This is an introductory book on supercomputer applications written by a researcher who is working on solving scientific and engineering application problems on parallel computers. The book is intended to quickly bring researchers and graduate students working on numerical solutions of partial differential equations with various applications into the area of parallel processing.The book starts from the basic concepts of parallel processing, like speedup, efficiency and different parallel architectures, then introduces the most frequently used algorithms for solving PDEs on parallel computers, with practical examples. Finally, it discusses more advanced topics, including different scalability metrics, parallel time stepping algorithms and new architectures and heterogeneous computing networks which have emerged in the last few years of high performance computing. Hundreds of references are also included in the book to direct interested readers to more detailed and in-depth discussions of specific topics. 1. Introduction. 1.1. Exploiting parallelism. 1.2. Parallel computers. 1.3. Performance evaluations -- 2. Parallel algorithms for solving PDE. 2.1. Discretization by finite difference method. 2.2. Parallel relaxation algorithms. 2.3. Parallel ADI algorithm. 2.4. Parallel multigrid method. 2.5. Parallel conjugate gradient algorithm -- 3. Implementations. 3.1. Intel iPSC/860 hypercubes. 3.2. Inter-processor communications on iPSC/860. 3.3. Communication analysis for domain decomposition method. 3.4. Bandwidth improvement using forced message type. 3.5. KSR-1 parallel computers. 3.6. Automatic, semi-automatic and manual parallelization -- 4. Applications. 4.1. Numerical solution of Poisson's equation. 4.2. Numerical simulations of multi-phase flow. 4.3. Discretization and parallelization. 4.4. Numerical experiments -- 5. Parallel time stepping algorithms. 5.1. A new dimension for parallelization. 5.2. Waveform relaxation. 5.3. Pipeline iteration. 5.4. Window relaxation. 5.5. Parabolic multigrid method. 5.6. General form of parallel time stepping algorithms. 5.7. Complexity analysis -- 6. Future development. 6.1. More on performance evaluations. 6.2. Programming language. 6.3. Automatic parallelization tools. 6.4. Distributed computing network. 6.5. Metacenters and metacomputers This is an introductory book on supercomputer applications written by a researcher who is working on solving scientific and engineering application problems on parallel computers. The book is intended to quickly bring researchers and graduate students working on numerical solutions of partial differential equations with various applications into the area of parallel processing. The book starts from the basic concepts of parallel processing, like speedup, efficiency and different parallel architectures, then introduces the most frequently used algorithms for solving PDEs on parallel computers, with practical examples. Finally, it discusses more advanced topics, including different scalability metrics, parallel time stepping algorithms and new architectures and heterogeneous computing networks which have emerged in the last few years of high performance computing. Hundreds of references are also included in the book to direct interested readers to more detailed and in-depth discussions of specific topics
