Parallel Computations

Garry Rodrigue

• Publisher: Academic Press
• Year: 2014
• ISBN:
  9781483276649
• Topic: Mathematik
• Subtopic: Mathematik Allgemein

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

• Front Cover
• Parallel Computations
• Copyright Page
• Table of Contents
• List of Contributors
• Preface
• Chapter 1. A Guide to Parallel Computation and Some Cray-1 Experiences
• Chapter 2. Vectorizing the FFTs
• Chapter 3. Solution of Single Tridiagonal Linear Systems and Vectorization of the ICCG Algorithm on the Cray-1
• Chapter 4. An Implicit Numerical Solution of the Two-Dimensional Diffusion Equation and Vectorization Experiments
• Chapter 5. Swimming Upstream: Calculating Table Lookups and Piecewise Functions
• Chapter 6. Trade-Offs in Designing Explicit Hydrodynamical Schemes for Vector Computers
• Chapter 7. Vectorized Computation of Reactive Flow
• Chapter 8. A Fully Implicit, Factored Code for Computing Three-Dimensional Flows on the ILLIAC IV
• Chapter 9. A Time-Split Difference Scheme for the Compressible Navier–Stokes Equations with Applications to Flows in Slotted Nozzles
• Chapter 10. Geophysical Fluid Simulation on a Parallel Computer
• Chapter 11. Experiences with a Floating Point Systems Array Processor
• Chapter 12. A Case Study in the Application of a Tightly Coupled Multiprocessor to Scientific Computations
• Chapter 13. Computer Modeling in Plasma Physics on the Parallel-Architecture CHI Computer
• Index