Scientific Computing on Supercomputers II

Scientific Computing on Supercomputers II

by J.T. Devreese (Editor)

Paperback(Softcover reprint of the original 1st ed. 1990)

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Product Details

ISBN-13: 9781461279143
Publisher: Springer US
Publication date: 10/04/2011
Edition description: Softcover reprint of the original 1st ed. 1990
Pages: 260
Product dimensions: 6.69(w) x 9.61(h) x 0.02(d)

Table of Contents

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.

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