Parallel Scientific Computing 1st Edition by Frédéric Magoules, Francois Xavier Roux, Guillaume Houzeaux 9781848215818 1848215819
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ISBN 10: 1848215819
ISBN 13: 9781848215818
Author: Frédéric Magoules, Francois Xavier Roux, Guillaume Houzeaux
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.
Table of contents:
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
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Tags: Frédéric Magoules, Francois Xavier Roux, Guillaume Houzeaux, Parallel