Applied Parallel Computing - Deng, Yuefan (World Scientific Publishing Company, 2012)
10.5. Diffusion Equation and Mechanical Engineering
Preface; CONTENTS; Chapter 1. Introduction; 1.1. Definition of Parallel Computing; 1.2. Evolution of Computers; 1.3. An Enabling Technology; 1.4. Cost Effectiveness; 1.4.1. Purchasing costs; 1.4.2. Operating costs; 1.4.3. Programming costs; Chapter 2. Performance Metrics and Models; 2.1. Parallel Activity Trace; 2.2. Speedup; 2.3. Parallel Efficiency; 2.4. Load Imbalance; 2.5. Granularity; 2.6. Overhead; 2.7. Scalability; 2.8. Amdahl's Law; Chapter 3. Hardware Systems; 3.1. Node Architectures; 3.2. Network Interconnections; 3.2.1. Topology; 3.2.2. Interconnect Technology
3.3. Instruction and Data Streams3.4. Processor-MemoryConnectivity; 3.5. IO Subsystems; 3.6. System Convergence; 3.7. Design Considerations; Chapter 4. Software Systems; 4.1. Node Software; 4.1.1. Operating systems; 4.1.2. Compilers and libraries; 4.1.3. Profilers; 4.2. Programming Models; 4.2.1. Message passing; 4.2.2. Shared-memory; 4.3. ParallelDebuggers; 4.4. Parallel Profilers; Chapter 5. Design of Algorithms; 5.1. Algorithm Models; 5.1.1. Master-slave; 5.1.2. Domain decomposition; 5.1.3. Control decomposition; 5.1.4. Virtual-shared-memory; 5.1.5. Comparison of programming models
5.1.6. Parallel algorithmic issues5.1.7. Levels of algorithmic complication; 5.2. Examples of Collective Operations; 5.2.1. Broadcast; 5.2.2. Gather and scatter; 5.2.3. Allgather; 5.3. Mapping Tasks to Processors; 5.3.1. Supply matrix; 5.3.2. Demand matrix; 5.3.3. Review of mapping models; 5.3.4. Mapping models and algorithms; Chapter 6. Linear Algebra; 6.1. Problem Decomposition; 6.2. Matrix Operations; 6.2.1. Matrix-vector multiplications; 6.2.2. Matrix-matrix multiplications; 6.3. Solution of Linear Systems; 6.3.1. Direct methods; 6.3.2. Iterative methods; 6.3.3. ADI.
Chapter 7. Differential Equations7.1. Integration and Differentiation; 7.1.1. Riemann summation for integration; 7.1.2. Monte Carlo method for integration; 7.1.3. Simple parallelization; 7.2. Partial Differential Equations; 7.2.1. Hyperbolic equations; 7.2.2. 3D Heat equation; 7.2.3. 2D Poisson equation; 7.2.4. 3D Poisson equation; 7.2.5. 3D Helmholtz equation; 7.2.6. Molecular dynamics; Chapter 8. Fourier Transforms; 8.1. Fourier Transforms; 8.2. Discrete Fourier Transforms; 8.3. Fast Fourier Transforms; 8.4. Simple Parallelization; 8.5. The Transpose Method; 8.6. Complexity Analysis for FFT.