Vectorization of Computer Programs with Applications to Computational Fluid Dynamics

ISBN-13: 9783528080822 / Angielski / Miękka / 1984 / 246 str.

Wolfgang Gentzsch

Opis

The scope of the present book is to offer the most efficient tools for the vectorization of serial computer programs. Here, by vectorization we understand the adaptation of computer programs to the special architecture of modern available vector computers to exploit fully their potential, which will often result in remarkable performance improvements. The book is written primarily for users working in the various fields of computational physics, for scientists as well as for programmers running their jobs on a vector computer. The text may, however, also be of value to those who are interested in numerical algorithms. Although the examples discussed in chapter 9 have been taken from Computational Fluid Dynamics, the numerical methods are well-known, and are applied in many fields of Computational Physics. The book is divided into four parts. After a short introduction which outlines the limits of conventional serial computers in contrast to the possibilities offered by the new vector machines, the second part is addressed to the discussion of some main features of existing computer architectures. We restrict ourselves to the vector computers CRAY-1S and CDC-CYBER 205, although, in the meantime, many vector and parallel computers and array processors are available such as DENELCOR's Heterogeneous Element Processor (HEP), ICL's Distributed Array Processor (DAP), SPERRY UNIVAC's Array Processing System (APS), STAR TECHNOLOGIES ST-l00, FLOATING POINT SYSTEMS' Array Processor (FPS), FUJITSU's FACOM VP-l00 and VP-200, HITACHI's Integrated Array Processor (lAP), HITACHI's S 810/10 and S 810/20 and others.

Spis treści

1. Introduction: Supercomputers in Computational Fluid Dynamics.- 2. Computer Architectures.- 2.1 The Basic Computer Systems.- 2.2. The CRAY-1 Series.- 2.3. The CDC CYBER 205.- 3. Vectorization of FORTRAN Programs.- 3.1 Implementation of Serial Programs on Vector Computers.- 3.2 Vectorization on the CRAY-1.- 3.3 Vectorization on the CDC CYBER 205.- 4. Vectorization of a Sample Program on Different Vector and Parallel Computers.- 4.1 Vectorization on the CRAY-1.- 4.2 Vectorization on the CDC CYBER 205.- 4.3 Vectorization on HITACHI’s S9 with IAP.- 4.4 Vectorization on the ICL DAP.- 4.5 Parallelization on DENELCOR’s HEP.- 5. Restructuring of Basic Linear Algebra Algorithms.- 5.1 Basic Vector Operations.- 5.2 Matrix Multiplication for Banded Matrices.- 5.3 Gaussian Elimination for the Solution of Algebraic Systems with Full Matrices.- 5.4 Linear and Nonlinear Recurrences.- 6. Iterative Methods for a Model Problem.- 6.1 Jacobi Type Methods.- 6.2 Gauss-Seidel Type Methods.- 6.3 Group Iterative Methods.- 7. Vectorization of Simple Numerical Algorithms.- 7.1 Polynomial Evaluation.- 7.2 The Power Method for the Computation of the Largest Eigenvalue of a Matrix.- 7.3 Cyclic Reduction.- 7.4 Systems of Nonlinear Equations.- 7.5 Runge-Kutta Time-Stepping Methods for Systems of Ordinary Differential Equations.- 7.6 An Explicit Superstep Method for the Solution of Parabolic Differential Equations.- 7.7 Finite Difference Smoothing.- 8. References to Chapters 1 to 7.- 8.1 Vector and Parallel Algorithms.- 8.2 Further Applications.- 9. Vectorization of Algorithms in Computational Fluid Dynamics on the CRAY-1 Vector Computer.- 9.1 MacCormack’s Methods and Vectorization.- 9.2 Vectorization of the Implicit Beam and Warming Scheme.- 9.3 Vectorization of an Implicit Finite Difference Method for the Solution of the Laminar Boundary-Layer Equations.- 9.4 Vectorization of the Galerkin-Method R. Kessler.- 9.5 Vectorization of the Direct Monte-Carlo Simulation.