Scientific Computing on Supercomputers II

252 Pages·1990·7.084 MB·English

by  Willi Schönauer, Hartmut Häfner (auth.), Jozef T. Devreese, Piet E. Van Camp (eds.)

Scientific
Computing on
Supercomputers II
Scientific
Computing on
Supercomputers II
Edited by
J ozef T. Devreese and
Piet E. Van Camp
University 0/ Antwerp
Antwerp, Belgium
PLENUM PRESS • NEW YORK AND LONDON
LIbrary of Congress CatalogIng-In-PublIcatIon Data
InternatIonal ~orkshop on the Use of Supercomputers in Theoretical
Science (5th : 1989 : University of Antwerp)
Scientific computing on supercomputers II I edited by Jozef T.
Devreese and Piet E. Van Camp.
p. em.
"Proceedings of the Fifth International ~orkshop on the Use of
Supercomputers in Theoretical Science. held November 29-30. 1989. at
the University of Antwerp. Antwerp. Belgium"--
Includes bibliographical references and indexes.
ISBN-13: 978-1-4612-7914-3
1. Supercomputers--Congresses. 2. Science--Data processing
-Congresses. I. Devreese. J. T. (Jozef T.) II, Van Camp. p, E.
(Piet E.) III. Title.
OA76.5.I623 1989a
004.1'l--dc20 90-7899
CIP
Proceedings of the Fifth International Workshop on
the Use of Supercomputers in Theoretical Science,
held November 29-30, 1989, at the University of Antwerp,
Antwerp, Belgium
ISBN-13: 978-1-4612-7914-3 e-ISBN-13: 978-1-4613-0659-7
DOI: 10.1007/978-1-4613-0659-7
© 1990 Plenum Press, New York
Softcover reprint of the hardcover 1s t edition 1990
A Division of Plenum Publishing Corporation
233 Spring Street, New York, N.Y. 10013
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
PREFACE
The International Workshop on "The Use of Supercomputers in Theoretical
Science" took place on November 29 and 30, 1989 at the University of Antwerp
(UIA), Antwerpen, Belgium. It was the fifth in a series of workshops, the first of
which took place in 1984.
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 - UIA) 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 index.
J.T. Devreese P.E. Van Camp
University of Antwerp
April 1990
v
CON1ENTS
Vectorization, Optimization and Supercomputer Architecture ............... 1
Willi SchOnauer and Hartmut Hafner
Abstract. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1
1. The architecture of vector computers . . . . . . . . . . . . . . . . . . . . . . .. 1
2. Arithmetic operations, memory bandwidth and memory access ........ 6
3. Data structures and the design of algorithms . . . . . . . . . . . . . . . . .. 10
4. Matrix multiplication and related problems ................... 11
5. Red-black SOR and diagonal storing of matrices ............... 15
6. The linear fIrst order recurrence . . . . . . . . . . . . . . . . . . . . . . . . .. 17
7. Generation of random numbers .......................... 18
8. Supercomputer software independent of a special architecture ....... 19
9. Concluding remarks ................................. 20
10. References ...................................... 21
Vectorization of Some General Purpose Algorithms . . . . . . . . . . . . . . . . . . . . 23
F. Brosens and J.T. Devreese
Abstract .......................................... . 23
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
II. The vector concept in Fortran-200 ....................... . 24
III. Main vector extensions in Fortran-200 .................... . 26
lIlA. Vector variables and vector assignments ............. . 26
III.A.I. Explicit vector reference ................. . 26
III.A.2. Implicit vector reference ................. . 28
III.A.3. Vector functions ...................... . 31
III.B. Vector flow control .......................... . 33
IV. Intrinsic functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 34
IV.A. Scalar functions with scalar arguments . . . . . . . . . . . . . .. 34
IV.B. The intrinsic V-functions ....................... 34
IV.C. The intrinsic Q8-functions . . . . . . . . . . . . . . . . . . . . . . .. 34
IV.C.l. Initialization of a vector .................. 35
IV.C.2. Extracting scalar information from vectors . . . . . .. 35
IV.C.3. Extracting vector information from vectors. . . . . .. 36
IV.C.4. Reversion, compression, expansion, merging, ... of
vectors ............................. . 36
IV.C.5. Gather and scatter operations .............. . 37
V. Practical examples ................................. . 40
V.A. Integration with equally-spaced abscissas ............. . 41
V.B. Gaussian quadrature .......................... . 43
V.C. Chebychev approximation ...................... . 46
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
References ............................... . . . . . . . . . . 50
vii
ASTRID: a Programming Environment for Scientific Applications on Parallel
Vector Computers .................................... 51
E. Bonomi, M. Fluck, R. Gruber, R. Herbin, S. Merazzi, T. Richner,
V. Schmidt and C.T. Tran
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 51
