Parallel Computations

List of ContributorsPrefaceA 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 ReferencesVectorizing 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 ReferencesSolution 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 ReferencesAn 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 ReferencesSwimming 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 ReferencesTrade-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 ReferencesVectorized 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 ReferencesA 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 ReferencesA 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 ReferencesGeophysical 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. ConclusionExperiences 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 ReferencesA 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 ReferencesComputer Modeling in Plasma Physics on the Parallel-Architecture CHI Computer I. Introduction II.