Scientific computing has become an indispensable tool in numerous fields, such as physics, biology, chemistry, finance and engineering. For example, it enables us, thanks to efficient algorithms adapted to current computers and supercomputers, to simulate complex phenomena, without the help of models or experimentations. Some examples are the structural behaviors of civil engineering structures, the sound level in a theater, a fluid flowing around an aircraft or a Formula 1 car, and the hydrodynamics of a racing yacht.
This book presents the scientific computing techniques applied to parallel computing for the numerical simulation of large-scale problems; these problems mainly result from systems modeled by partial differential equations. Computing concepts are tackled via examples. Implementation and programming techniques resulting from the finite element, finite volume and finite difference methods are presented for direct solvers, iterative solvers and domain decomposition methods, along with an introduction to MPI and OpenMP.
1. Computer Architectures.
2. Parallelization and Programming Models.
3. Parallel Algorithm.
4. Basics of Numerical Matrix.
5. Sparse Matrices.
6. Solving Linear Systems.
7. LU Methods for Solving Linear Systems.
8. Parallelization of LU Methods for Dense Matrices.
9. LU Methods for Sparse Matrices.
10.Basics of Krylov Subspaces.
11. Methods with Complete Orthogonalization for Symmetric Positive.
12. Exact Orthogonalization Methods for Arbitrary Matrices.
13. Biorthogonalization Methods for Non-symmetric.
14. Parallelization of Krylov Methods.
15. Parallel Preconditioning Methods.
Frédéric Magoulès is Professor at Ecole Centrale Paris in France and Honorary Professor at the University of Pecs in Hungary. His research focuses on parallel computing and numerical linear algebra.
François-Xavier Roux is Professor at Université Pierre et Marie Curie and an Engineer at ONERA, in France. His research focuses on parallel computing and numerical analysis.
Guillaume Houzeaux is Team Leader at the Barcelona Supercomputing Center in Spain. His research focuses on high performance computational mechanics.
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