SCHEDULE: NOV 16-22, 2013

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Scalable Domain Decomposition Preconditioners For Heterogeneous Elliptic Problems

SESSION: Preconditioners and Unstructured Meshes

EVENT TYPE: Papers, Awards, Best Paper Finalists

TIME: 2:00PM - 2:30PM

SESSION CHAIR: George Biros

AUTHOR(S):Pierre Jolivet, Frédéric Hecht, Frédéric Nataf, Christophe Prud'homme

ROOM:401/402/403

ABSTRACT:
Domain decomposition methods are, alongside multigrid methods, one of the dominant paradigms in contemporary large-scale partial differential equation simulation. In this paper, a lightweight implementation of a theoretically and numerically scalable preconditioner is presented in the context of overlapping methods. The performance of this work is assessed by numerical simulations executed on thousands of cores, for solving various highly heterogeneous elliptic problems in both 2D and 3D with billions of degrees of freedom. Such problems arise in computational science and engineering, in solid and fluid mechanics. While focusing on overlapping domain decomposition methods might seem too restrictive, it will be shown how this work can be applied to a variety of other methods, such as non-overlapping methods and abstract deflation based preconditioners. It is also presented how multilevel preconditioners can be used to avoid communication during an iterative process such as a Krylov method.

Chair/Author Details:

George Biros (Chair) - University of Texas at Austin

Pierre Jolivet - Laboratoire Jacques-Louis Lions

Frédéric Hecht - Laboratoire Jacques-Louis Lions

Frédéric Nataf - Laboratoire Jacques-Louis Lions

Christophe Prud'homme - Institut de Recherche Mathématique Avancée

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The full paper can be found in the ACM Digital Library