1. Introduction ...................................... 51
2. Organization of ASTRID .............................. 52
2.1. Application modules ........................... 52
2.2. Special characteristics . . . . . . . . . . . . . . . . . . . . . . . . . .. 52
Hardware environment ........................ 53
Subdomain decomposition ...................... 54
Structured meshing . . . . . . . . . . . . . . . . . . . . . . . . . .. 54
Adaptive mesh refinement ...................... 54
3. ASTRID command language . . . . . . . . . . . . . . . . . . . . . . . . . . .. 54
3.1. User interface ............................... 54
3.2. Command syntax ............................. 55
Lne syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 55
Keywords ................................ 55
Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 55
Comments ................................ 55
Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 55
Macro lines ............................... 55
Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 55
Variables and expressions ...................... 56
Control statements ........................... 56
Scripts .................................. 56
3.2. Database commands . . . . . . . . . . . . . . . . . . . . . . . . . . .. 56
4. MiniM: mini-modeller to define the geometry ................. 57
4.1. Create database objects . . . . . . . . . . . . . . . . . . . . . . . . .. 57
4.2. Modify database objects ... . . . . . . . . . . . . . . . . . . . . .. 58
4.3. Remove database objects . . . . . . . . . . . . . . . . . . . . . . . .. 58
5. CASE: interface to define physical quantities ................. 59
5.1. Analysis directives ............................ 59
5.2. Boundary conditions ........................... 59
5.3. Material constants . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 59
6. Mesh: numerical mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 60
6.1. Autoadaptive mesh ............................ 60
6.2. Mesh one subdomain . . . . . . . . . . . . . . . . . . . . . . . . . .. 61
6.3. Mesh all subdomains ................... . . . . . . .. 61
7. Solve: solves the problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 62
7.1. Construction of the matrix and right hand side . . . . . . . . . .. 62
7.2. Direct matrix solver . . . . . . . . . . . . . . . . . . . . . . . . . . .. 62
7.3. Iterative matrix solvers . . . . . . . . . . . . . . . . . . . . . . . . .. 63
8. BASPL: graphics system .............................. 66
8.1. Fundamental remarks ... . . . . . . . . . . . . . . . . . . . . . . .. 66
8.2. Functionalities of BASPL ........................ 66
9. Application: distribution of electrical contacts ................. 68
9.1. The physical problem ... '. . . . . . . . . . . . . . . . . . . . . . .. 68
9.2. MiniM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 70
9.3. CASE .................................... 71
9.4. SOLVE .................................... 73
9.5. Numerical results ............................. 73
9.6. BASPL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 81
Acknowledgments .................................... 81
References ......................................... 81
viii
Large Scale Computations in Solid State Physics ..................... 83
P.E. Van Camp, V.E. Van Doren and J.T. Devreese
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 83
II. Numerical procedures ................................ 83
1. Matrix diagonalization ........................... 84
1.1. The recursive method ...................... 85
1.2. The RMS-DIlS method ..................... 86
2. Iterative solution of the self-consistent matrix . . . . . . . . . . . " 88
2.1. Simple iterations ......................... 88
2.2. Mixing procedures ........................ 89
2.3. An improved iteration scheme . . . . . . . . . . . . . . . .. 90
m. Summary of the results .............................. 91
IV. Acknowledgment .................................. 92
Appendix A: the density functional theory . . . . . . . . . . . . . . . . . . . .. 93
Appendix B: the pseudopotential theory and plane wave expansion ..... 94
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 96
Could User-friendly Supercomputers be Designed? .................... 99
Willi SchOnauer and Reinhard Strebler
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 99
1. Introduction ...................................... 99
2. The requirements for a supercomputer in engineering sciences . . . . . .. 100
2.1. Performance and balanced system " ................ , 100
2.2. Data transfer operations .......................... 101
2.3. Scalar performance ............................ 101
2.4. Programming language . . . . . . . . . . . . . . . . . . . . . . . . .. 101
2.5. Summary of requirements ........... . . . . . . . . . . . .. 101
3. Parallel architectures ...... . . . . . . . . . . . . . . . . . . . . . . . . . .. 102
