Parallel Scientific Computing

Scientific computing has become an indispensable tool in numerous fields, such as physics, mechanics, biology, finance and industry. For example, it enables us, thanks to efficient algorithms adapted to current computers, tosimulate, without the help of models or experimentations, the deflection of beams in bending, the sound level in a theater room or a fluid flowing around an aircraft wing. This book presents the scientific computing techniques applied to parallel computing for the numerical simulation of large-scale problems; these problems result from systems modeled by partial differential equations. Computing concepts will be tackled via examples. Implementation and programming techniques resulting from the finite element method will be presented for direct solvers, iterative solvers and domain decomposition methods, along with an introduction to MPI and OpenMP.

Table of Contents -- Title -- Copyright -- Preface -- Introduction -- 1 Computer Architectures -- 1.1. Different types of parallelism -- 1.2. Memory architecture -- 1.3. Hybrid architecture -- 2 Parallelization and Programming Models -- 2.1. Parallelization -- 2.2. Performance criteria -- 2.3. Data parallelism -- 2.4. Vectorization: a case study -- 2.5. Message-passing -- 2.6. Performance analysis -- 3 Parallel Algorithm Concepts -- 3.1. Parallel algorithms for recurrences -- 3.2. Data locality and distribution: product of matrices -- 4 Basics of Numerical Matrix Analysis -- 4.1. Review of basic notions of linear algebra -- 4.2. Properties of matrices -- 5 Sparse Matrices -- 5.1. Origins of sparse matrices -- 5.2. Parallel formation of sparse matrices: shared memory -- 5.3. Parallel formation by block of sparse matrices: distributed memory -- 6 Solving Linear Systems -- 6.1. Direct methods -- 6.2. Iterative methods -- 7 LU Methods for Solving Linear Systems -- 7.1. Principle of LU decomposition -- 7.2. Gauss factorization -- 7.3. Gauss-Jordan factorization -- 7.4. Crout and Cholesky factorizations for symmetric matrices -- 8 Parallelization of LU Methods for Dense Matrices -- 8.1.…