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.
It is primarily intended for Masters students in engineering or applied mathematics and presumes some knowledge in numerical analysis, as well as a basic knowledge of computing concepts. It could also be interesting for any engineer faced with the numerical simulation of large-scale problems resulting from systems that are modeled by partial differential equations.

Fr&Eeacute;déric Magoulès is Professor at LISA / MAS école Centrale Paris, France.

François-Xavier Roux is Professor at University Pierre & Marie Curie - Paris 6, France.

Preface

Part 1 – Parallel calculators, programming and algorithms

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 full matrices

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 for symmetric and positive matrices

Chapter 12 – Methods with exact orthogonalization for any matrix

Chapter 13 – Methods with biorthogonalization for nonsymmetrical matrices

Chapter 14 – Parallelization of Krylov methods

Chapter 15 – Parallel preconditioning methods

Bibliography

Exercises

Bibliography

Index