4. The continuous pipe vector computer (CPVC) . . . . . . . . . . . . . . . .. 103
4.1. Memory bandwidth- ........................... 104
4.2. Local and extended memory ...................... 105
4.3. Number of pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 105
4.4. Memory organization . . . . . . . . . . . . . . . . . . . . . . . . . .. 106
4.5. Pipe switch and delay register ..................... 107
4.6. Building blocks and marketing considerations . . . . . . . . . . .. 108
4.7. Fail-safe system .............................. 109
4.8. The continuous pipe ........................... 109
4.9. Vector dependencies ........................... 111
4.10. Combination pipeline .......................... 112
4.11. Scalar speed ............................... , 113
4.12. Program execution . . . . . . . . . . . . . . . . . . . . . . . . . . .. 114
4.13. Data transfer operations. . . . . . . . . . . . . . . . . . . . . . . .. 115
4.14. Software .................................. 119
5. Concluding remarks ................................. 119
6. Weak points of present supercomputer architectures ............. 120
7. References ....................................... 121
The Use of Transputers in Quantum Chemistry ...................... 123
U. Wedig, A. Burkhardt and H.G. von Schnering
Quantum chemistry and computer .......................... 123
Parallel computer architectures or why we use transputers ........... 123
Programming environment for transputer systems . . . . . . . . . . . . . . . .. 125
IDS, MultiTool ................................. 125
Helios ....................................... 125
ix
Developing programs for transputer systems . . . . . . . . . . . . . . . . . . .. 126
Programming in OCCAM . . . . . . . . . . . . . . . . . . . . . . . . . .. 126
Farming ...................................... 126
Farming on the program level . . . . . . . . . . . . . . . . . . " 126
Farming on the subroutine level .................. 127
A direct SCF-program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 127
Testing the direct SCF-program . . . . . . . . . . . . . . . . . . . . . . . . . . .. 130
Improving the performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 132
More and faster nodes ... . . . . . . . . . . . . . . . . . . . . . . . . .. 132
Faster algorithms for the calculation of the two electron integrals .. 132
Better utilization of intermediate results .................. 133
First experience with Hellos . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 133
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 135
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 136
Domain Decomposition Methods for Partial Differential Equations and Parallel
Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 139
Francois-Xavier Roux
Abstract ......................................... " 139
1. Introduction ...................................... 139
2. The Schwarz alternative principle . . . . . . . . . . . . . . . . . . . . . . . .. 140
2.1. Presentation of the method ....................... 140
2.2. Formulation of the method in terms of the interface operator .. 141
2.3. Parallel implementation of the Schwarz alternative procedure .. 142
2.4. Some remarks about the Schwarz algorithm. . . . . . . . . . . .. 143
3. The Schur complement method .......................... 143
3.1. Presentation of the method ....................... 143
3.2. A preconditioner for the Schur complement method. . . . . . .. 145
4. The hybrid element method ............................ 146
4.1. Principle of the hybrid method . . . . . . . . . . . . . . . . . . . .. 146
4.2. Discretization of the hybrid formulation ............... 148
4.3. Solution of the discrete hybrid problem ............... 149
4.4. Topology of the interface for conforming and non-conforming
domain decomposition methods . . . . . . . . . . . . . . . . . .. 151
5. Implementation of the hybrid method for solving a three-dimensional
structural analysis problem .......................... 153
5.1. Presentation of the problem . . . . . . . . . . . . . . . . . . . . . .. 153
5.2. Choice of the local solver . . . . . . . . . . . . . . . . . . . . . . .. 154
5.3. Some comparisons of the performances of the hybrid domain
decomposition method and the global Choleski factorization. 155
6. Conclusions ...................................... 156
References ............................... . . . . . . . . .. 157
TERPSICHORE: A Three-Dimensional Ideal Magnetohydrodynamic Stability
Program .......................................... 159
David V. Anderson, W. Anthony Cooper, Ralf Gruber, Silvio Merazzi and
Ulrich Schwenn
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 159
1. Introduction ...................................... 159
2. The physics problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 161
