Riassunto
The International Workshops on "The Use of Supercomputers in Theoretical Science" have become a tradition at the Univer sity of Antwerp, Belgium. The first one took place in 1984. This volume combines the proceedings of the second work shop (December 12, 1985), of the third (June 16, 1987) and of the fourth (June 9, 1988). The principal aim of the International Workshops is to present the state-of-the-art in scientific high speed computa tion. Indeed, during the past ten years computational science has become a third methodology with merits equal to the theo retical and experimental sciences. Regretfully, access to supercomputers remains limited for academic researchers. None theless, supercomputers have become a major tool for scientists in a wide variety of scientific fields, and they lead to a realistic solution of problems that could not be solved a decade ago. It is a pleasure to thank the Belgian National Science Foundation (NFWO-FNRS) for the sponsoring of all the workshops. These workshops are organized in the framework of the Third Cy cle "Vectorization, Parallel Processing and Supercomputers", which is also funded by the NFWO-FNRS. The other sponsor I want to thank is the University of Antwerp, where the workshops took place. The University of Antwerp (UIA), together with the NFWO-FNRS, are also the main sponsors of the ALPHA-project, which gives the scientists of Belgium the opportunity to obtain an easy supercomputer connection.
Contenuti
I. Supercomputer Architectures.- Performance Modelling of Supercomputer Architectures and Algorithms.- Abstract.- I. Introduction: the spectrum of computers.- II. The need for fast processing and its solution.- 2.1. Increasing the memory speed.- 2.2. Increasing the processor speed.- III. Architectural and program performance characterization.- 3.1. Pipelining.- 3.2. Array processing.- 3.3. Pipelining versus array processing architecture.- IV. Dynamic performance models.- 4.1. Pipelined services.- 4.2. Chaining pipes.- 4.3. Processor — memory pipes.- V. Queueing models of supercomputers.- 5.1. CRAY-1.- 5.2. CDC CYBER 205.- 5.3. Floating point systems AP-120B.- 5.4. Burroughs Scientific Processor (BSP).- VI. Conclusion.- References.- Parallel Processing based on Active-Data.- Abstract.- 1. The exploitation of parallelism.- 2. The declarative versus the objective style.- 3. The active-data model of parallelism.- 4. Load balancing.- 5. An example algorithm.- 6. The implementation issue.- 7. VLSI: the future and the sequential mould.- 8. Selective bibliography.- Architectures for simulation environment.- Abstract.- 1. Introduction.- 2. Continuous time parallel simulation.- 2.1. Continuous time processing.- 2.2. The EAI Simstar system.- 3. MIMD parallel computers in simulation.- 3.1. Parallel implementation of well-known integration algorithms.- 3.2. The DPP81 and its use in simulation.- 4. The AD10 system and simulation.- 4.1. Hardware features.- 4.2. Software features.- 4.2.1. The MPS10 System.- 4.2.2. Special programming techniques 59 4.3. An example: simulation of a transmission line.- 4.3. An example: simulation of a transmission line.- 4.3.1. The model.- 4.3.2. The program.- 4.3.3. Performance and real time simulation.- 4.3.4. Using Arpalgebra.- 5. Conclusion.- References.- Appendix: The Delft Parallel Differential.- The Numerical Solution of Elliptic Partial Differential.- I. Introduction.- II. Hypercube parallel processors.- A. Introduction.- B. The hypercube topology.- C. The Intel iPSC/2.- D. The communication system.- E. Some timing results.- 1. Computation speed.- 2. Communication speed.- F. Some definitions and further considerations.- III. Problem class and discretization.- A. Problem class.- B. The finite difference discretization.- 1. Discretization of the differential equation.- 2. Discretization of the boundary conditions.- IV. The parallel solution method.- A. Decomposition of the domain.- B. The Basic solution scheme.- V. The iterative algorithms.- A. Introduction.- B. The Jacobi method.- C. The Gauss-Seidel method.- D. The successive overrelaxation method.- E. The preconditioned conjugate gradient method.- F. The multigrid method.- 1. Introduction.- 2. The multigrid algorithm.- 3. Parallelism.- VI. Timing results.- A. Introduction.- B. Parallel efficiency.- C. Numerical efficiency versus parallel efficiency.- Acknowledgment.- II. Supercomputer Languages and Algorithms.- Design of Numerical Algorithms for Supercomputers.- 1. Introduction.- 2. Numerical parallel algorithms.