Parallel Computations

Parallel Computations

1st Edition - October 28, 1982

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  • Editor: Garry Rodrigue
  • eBook ISBN: 9781483276649

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Parallel Computations focuses on parallel computation, with emphasis on algorithms used in a variety of numerical and physical applications and for many different types of parallel computers. Topics covered range from vectorization of fast Fourier transforms (FFTs) and of the incomplete Cholesky conjugate gradient (ICCG) algorithm on the Cray-1 to calculation of table lookups and piecewise functions. Single tridiagonal linear systems and vectorized computation of reactive flow are also discussed. Comprised of 13 chapters, this volume begins by classifying parallel computers and describing techniques for performing matrix operations on them. The reader is then introduced to FFTs and the tridiagonal linear system as well as the ICCG method. Different versions of the conjugate gradient method for solving the time-dependent diffusion equation are considered. Subsequent chapters deal with two- and three-dimensional fluid flow calculations, paying particular attention to the principal issues in designing efficient numerical methods for hydrodynamic calculations; the decisions that a numerical modeler must make to optimize chemically reactive flow simulations; and how to handle disk-to-core data transfer and storage allocation for the solution of the implicit equations for three-dimensional flows. The book also describes the time-split finite difference scheme for solving the two-dimensional Navier-Stokes equation for flows through slotted nozzles. Finally, the large-scale stimulation of plasmas, as carried out on a small computer with an array processor, is discussed. This monograph should be of interest to specialists in computer science.

Table of Contents

  • List of Contributors


    A Guide to Parallel Computation and Some Cray-1 Experiences

    I. Introduction

    II. Hardware

    III. Theoretical Considerations

    IV. Applications

    Appendix A. A Register Assignment for Sparse-Banded Matrix Multiply

    Appendix B. Factor and Forward Substitution

    Appendix C. Backward Substitution

    Appendix D. Factorization Only


    Vectorizing the FFTs

    I. Introduction

    II. Preliminaries

    III. The Complex FFT Algorithms

    IV. Vectorizing Multiple Transforms

    V. Transforming Real Sequences

    VI. The Symmetric Transforms

    VII. Software and Summary


    Solution of Single Tridiagonal Linear Systems and Vectorization of the ICCG Algorithm on the Cray-1

    I. A Vector Algorithm for Tridiagonal Linear Systems

    II. An Incomplete Cholesky Conjugate Gradient (ICCG) Algorithm for the Cray-1 Computer

    III. Cyclic Reduction on Future Machines


    An Implicit Numerical Solution of the Two-Dimensional Diffusion Equation and Vectorization Experiments

    I. Introduction

    II. Spatial Differencing

    III. Matrix Formulation

    IV. Properties of the Matrix A

    V. Method of Lines

    VI. The Generalized Conjugate Gradient Algorithm

    VII. Computational Example

    VIII. Comments and Conclusions


    Swimming Upstream: Calculating Table Lookups and Piecewise Functions

    I. Introduction to Table Lookup

    II. Evaluating Algorithms on Vector Processors

    III. Basic Processes on Vector Processors

    IV. One-Dimensional Problems

    V. Two-Dimensional Problems: Equations of State


    Trade-Offs in Designing Explicit Hydrodynamical Schemes for Vector Computers

    I. Introduction

    II. Why Vectorization of Explicit Hydrodynamical Schemes Should Be Easy

    III. Why Vectorization of Explicit Hydrodynamical Schemes Can Be Difficult

    IV. Alternative Approaches and Their Costs on Vector Computers 160

    V. The Example of the Interaction of Two Blast Waves

    VI. Conclusions


    Vectorized Computation of Reactive Flow

    I. Introduction and Statement of the Problem

    II. Vectorization and Optimization

    III. Techniques for Modeling Fast Time Scales

    IV. Techniques for Modeling Short Space Scales

    V. Techniques for Dealing with Physical and Geometric Complexity

    VI. Programming Guidelines and Summary of Parallelism Principles


    A Fully Implicit, Factored Code for Computing Three-Dimensional Flows on the ILLIAC IV

    I. Introduction

    II. Basic Equations

    III. ILLIAC Architecture

    IV. Data-Base Considerations

    V. The ILLIAC Code ARC3

    VI. Results

    VII. Concluding Remarks


    A Time-Split Difference Scheme for the Compressible Navier-Stokes Equations with Applications to Flows in Slotted Nozzles

    I. Introduction

    II. The Difference Scheme

    III. The Application

    IV. The Implementation

    V. Results

    Appendix. Numerical Grid Generation


    Geophysical Fluid Simulation on a Parallel Computer

    I. Introduction

    II. The Salient Characteristics of the ASC

    III. The FORTRAN Compiler on the ASC

    IV. The Physical Processes of a Model

    V. Estimating Parallelism in Models

    VI. Conclusion

    Experiences with a Floating Point Systems Array Processor

    I. Introduction

    II. Scientific Computing beyond the CDC 7600

    III. The AP-190L Installation at Cornell

    IV. FPS Array Processors and Parallel Computing

    V. Examples of Optimal Programming for the AP

    VI. The Two-Machine Environment

    VII. Practical Problems of AP Ownership

    VIII. Conclusions


    A Case Study in the Application of a Tightly Coupled Multiprocessor to Scientific Computations

    I. Introduction

    II. Tightly Coupled Multiprocessors

    III. Case Studies

    IV. Conclusions

    Appendix. Implementing Parallel Algorithms


    Computer Modeling in Plasma Physics on the Parallel-Architecture CHI Computer

    I. Introduction

    II. Formulation of the Simulation Problems

    III. Design of the Computer System

    IV. Programming for Efficiency

    V. Observations and Speculations



Product details

  • No. of pages: 416
  • Language: English
  • Copyright: © Academic Press 1982
  • Published: October 28, 1982
  • Imprint: Academic Press
  • eBook ISBN: 9781483276649

About the Editor

Garry Rodrigue

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