3. The organization of TERPSICHORE ...................... , 164
4. The test case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ., 168
5. Performance measurements ............................. 170
5.1. Operation counts ............................. , 170
5.2. Parallellzation procedure . . . . . . . . . . . . . . . . . . . . . . . .. 171
x
5.3. Timings ................................... 171
(a) CRAY-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 171
(b) Eight processor CRAY-YMP parallelized .......... 172
Acknowledgments .................................... 172
References ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 172
The Bridge from Present (Sequential) Systems to Future (Parallel) Systems: the
Parallel Programming Environments Express and CSTools. . . . . . . . . . .. 175
Patrick Van Renterghem
Abstract. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 175
Introduction ........................................ 175
Requirements of a good parallel programming environment .......... 176
An overview of parallel programming environments and languages 177
New programming languages ....................... " 178
New environments ............................... 178
New operating systems. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 178
The CSToois cross-development toolset . . . . . . . . . . . . . . . . . . . . . .. 179
The Express portable parallel programming environment ............ 181
What is Express? ................................ 181
Why Express? .................................. 182
Some features of Express. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 182
Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 182
Interprocessor communication. . . . . . . . . . . . . . . . . . . . . . . .. 183
Non-blocking communication functions. . . . . . . . . . . . . . . . . .. 184
Topology independent communication (the exgridO library) . . . . .. 184
Cubix ....................................... 186
Plotix ...................................... " 186
An example: transputer implementation of the Kohonen feature map .... 187
The main advantages of Express. . . . . . . . . . . . . . . . . . . . . .. 190
A comparison of Express and CSToois ....................... 190
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 192
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 193
Parallel processing ............................... 193
Transputers .......................... . . . . . . . . " 193
CSTools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 193
Express ...................................... 193
Neural networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 193
Linda. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 194
Helios ....................................... 194
Monte Carlo Methods in Classical Statistical Mechanics . . . . . . . . . . . . . . . .. 195
Martin Schoen, Dennis J. Diestler and John H. Cushman
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 195
1.1. General remarks .............................. 195
1.2. Low density systems ........................... 196
1.3. Dense fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 196
1.4. Computer simulation ........................... 197
II. Monte Carlo calculations ... . . . . . . . . . . . . . . . . . . . . . . . . . .. 198
11.1. A simple example ........................... " 198
11.2. Outline of fundamental aspects .................... 199
m. The scheme in practice: Monte Carlo in the canonical ensemble . . . .. 203
m.l. Implementation ... . . . . . . . . . . . . . . . . . . . . . . . . . .. 203
m.2. Computational aspects . . . . . . . . . . . . . . . . . . . . . . . . " 205
IV. Monte Carlo calculations in the grand canonical ensemble ........ 211
IV.l. The model system . . . . . . . . . . . . . . . . . . . . . . . . . . .. 212
xi
IV.2. A Monte Carlo algorithm for the grand canonical ensemble.. 216
IV.3. An illustration: liquid-gas phase transitions in slit pores .... 218
V. Final remarks ..................................... 226
Acknowledgement .................................... 227
References ....................................... .. 227
The Usefulness of Vector Computers for Performing Simultaneous Experiments .. 229
Pieter Moerman
1. Basic principles .................................... 229
2. Example: throwing a dice . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 229
3. Example: path integrals ............................... 232
a) Outline of path integral formulation of quantum mechanics .... 232
b) Application of the Monte Carlo and Metropolis technique . . . .. 234
c) Sequential program ............................. 235
d) Vectorization of the program ., . . . . . . . . . . . . . . . . . . . .. 237
Conclusions ........................................ 239
Acknowledgments .................................... 240
References ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 240
xii