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 Open MP.
สารบัญ
Preface
Part 1 – Parallel calculators, programming andalgorithms
Chapter 1 – Calculator architectures
Chapter 2 – Parallelization and programming models
Chapter 3 – Concepts of parallel algorithmics
Bibliography
Exercises
Part 2 – Additional numerical matrix analysis
Chapter 4 – Introduction to numerical matrix analysis
Chapter 5 – Sparse matrices
Chapter 6 – Linear system resolution
Bibliography
Exercises
Part 3 – Direct resolution methods
Chapter 7 – Linear system resolution by LU methods
Chapter 8 – Parallelization of LU methods for fullmatrices
Chapter 9 – LU methods for sparse matrices
Bibliography
Exercises
Part 4 – Iterative resolution methods
Chapter 10 – Introduction to Krylov spaces
Chapter 11 – Methods with complete orthogonalization forsymmetric and positive matrices
Chapter 12 – Methods with exact orthogonalization for anymatrix
Chapter 13 – Methods with biorthogonalization fornonsymmetrical matrices
Chapter 14 – Parallelization of Krylov methods
Chapter 15 – Parallel preconditioning methods
Bibliography
Exercises
Bibliography
Index
เกี่ยวกับผู้แต่ง
Frdéric Magoulès is Professor at LISA / MAS école Centrale Paris, France.
François-Xavier Roux is Professor at University Pierre & Marie Curie – Paris 6, France.
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