Parallel scientific computing / Frédéric Magoulès, François-Xavier Roux, Guillaume Houzeaux.

Format:

Book

Author/Creator:

Magoulès, F. (Frédéric), author.

Roux, François-Xavier, author.

Houzeaux, G. (Guillaume), author.

Language:

English

Subjects (All):

Parallel processing (Electronic computers)--Industrial applications.

Parallel processing (Electronic computers).

Parallel algorithms--Industrial applications.

Parallel algorithms.

Industrial engineering--Mathematics.

Industrial engineering.

Physical Description:

1 online resource (287 p.)

Edition:

1st ed.

Place of Publication:

London, England ; Hoboken, New Jersey : ISTE : Wiley, 2016.

Summary:

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, to simulate, 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.

Contents:

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 matrices5 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. Block factorization

8.2. Implementation of block factorization in a message-passing environment8.3. Parallelization of forward and backward substitutions; 9 LU Methods for Sparse Matrices; 9.1. Structure of factorized matrices; 9.2. Symbolic factorization and renumbering; 9.3. Elimination trees; 9.4. Elimination trees and dependencies; 9.5. Nested dissections; 9.6. Forward and backward substitutions; 10 Basics of Krylov Subspaces; 10.1. Krylov subspaces; 10.2. Construction of the Arnoldi basis; 11 Methods with Complete Orthogonalization for Symmetric Positive Definite Matrices

11.1. Construction of the Lanczos basis for symmetric matrices11.2. The Lanczos method; 11.3. The conjugate gradient method; 11.4. Comparison with the gradient method; 11.5. Principle of preconditioning for symmetric positive definite matrices; 12 Exact Orthogonalization Methods for Arbitrary Matrices; 12.1. The GMRES method; 12.2. The case of symmetric matrices: the MINRES method; 12.3. The ORTHODIR method; 12.4. Principle of preconditioning for non-symmetric matrices; 13 Biorthogonalization Methods for Non-symmetric Matrices; 13.1. Lanczos biorthogonal basis for non-symmetric matrices

13.2. The non-symmetric Lanczos method13.3. The biconjugate gradient method: BiCG; 13.4. The quasi-minimal residual method: QMR; 13.5. The BiCGSTAB; 14 Parallelization of Krylov Methods; 14.1. Parallelization of dense matrix-vector product; 14.2. Parallelization of sparse matrix-vector product based on node sets; 14.3. Parallelization of sparse matrix-vector product based on element sets; 14.4. Parallelization of the scalar product; 14.5. Summary of the parallelization of Krylov methods; 15 Parallel Preconditioning Methods; 15.1. Diagonal; 15.2. Incomplete factorization methods

15.3. Schur complement method

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed January 13, 2016).

ISBN:

9781118761724

1118761723

9781118761717

1118761715

OCLC:

933442910