Scientific Computing on Supercomputers III

Transcription

1 Scientific Computing on Supercomputers III

2 Scientific Computing on Supercomputers III Edited by J ozef T. Devreese and Piet E. Van Camp Universiteit Antwerpen Antwerpen, Belgium SPRINGER SCIENCE+BUSINESS MEDIA, LLC

3 Proceedings of the Sixth International Workshop on the Use of Supercomputers in Theoretical Science, held January 24-25, 1991, at Universiteit Antwerpen, Antwerpen, Belgium ISBN ISBN (ebook) DOI / Springer Science+Business Media New York 1992 Originally published by Plenum Press, New York in 1992 Softcover reprint of the hardcover 1st edition 1992 All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher

4 PREFACE The International Workshop on "The Use of Supercomputers in Theoretical Science" took place on January 24 and 25, 1991, at the University of Antwerp (UIA), Antwerpen, Belgium. It was the sixth in a series of workshops, the first of which took place in The principal aim of these workshops is to present the state of the art in scientific large-scale and high speed-computation. Computational science has developed into a third methodology equally important now as its theoretical and experimental companions. Gradually academic researchers acquired access to a variety of supercomputers and as a consequence computational science has become a major tool for their work. It is a pleasure to thank the Belgian National Science Foundation (NFWO-FNRS) and the Ministry of ScientifIc Affairs for sponsoring the workshop. It was organized both in the framework of the Third Cycle "Vectorization, Parallel Processing and Supercomputers" and the "Governemental Program in Information Technology". We also very much would like to thank the University of Antwerp (Universitaire Instelling Antwerpen - VIA) for financial and material support. Special thanks are due to Mrs. H. Evans for the typing and editing of the manuscripts and for the preparation of the author and subject indexes. J.T. Devreese P.E. Van Camp University of Antwerp July 1991 v

5 CONlENTS High Perfonnance Numerically Intensive Applications on Distributed Memory Parallel Computers.... F.W. Wray Abstract Introduction A Parallel Implementation of Gaussian Elimination The Parallel Solution of Tridiagonal Systems of Equations The Parallel Solution of Computational Fluid Dynamics Problems Conclusions References Parallel Computational Fluid Dynamics on a Meiko Transputer System with Express in Comparison to ipsc Systems L. Beemaert, D. Roose and W. Verhoeven Abstract Introduction Express Benchmark Results for Express on a Meiko Transputer System Computation benchmarks Communication benchmarks Nearest neighbour communication Multi-hop communication Message exchange Global communication Parallelization of a Fluid Dynamics Application The Euler equations and numerical solution techniques The test problem Solution methods: relaxation and multigrid Parallelization of the Code Relaxation solvers Multigrid solver Implementation details..., 53 vii

6 6. Timing and Efficiency Results Relaxation methods , Red-black point Gauss-Seidel relaxation Red-black line Gauss-Seidel relaxation., Multigrid methods Conclusion Acknowledgement References Preconditioned Conjugate Gradients on the PUMA Architecture R. Cook Abstract Introduction Preconditioned Conjugate Gradient The algorithm Preconditioner Matrix vector multiplications Vector updates Dot products Parallel implementation Reformulation... " Timing Models Sparse matrix multiply Vector updates... " Dot product Preconditioned conjugate gradients Preconditioned conjugate gradients (reformulated) Conclusions References Parallel Discrete Event Simulation: Opportunities and Pitfalls E. Dirkx and F. Verboven Abstract Introduction Discrete event simulation Modellization Implementation Discrete Event Simulation..." Event and time driven simulation Sequential event driven simulati.m Experimental results Parallel Discrete Event Simulation Parallel computer architectures Heuristics Algorithmic parallelism Farming Interconnection topology viii

7 4. Conclusion Acknowledgements References Parallel Programming on Amoeba Using Different Distributed Shared Memory H.E. Bal, M.P. Kaashoek and A.S. Tanenbaum Abstract l. Introduction A Distributed Shared Memory Model Based on Shared Objects A RPC-Based Implementation l. The invalidation protocol The update protocol Performance A Multicast-Based Implementation l. Reliable multicast An update protocol using reliable multicasts Performance Example Applications and Their Performance The all-pairs shortest paths problem Branch-and-bound Successive overrelaxation A Comparison with Other DSM Systems Conclusions References D Shallow Water Model on the CRA Y Y-MP4/ E.D. de Goede Abstract Introduction Mathematical Model Implementation Scalar and Vector Performance Parallelism Numerical Results Conclusions References Simulating Compressible Flow on a Distributed Memory Machine P. Batten, O. Tutty and J. Reeve Abstract l. Introduction Software Tools and Current Hardware The T800 transputer Transputer based machines CAD and domain decomposition tool The SHAPE router IX

8 2.5. Parallel mesh generator Shock Capturing Conservation form and the entropy condition Total variation diminishing methods Simplified TVD schemes... ; Extension to systems of equations (the Euler equations) Parallel Implementation Finite volume Artificial viscosity method Geometric parallelism The TVD method Future hardware Virtual channel router (VCR) Summary and Results References Principles of Code Optimization on Convex-C F. Brosens Abstract I. Introduction II. Basic Vector Concept III. Subarray Syntax (FORTRAN-XX) I1I.A. FORTRAN ARRAY LAYOUT in memory I1I.B. FORTRAN-XX ARRAY SECTIONS, WHERE and VECTOR statements I1I.B.l. Array section syntax I1I.B.2. VECTORIZATION and PARALLEL processing 146 IV. VECTORIZABLE DO-loops IV.A. Non-vectorizable statements in DO-loops IV.A.I. Recurrence IV.A.2. I/O statements IV.A.3. OOTO statements IV.A.4. Subprogram calls IV.A.5. Nested IF-blocks IV.B. VECTORIZATION of the CANDIDATES FOR VECTORIZATION IV.B.l. Vectorization of SCALAR references IV.B.2. Vectorization of ARRAY references IV.B.3. Recurrence V. VECLIB Library V.A. DYNAMIC MEMORY allocation V.A.l. DYNAMIC V.A.2. MALLOC V.A.3. NALLOC, RALLOC, DALLOC V.B. VECTOR programs provided by VECLIB VI. Some Worked Examples VI.A. Solution of a set of linear equations VI.B. Polynomial evaluation x

9 VI.c. Integration with equally spaced abscissas VI.D. Gaussian quadrature VI.E. Chebychev approximation Conclusion Acknowledgement..., 184 References On the Vectorization and Parallelization of a Finite Difference Scheme R.I. van der Pas Abstract Introduction The Convex C2 Architecture A Block Iterative Method An Implementation Performance Considerations An Improved Implementation Conclusions Acknowledgements References Author Index Subject Index.. 211