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Parallel Programming: for Multicore and Cluster Systems- P2

Parallel Programming: for Multicore and Cluster Systems- P2: Innovations in hardware architecture, like hyper-threading or multicore processors, mean that parallel computing resources are available for inexpensive desktop computers. In only a few years, many standard software products will be based on concepts of parallel programming implemented on such hardware, and the range of applications will be much broader than that of scientific computing, up to now the main application area for parallel computing | x Contents 6.2.5 Thread Scheduling in Java.331 6.2.6 Package java.util.concurrent.332 6.3 OpenMP.339 6.3.1 Compiler Directives.340 6.3.2 Execution Environment Routines.348 6.3.3 Coordination and Synchronization of Threads .349 6.4 Exercises for Chap. 6.353 7 Algorithms for Systems of Linear Equations .359 7.1 Gaussian Elimination .360 7.1.1 Gaussian Elimination and LU Decomposition.360 7.1.2 Parallel Row-Cyclic Implementation.363 7.1.3 Parallel Implementation with Checkerboard Distribution . 367 7.1.4 Analysis of the Parallel Execution Time .373 7.2 Direct Methods for Linear Systems with Banded Structure.378 7.2.1 Discretization of the Poisson Equation.378 7.2.2 Tridiagonal Systems.383 7.2.3 Generalization to Banded Matrices.395 7.2.4 Solving the Discretized Poisson Equation.397 7.3 Iterative Methods for Linear Systems.399 7.3.1 Standard Iteration Methods.400 7.3.2 Parallel Implementation of the Jacobi Iteration.404 7.3.3 Parallel Implementation of the Gauss-Seidel Iteration.405 7.3.4 Gauss-Seidel Iteration for Sparse Systems.407 7.3.5 Red-Black Ordering.411 7.4 Conjugate Gradient Method.417 7.4.1 Sequential CG Method.418 7.4.2 Parallel CG Method.420 7.5 Cholesky Factorization for Sparse Matrices.424 7.5.1 Sequential Algorithm.424 7.5.2 Storage Scheme for Sparse Matrices .430 7.5.3 Implementation for Shared Variables.432 7.6 Exercises for Chap. 7.437 References.441 Index.449 Chapter 1 Introduction In this short introduction we give an overview of the use of parallelism and try to explain why parallel programming will be used for software development in the future. We also give an overview of the rest of the book and show how it can be used for courses with various foci. 1.1 Classical Use of Parallelism Parallel programming and the design of efficient parallel programs have been well established in high-performance scientific computing for many years. The simulation of scientific problems is an important area in natural and engineering sciences of growing .