Scientific Computing on Supercomputers

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.