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An Introduction to Domain Decomposition Methods: Algorithms, Theory, and Parallel Implementation

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by Victorita Dolean, Pierre Jolivet, and Frédéric Nataf


2015 / x + 238 pages / Softcover / ISBN 978-1-611974-05-8 / List Price $81.50 / SIAM Member Price $57.05 / Order Code OT144

Keywords: parallel computing, iterative methods, domain decomposition methods, scientific computing, high performance computing


The purpose of this book is to offer an overview of the most popular domain decomposition methods for partial differential equations (PDEs). These methods are widely used for numerical simulations in solid mechanics, electromagnetism, flow in porous media, etc., on parallel machines from tens to hundreds of thousands of cores. The appealing feature of domain decomposition methods is that, contrary to direct methods, they are naturally parallel. The authors focus on parallel linear solvers.

The authors present

  • all popular algorithms both at the PDE level and at the discrete level in terms of matrices,
  • systematic scripts for sequential implementation in a free open-source finite element package as well as some parallel scripts, and
  • a new coarse space construction (two-level method) that adapts to highly heterogeneous problems.

This book is intended for those working in domain decomposition methods, parallel computing, and iterative methods, in particular those who need to implement parallel solvers for PDEs. It will also be of interest to mechanical, civil, and aeronautical engineers, physical and environmental scientists, and physicists in need of parallel PDE solvers.

About the Authors
Victorita Dolean is currently a Reader in the Department of Mathematics and Statistics, University of Strathclyde, Glasgow, United Kingdom. She has been a research assistant at the CMAP (Center of Applied Mathematics) at the École Polytechnique in Paris, assistant professor at the University of Evry and at the University of Nice, and visiting professor at the University of Geneva. Her research has been oriented toward practical and modern applications of scientific computing by developing interactions between academic and industrial partners and taking part in the life of the scientific community as a member of the Board of Directors of SMAI (Society of Industrial and Applied Mathematics in France).

Pierre Jolivet is a scientist at CNRS in the Toulouse Institute of Computer Science Research, France, working mainly in the field of parallel computing. Before that, he was an ETH Zürich Postdoctoral Fellow of the the Scalable Parallel Computing Lab, Zürich, Switzerland. He received his Ph.D. from Université de Grenoble, France, in 2014 for his work on domain decomposition methods and their applications on massively parallel architectures. During his Ph.D., Pierre visited the Oak Ridge National Laboratory, Tennessee, for three months in 2013. One of his papers was nominated for the best paper award at Supercomputing 2013.

Frédéric Nataf is a senior scientist at CNRS in Laboratory J.L. Lions at University Pierre and Marie Curie, France. He is also part of an INRIA team. His field of expertise is in high performance scientific computing (domain decomposition methods/approximate factorizations), absorbing/PML boundary conditions, and inverse problems. He has coauthored nearly 100 papers and given several invited plenary talks on these subjects. He developed the theory of optimized Schwarz methods and very recently the GENEO coarse space. This last method enables the solving of very large highly heterogeneous problems on large scale computers. The related paper was nominated for the best paper award at Supercomputing 2013.


ISBN: 9781611974058

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