For Research in Scientific Computation Box 8205 North Carolina State University Raleigh, NC 27695-8205 Telephone: (919) 515-3265 Fax: (919) 515-3798 e-mail: tran@control.math.ncsu.edu ------------------------------ From: Ian Gladwell Date: Thu, 16 Mar 95 15:45:16 CST Subject: Method of Lines Workshop METHOD OF LINES WORKSHOP A Workshop on the Method of Lines for Time-Dependent Problems will be held at the University of Kentucky in Lexington, Kentucky, from Wednesday, May 31 1995 until Saturday, June 3 1995. Total attendance at the conference will be limited to sixty participants. The invited speakers are: Martin Berzins (Leeds), Kevin Burrage (Queensland), George Byrne (Illinois Institute of Technology), Joe Flaherty (Rensselaer Polytechnic Institute), Mac Hyman (Los Alamos), Ken Jackson (Toronto), Ohannes Karakashian (Tennessee), Linda Petzold (Minnesota), Bob Russell (Simon Fraser), Bill Schiesser (Lehigh), Skip Thompson (Radford), Jan Verwer (CWI, Amsterdam). Participants will have the opportunity to propose a presentation on a topic associated with the method of lines for time-dependent partial differential equations or with aspects of the (parallel) solution of ordinary differential equations which may have implications for the method of lines for time-dependent problems. Presentations on applications of the Method of Lines will be welcomed. Some discussion panels will also be organised. There will be a refereed conference proceedings published in a special issue of Applied Numerical Mathematics. Presenters of invited and contributed papers will be encouraged to submit papers for the proceedings. Further details may be obtained by e-mailing mol@glenclova.mines.colorado.edu The workshop is supported by the National Science Foundation, the Institute for Mathematics and its Applications, the Center for Computational Sciences of the University of Kentucky, Dedman College of Southern Methodist University, and the Colorado School of Mines. == Graeme Fairweather and Ian Gladwell ------------------------------ From: Chris Bischof Date: Fri, 17 Mar 1995 08:38:49 -0600 Subject: Postdoc Position at Argonne National Laboratory POSTDOCTORAL POSITION MATHEMATICS AND COMPUTER SCIENCE DIVISION ARGONNE NATIONAL LABORATORY Argonne National Laboratory has openings for postdoctoral research positions in the Mathematics and Computer Science Division and invites outstanding candidates to apply. One position is expected to be on assignment at the Supercomputing Research Center in Bowie, Maryland. Candidates should have a Ph.D. in applied mathematics, computer science, computational chemistry or a related discipline and comprehensive knowledge in numerical linear algebra and parallel computing. The successful candidate will participate in the development of algorithms and software tools for large-scale dense eigenvalue and orthogonal reduction problems under the umbrella of the PRISM (Parallel Research in Invariant Subspace Methods) project. Information on the PRISM project can be found in pub/prism on ftp.super.org. This project is interdisciplinary in nature and interfaces with efforts in computational chemistry. The Mathematics and Computer Science Division supports an excellent computational environment that includes access to high-performance scientific workstations, a scientific visualization and virtually reality laboratory, and state-of-the-art parallel computers. Argonne is located in the southwestern Chicago suburbs, offering the advantages of affordable housing and good schools, as well as easy access to the cultural attractions of the city. Applicants must have received their Ph.D. not more than three years prior to the beginning of the appointment. The appointment is available immediately and for a one-year term (renewable). Applications should be addressed to Walter McFall, Box mcs-postdoc9, Employment and Placement, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439, and must include a resume' and the names and addresses of three references. For additional information, contact Chris Bischof (bischof@mcs.anl.gov). Argonne is an affirmative action/equal opportunity employer. ------------------------------ From: Grant Guevremont Date: Fri, 17 Mar 1995 18:02:18 -0500 Subject: Contents, Computational Fluid Dynamics Contents INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS Vol. 3, No. 1, 1994 A Least Squares Finite Element Method for Doubly-Diffusive Convection L. Q. Tang and T. T. H. Tsang Finite Element Method for Two-Layer Tidal Current Analysis With an Open Boundary Condition T. Kodama and M. Kawahara Analysis/Design Calculations of Transonic Flows Z. Q. Zhu, J. C. Su and B. Y. Chen