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Parallel Computations.

By: Rodrigue, Garry.
Material type: materialTypeLabelBookSeries: eBooks on Demand.Publisher: Saint Louis : Elsevier Science & Technology, 2014Copyright date: ©1982Description: 1 online resource (416 pages).Content type: text Media type: computer Carrier type: online resourceISBN: 9781483276649.Subject(s): Parallel processing (Electronic computers) | Science -- Data processingGenre/Form: Electronic books.Additional physical formats: Print version:: Parallel ComputationsDDC classification: 004/.35 Online resources: Click here to view this ebook.
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 -- 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 -- ACKNOWLEDGMENTS -- REFERENCES -- Chapter 2. 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 -- REFERENCES -- Chapter 3. 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 -- ACKNOWLEDGMENTS -- REFERENCES -- Chapter 4. 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 -- REFERENCES -- Chapter 5. 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 -- REFERENCES -- Chapter 6. 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 -- V. THE EXAMPLE OF THE INTERACTION OF TWO BLAST WAVES -- VI. CONCLUSIONS -- REFERENCES -- Chapter 7. 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 -- ACKNOWLEDGMENTS -- REFERENCES -- Chapter 8. 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 -- REFERENCES -- Chapter 9. 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 -- ACKNOWLEDGMENTS -- REFERENCES -- Chapter 10. 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 -- ACKNOWLEDGMENTS -- Chapter 11. 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.
VI. THE TWO-MACHINE ENVIRONMENT -- VII. PRACTICAL PROBLEMS OF AP OWNERSHIP -- VIII. CONCLUSIONS -- ACKNOWLEDGMENTS -- REFERENCES -- Chapter 12. 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 -- Chapter 13. 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 -- ACKNOWLEDGMENTS -- REFERENCES -- Index.
Summary: 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.
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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 -- 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 -- ACKNOWLEDGMENTS -- REFERENCES -- Chapter 2. 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 -- REFERENCES -- Chapter 3. 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 -- ACKNOWLEDGMENTS -- REFERENCES -- Chapter 4. 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 -- REFERENCES -- Chapter 5. 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 -- REFERENCES -- Chapter 6. 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 -- V. THE EXAMPLE OF THE INTERACTION OF TWO BLAST WAVES -- VI. CONCLUSIONS -- REFERENCES -- Chapter 7. 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 -- ACKNOWLEDGMENTS -- REFERENCES -- Chapter 8. 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 -- REFERENCES -- Chapter 9. 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 -- ACKNOWLEDGMENTS -- REFERENCES -- Chapter 10. 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 -- ACKNOWLEDGMENTS -- Chapter 11. 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.

VI. THE TWO-MACHINE ENVIRONMENT -- VII. PRACTICAL PROBLEMS OF AP OWNERSHIP -- VIII. CONCLUSIONS -- ACKNOWLEDGMENTS -- REFERENCES -- Chapter 12. 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 -- Chapter 13. 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 -- ACKNOWLEDGMENTS -- REFERENCES -- Index.

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.

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