Scientific Computing on Supercomputers II

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.

Vectorization, Optimization and Supercomputer Architecture.- Abstract.- 1. The architecture of vector computers.- 2. Arithmetic operations, memory bandwidth and memory access.- 3. Data structures and the design of algorithms.- 4. Matrix multiplication and related problems.- 5. Red-black SOR and diagonal storing of matrices.- 6. The linear first order recurrence.- 7. Generation of random numbers.- 8. Supercomputer software independent of a special architecture.- 9. Concluding remarks.- 10. References.- Vectorization of Some General Purpose Algorithms.- Abstract.- I. Introduction.- II. The vector concept in Fortran-200.- III. Main vector extensions in Fortran-200.- III.A. Vector variables and vector assignments.- III.A.1. Explicit vector reference.- III.A.2. Implicit vector reference.- III.A.3. Vector functions.- III.B. Vector flow control.- IV. Intrinsic functions.- IV.A. Scalar functions with scalar arguments.- IV.B. The intrinsic V-functions.- IV.C. The intrinsic Q8-functions.- IV.C.1. Initialization of a vector.- IV.C.2. Extracting scalar information from vectors.- IV.C.3. Extracting vector information from vectors.- IV.C.4. Reversion, compression, expansion, merging, … of vectors.- IV.C.5. Gather and scatter operations.- V. Practical examples.- V.A. Integration with equally-spaced abscissas.- V.B. Gaussian quadrature.- V.C. Chebychev approximation.- Conclusion.- References.- ASTRID: a Programming Environment for Scientific Applications on Parallel Vector Computers.- Abstract.- 1. Introduction.- 2. Organization of ASTRID.- 2.1. Application modules.- 2.2. Special characteristics.- Hardware environment.- Subdomain decomposition.- Structured meshing.- Adaptive mesh refinement.- 3. ASTRID command language.- 3.1. User interface.- 3.2. Command syntax.- Lne syntax.- Keywords.- Attributes.- Comments.- Procedures.- Macro lines.- Constants.- Variables and expressions.- Control statements.- Scripts.- 3.2. Database commands.- 4. MiniM: mini-modeller to define the geometry.- 4.1. Create database objects.- 4.2. Modify database objects.- 4.3. Remove database objects.- 5. CASE: interface to define physical quantities.- 5.1. Analysis directives.- 5.2. Boundary conditions.- 5.3. Material constants.- 6. Mesh: numerical mesh.- 6.1. Autoadaptive mesh.- 6.2. Mesh one subdomain.- 6.3. Mesh all subdomains.- 7. Solve: solves the problem.- 7.1. Construction of the matrix and right hand side.- 7.2. Direct matrix solver.- 7.3. Iterative matrix solvers.- 8. BASPL: graphics system.- 8.1. Fundamental remarks.- 8.2. Functionalities of BASPL.- 9. Application: distribution of electrical contacts.- 9.1. The physical problem.- 9.2. MiniM.- 9.3. CASE.- 9.4. SOLVE.- 9.5. Numerical results.- 9.6. BASPL.- Acknowledgments.- References.- Large Scale Computations in Solid State Physics.- I. Introduction.- II. Numerical procedures.- 1. Matrix diagonalization.- 1.1. The recursive method.- 1.2. The RMS-DIIS method.- 2. Iterative solution of the self-consistent matrix.- 2.1. Simple iterations.- 2.2. Mixing procedures.- 2.3. An improved iteration scheme.- III. Summary of the results.- IV. Acknowledgment.- Appendix A: the density functional theory.- Appendix B: the pseudopotential theory and plane wave expansion.- References.- Could User-friendly Supercomputers be Designed?.- Abstract.- 1. Introduction.- 2. The requirements for a supercomputer in engineering sciences.- 2.1. Performance and balanced system.- 2.2. Data transfer operations.- 2.3. Scalar performance.- 2.4. Programming language.- 2.5. Summary of requirements.- 3. Parallel architectures.- 4. The continuous pipe vector computer (CPVC).- 4.1. Memory bandwidth.- 4.2. Local and extended memory.- 4.3. Number of pipes.- 4.4. Memory organization.- 4.5. Pipe switch and delay register.- 4.6. Building blocks and marketing considerations.- 4.7. Fail-safe system.- 4.8. The continuous pipe.- 4.9. Vector dependencies.- 4.10. Combination pipeline.- 4.11. Scalar speed.- 4.12. Program execution.- 4.13. Data transfer operations.- 4.14. Software.- 5. Concluding remarks.