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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Magoulès, F. (Frédéric)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Wiley, 2015.
Colección:Iste
Temas:
Parallel processing > Industrial applications.
Parallel algorithms > Industrial applications.
Industrial engineering > Mathematics.
Algorithmes parallèles > Applications industrielles.
COMPUTERS > Computer Engineering.
Industrial engineering > Mathematics
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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. Block factorization
  • 8.2. Implementation of block factorization in a message-passing environment
  • 8.3. 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 matrices.
  • 11.2. 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 method
  • 13.3. 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
  • 15.4. Algebraic multigrid
  • 15.5. The Schwarz additive method of preconditioning
  • 15.6. Preconditioners based on the physics
  • Appendices
  • Appendix 1: Exercises
  • A1.1. Parallelization techniques
  • A1.2. Matrix analysis
  • A1.3. Direct methods
  • A1.4. Iterative methods
  • A1.5. Domain decomposition methods
  • Appendix 2: Solutions
  • A2.1. Parallelization techniques
  • A2.2. Matrix analysis
  • A2.3. Direct methods
  • A2.4. Iterative methods
  • A2.5. Domain decomposition methods
  • Appendix 3: Bibliography and Comments
  • A3.1. Parallel algorithms
  • A3.2. OpenMP
  • A3.3. MPI
  • A3.4. Performance tools
  • A3.5. Numerical analysis and methods.
  • A3.6. Finite volume method
  • A3.7. Finite element method
  • A3.8. Matrix analysis
  • A3.9. Direct methods
  • A3.10. Iterative methods
  • A3.11. Mesh and graph partitioning
  • A3.12. Domain decomposition methods
  • Bibliography
  • Index
  • End User License Agreement.

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