Abstract

Existing numerical algorithms face their limits when running on a large number of cores. For instance, parallel iterative methods meet serious scalability limitation due to the syn- chronization procedure occurring between the processors at the end of each iteration. The traditional scheme for parallel iterative algorithms is synchronous iterations. This describes a method where a new iteration is only started when all the data from the previous one has been received. These iterative algorithms have been widely studied and are often simply called parallel iterative algorithms, synchronous being omitted. Another kind of iterative scheme, called chaotic iterations, can help solve these scalability problems.

Iterative domain decomposition methods are well suited for parallel computations. Indeed, the division of a problem into smaller subproblems, through artificial subdivisions of the do- main, is a means for introducing parallelism. Iterative domain decomposition strategies include in one way or another the following ingredients : (i) a decomposer to split a mesh into subdo- mains ; (ii) local solvers to find solutions for the subdomains for specific boundary conditions on the interface; (iii) interface conditions enforcing compatibility and equilibrium between overlapping or non-overlapping subdomains; (iv) an iterative solution strategy for the inter- face problem. The differences between the methods lies in how those ingredients are actually put to work and how they are combined to form an efficient solution strategy for the problem at hand.

This talk shows how iterative domain decomposition methods have efficiently evolved over the years. In order to use such methods on massive parallel computers, the iterative scheme should be modified, and chaotic iterations are here proposed for the solution strategy of the interface problem, leading to some convergence difficulties. After the presentation of the method, numerical experiments are performed in parallel on large scale engineering problems to illustrate the robustness and efficiency of the proposed method.

Bio

Frederic Magoules is Professor of Applied Mathematics and Computer Science at CentraleSupelec, Universite Paris-Saclay (France).

Frederic Magoules graduated with a B.Sc. in Engineering Sciences in 1993, a M.Sc. in Applied Mathematics in 1994 and a M.Sc. in Numerical Analysis in 1995, from Universite Pierre & Marie Curie. He received his Ph.D. in Applied Mathematics from Universite Pierre Marie Curie in 2000. He then post-doc'ed and taught there for one year, as Assistant Professor of Numerical Analysis, prior to joining Universite Henri Poincare in 2000 as Assistant and then Associate Professor of Applied Mathematics and Engineering. He received his HDR (Habilitation a Diriger des Recherches) from Universite Pierre & Marie Curie in 2005. He joined Ecole Centrale des Arts et Manufactures in 2006 as Professor of Applied Mathematics (in 2015, Ecole Centrale des Arts et Manufactures merged with Supelec and became CentraleSupelec).

With backgrounds in Computational Science and Engineering, Applied Mathematics, Computer Science, and consulting experience with industry and national laboratories, Frederic Magoules works at the algorithmic interface between parallel computing and the numerical analysis of partial differential equations and algebraic differential equations. Frederic Magoules and his research group design, analyze, develop, and validate mathematical models and computational methods for the high-performance simulation of multidisciplinary scientific and engineering problems.

Frederic Magoules was awarded the IBM Faculty Award (IBM, USA), the CUDA Research Center Award (Nvidia, USA), the Microsoft Research Academic Award (Microsoft, USA), the CUDA Teaching Center Award (Nvidia, USA). He is a Fellow of two international societies: the Institute of Mathematics and its Applications (IMA, United Kingdom), the British Computer Society (BCS, United Kingdom). He is also Fellow of the Institute of Intelligent Computing, Communication and Control (China). He has been conferred the title of Adjunct Professor at Ecole Polytechnique (France), Visiting Professor at University of Greenwich (United Kingdom), Honorary Professor of the University of Pecs (Hungary), Visiting Professor at Jianghan University (China), Guest Professor at Wuhan University of Science and Technology (China), Visiting Professor at Doshisha University (Japan).

Author or co-author of over 150 refeered publications in Computational Science and Engineering, Applied Mathematics, and Computer Science, Frederic Magoules has authored 8 books, and edited 8 books. Frederic Magoules is Editor of International Journal of Computer Mathematics (Taylor & Francis), Frontiers of Computer Science (Springer), Advances in Engineering Software (Elsevier), Engineering Applications of Computational Fluid Mechanics (Taylor & Francis), Pollack Periodica (Akademiai Kiado), Journal of Algorithms and Computational Technologies (Sage). He also serves as Guest Editor of thirteen Journal Special Issues of international scientific journals