- 2.1. Algorithm structure.- 2.2. Parallel methods for the tridiagonal eigenvalue problem.- 2.3. Analysis of the alternative solution methods.- 2.4. Results.- 3. The solution of ordinary differential equations for initial value problems by the use of recurrence relations.- 3.1. Initial value problem.- 3.2. A new explicit method for two-point boundary value problems.- 4. Numerical results.- 5. A fast explicit method for parabolic equations.- 6. Parallel algorithms for linear systems.- 7. The parallel solutions of banded linear systems.- 8. References.- Developments in Supercomputer Languages.- Abstract.- 1. Introduction.- 2. Multiprocessing/distributed programming.- 3. Language approaches.- Detection of parallelism languages.- Expression of machine parallelism languages.- Expression of problem parallelism languages.- 4. Language features.- Data declarations.- Statements.- Data movement.- 5. Concluding remarks.- References.- III. Supercomputer Applications.- Vectorization Techniques and Dynamic Electron Correlations.- Abstract.- 1. Introduction.- 2. Numerical solution of the TDHF-equation.- Appendix A: “devectorization”.- Appendix B: Physical background of the TDHF equation.- Acknowledgment.- References.- Application of Vectorization on Ab-Initio Calculations of Silicon Carbide and Boron Nitride.- I. Introduction.- II. Theoretical framework.- III. Computational details.- A. Input parameters.- B. Numerical procedures.- 1. The Fast Fourier transform.- 2. The self-consistent iteration scheme.- 3. Matrix diagonalization.- IV. Results.- V. Conclusion.- Acknowledgments.- References.- Applications of Supercomputers in Mathematics.- Abstract.- 1. Introduction.- 2. Some general concepts concerning vector and parallel computing.- 2.1. Some definitions.- 2.2. Classification.- 2.3. Algorithm parallelism.- 2.4. Organization of data.- 2.5. Numerical stability.- 3. Applications.- 3.1. Solution of systems of linear equations.- 3.2. Expressions: evaluating a polynomial.- 3.3. ODEs.- 3.4. PDEs.- 3.5. FFT.- 3.6. Number theory.- 3.7. Numerical verification of the Riemann hypothesis.- 4. Vectorization and parallelization techniques.- 4.1. Recursive doubling.- 4.2. Cyclic reduction.- 4.3. Matrix-vector and matrix-matrix multiplication.- 4.4. Extended BLAS.- 5. References.- Vectorization of Large Quantum Chemical Projects: Methods and Illustrations.- 1. Introduction.- 2. Computational aspects of one-electron methods.- 2.1. The Hartree-Fock method.- 2.2. The Hartree-Fock-Slater-LCAO method.- 3. Vectorization strategy.- 3.1. Vectorization of the algorithm.- 3.2. Implementation of the algorithm.- 4. Illustrations.- 4.1. Construction of Fock matrix in HFS-LCAO.- 4.2. Matrix multiplication.- Conclusions.- Acknowledgments.- References.- Jacobi-type Algorithms for Eigenvalues on Vector and Parallel Computers.- Abstract.- 1. Introduction.- 2. Jacobi methods for the symmetric eigenvalue problem.- 3. A parallel norm-reducing algorithm for the non-symmetric eigenproblem.- References.- Postscriptum.- Additional references.- High Performance Computing in Economics.- Abstract.- 1. Introduction.- 2. Fields of applications in economics.- 3. An example.- 4. Conclusion.- 5. References.- Benchmark on Supercomputers for an Industrial Environment.- Abstract.- 1. Introduction.- 2. The “classical” benchmark.- 2.1. General purpose information.- 2.2. Practical testcases.- 2.3. Linear algebra.- 2.4. Application programs.- 3. The computer environments.- Results from the basic operations.- Results from linear algebra.- Results from the applications.- Overall performances.- 4. Complementary studies.- Adaptation of a fluid dynamic code.- In line inserting pre-processor.- 5. Conclusions.- References.- Appendix: Summary of the benchmark’s results.- Solving Partial Differential Equations on a Network of Transputers.- Abstract.- I. Solving the equation of Laplace.- Overview.- 1. The transputer.- 2. OCCAM.- 3. Hardware configurations.- 4. Derivation of numerical approximations.- 5. The parallel algorithms.- 5.1. The packet-sending method.- 5.2. Distributed calculation method.- 6. Results and discussion.- II. A high level programming environment for PDE.- Overview.- 1. Rationale for the project.- 2. Architecture of the environment.- 2.1. The user interface.- 2.2. The codegenerator kernel.- 2.3. The network manager.- 3. Additional design of objectives.- 3.1. Input/output.- 3.2. Error recovery and reporting.- References.- IV. Indexes.- Author Index.
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