- 6. Weak points of present supercomputer architectures.- 7. References.- The Use of Transputers in Quantum Chemistry.- Quantum chemistry and computer.- Parallel computer architectures or why we use transputers.- Programming environment for transputer systems.- TDS, MultiTool.- Helios.- Developing programs for transputer systems.- Programming in OCCAM.- Farming.- Farming on the program level.- Farming on the subroutine level.- A direct SCF-program.- Testing the direct SCF-program.- Improving the performance.- More and faster nodes.- Faster algorithms for the calculation of the two electron integrals.- Better utilization of intermediate results.- First experience with Helios.- Conclusion.- References.- Domain Decomposition Methods for Partial Differential Equations and Parallel Computing.- Abstract.- 1. Introduction.- 2. The Schwarz alternative principle.- 2.1. Presentation of the method.- 2.2. Formulation of the method in terms of the interface operator.- 2.3. Parallel implementation of the Schwarz alternative procedure.- 2.4. Some remarks about the Schwarz algorithm.- 3. The Schur complement method.- 3.1. Presentation of the method.- 3.2. A preconditioner for the Schur complement method.- 4. The hybrid element method.- 4.1. Principle of the hybrid method.- 4.2. Discretization of the hybrid formulation.- 4.3. Solution of the discrete hybrid problem.- 4.4. Topology of the interface for conforming and non-conforming domain decomposition methods.- 5. Implementation of the hybrid method for solving a three-dimensional structural analysis problem.- 5.1. Presentation of the problem.- 5.2. Choice of the local solver.- 5.3. Some comparisons of the performances of the hybrid domain decomposition method and the global Choleski factorization.- 6. Conclusions.- References.- TERPSICHORE: A Three-Dimensional Ideal Magnetohydrodynamic Stability Program.- Abstract.- 1. Introduction.- 2. The physics problem.- 3. The organization of TERPSICHORE.- 4. The test case.- 5. Performance measurements.- 5.1. Operation counts.- 5.2. Parallelization procedure.- 5.3. Timings.- (a) CRAY-2.- (b) Eight processor CRAY-YMP parallelized.- Acknowledgments.- References.- The Bridge from Present (Sequential) Systems to Future (Parallel) Systems: the Parallel Programming Environments Express and CSTools.- Abstract.- Requirements of a good parallel programming environment.- An overview of parallel programming environments and languages.- New programming languages.- New environments.- New operating systems.- The CSTools cross-development toolset.- The Express portable parallel programming environment.- What is Express?.- Why Express?.- Some features of Express.- Configuration.- Interprocessor communication.- Non-blocking communication functions.- Topology independent communication (the exgrid() library).- Cubix.- Plotix.- An example: transputer implementation of the Kohonen feature map.- The main advantages of Express.- A comparison of Express and CSTools.- Conclusion.- Parallel processing.- Transputers.- CSTools.- Express.- Neural networks.- Linda.- Helios.- Monte Carlo Methods in Classical Statistical Mechanics.- I. Introduction.- I.1. General remarks.- I.2. Low density systems.- I.3. Dense fluids.- I.4. Computer simulation.- II. Monte Carlo calculations.- II.1. A simple example.- II.2. Outline of fundamental aspects.- III. The scheme in practice: Monte Carlo in the canonical ensemble.- III.1. Implementation.- III.2. Computational aspects.- IV. Monte Carlo calculations in the grand canonical ensemble.- IV.1. The model system.- IV.2. A Monte Carlo algorithm for the grand canonical ensemble.- IV.3. An illustration: liquid-gas phase transitions in slit pores.- V. Final remarks.- Acknowledgement.- References.- The Usefulness of Vector Computers for Performing Simultaneous Experiments.- 1. Basic principles.- 2. Example: throwing a dice.- 3. Example: path integrals.- a) Outline of path integral formulation of quantum mechanics.- b) Application of the Monte Carlo and Metropolis technique.- c) Sequential program.- d) Vectorization of the program.- Conclusions.- Acknowledgments.- References.