SHORT COMMUNICATION Finite Diffeence Techniques Applied to the Simulation of Surges and Currents Around Sri Lanka and Southern Indian Peninsula A. D. Rao, S. K. Dube and P. Chittibabu Vol. 3, No. 2, 1994 Adaptive Remeshing for Hyperbolic Transport Problems D. Pelletier, A. Zaki and A. Fortin Parallelization of Inviscid and Viscous Flow Solvers D. Drikakis and F. Durst Finite Difference Simulation of a Stratified Two-Phase System C. Tsai and T. Liu SHORT COMMUNICATION Flux Limited Non-Oscillatory CUD-3 Schemes for 1-D Euler Equations K. S. Ravichandran Thanks, Grant Guevremont CERCA Tel. (514) 369-5273 email : grantg@cerca.umontreal.ca ------------------------------ From: R. Baker Kearfott Date: Mon, 13 Mar 1995 10:09:35 -0600 Subject: Contents, Interval Computations Interval Computations. - 1994. - N 2. - 132 p. CONTENTS >From the Editor 2 >From the Editor (in Russian) 4 Mathematical Research S. P. Shary Solving the Tolerance Problem for Interval Linear Systems 6 N. S. Dimitrova and S. M. Markov On Validated Newton Type Method for Nonlinear Equations 27 V. A. Podchukayev and I. M. Svetlov An Analytical Method of Constructing Hurwitz Interval Polynomials 52 Applications and Studies of Related Disciplines M. Berz and G. Hoffstaetter Exact Bounds on the Long Term Stability of Weakly Nonlinear Systems Applied to the Design of Large Storage Rings 68 V. Kreinovich, T. Swenson, and A. Elentukh Interval Approach to Testing Software 90 Meetings 1st All-Russian Conference on Countinuous Logic and Its Applications 110 1st All-Russian Conference on Countinuous Logic and Its Applications (in Russian) 110 Bibliography Bibliography of Soviet Works on Interval Computations. Part VI 116 Requirements for manuscript preparation 127 Requirements for manuscript preparation (in Russian) 128 Addresses of the editorial board members 129 Contents 131 ==================================================================== Interval Computations. - 1994. - N 3. - 128 p. Parallel Algorithms for Interval Computations CONTENTS Foreword by the Invited Editors of the Special Issue 2 Foreword by the Invited Editors of the Special Issue (in Russian) 4 V. Kreinovich and A. Bernat Parallel Algorithms for Interval Computations: An Introduction 6 E. Lyager Finding Local Extremal Points by Using Parallel Interval Methods 63 K. Madsen and O. Toft A Parallel Method for Linear Interval Equations 81 M. Plum Enclosures for Solutions of Parameter-Dependent Nonlinear Elliptic Boundary Value Problems: Theory and Implementation on a Parallel Computer 106 Requirements for manuscript preparation 122 Requirements for manuscript preparation (in Russian) 123 Addresses of the editorial board members 124 Contents 126 ==================================================================== Interval Computations. - 1994. - N 4. - 128 p. Proceedings of SCAN-93 CONTENTS Foreword by Prof. H. Stetter 2 Foreword by Prof. H. Stetter (in Russian) 3 S. Christiansen Interval Methods and Condition Numbers of Linear Algebraic Systems 4 M. Daumas and D. W. Matula Rounding of Floating Point Intervals 28 M. Daumas, Ch. Mazenc, and J.-M. Muller Towards a User Transparent Interval Arithmetic 46 M. T. Nakao Numerical Verifications of Solutions for Nonlinear Hyperbolic Equations 64 W. Luther and W. Otten Computation of Standard Interval Functions in Multiple-Precision Interval Arithmetic 78 E. D. Popova Extended Interval Arithmetic in IEEE Floating-Point Environment 100 Addresses of the editorial board members 130 Contents 132 ------------------------------ From: Heinz W. Engl Date: Tue, 14 Mar 1995 09:26:40 EST Subject: Contents, Surveys on Mathematics for Industry Surveys on Mathematics for Industry (Springer-Verlag Vienna/New York) Table of Contents, Vol4. No.4 H.Guillard, M.Mallet, J.Periaux (Guest Editors of this Volume), Numerical Tools for Scientific Computation with Applications to Flow, Turbulence and Combustion P.George, Automatic Mesh Generator Using the Delaunay Voronoi Principle E.Hirschel, W.Schwarz, Mesh Generation for Aerospace CFD Applications O.Jacquotte, F.Montigny, G.Coussement, Generation, Optimization, and Adaption of Multiblock Structured Grids for Complex Configurations T.Hughes, K.Jansen, A Stabilized Finite Element Formulation for the Reynolds-Averaged Navier-Stokes Equations P.Gervasio, A.Quarteroni, L.Valdettaro, Effective Algorithms for Spectral Methods with Applications K.Papailiou, Selected Contributions to the Field of CFD by the Thermal Turbomachinery Laboratory J.Hanson, Visulaization Techniques for Turbulence in CFD == Heinz W.Engl, Managing Editor ------------------------------ End of NA Digest ************************** -------