Efficient Parallel Resolution of The Simplified Transport Equations in Mixed-Dual Formulation

Maxime Barrault (1) , Bruno Lathuilière (1) , Pierre Ramet (2, 3) , Jean Roman (2, 4)

1 EDF - EDF
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique
3 BACCHUS - Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems
4 HiePACS - High-End Parallel Algorithms for Challenging Numerical Simulations

A reactivity computation consists of computing the highest eigenvalue of a generalized eigenvalue problem, for which an inverse power algorithm is commonly used. Very fine modelizations are difficult to treat for our sequential solver, based on the simplified transport equations, in terms of memory consumption and computational time. A first implementation of a Lagrangian based domain decomposition method brings to a poor parallel efficiency because of an increase in the power iterations. In order to obtain a high parallel efficiency, we improve the parallelization scheme by changing the location of the loop over the subdomains in the overall algorithm and by benefiting from the characteristics of the Raviart-Thomas finite element. The new parallel algorithm still allows us to locally adapt the numerical scheme (mesh, finite element order). However, it can be significantly optimized for the matching grid case. The good behavior of the new parallelization scheme is demonstrated for the matching grid case on several hundreds of nodes for computations based on a pin-by-pin discretization.

Domaines: Calcul parallèle, distribué et partagé [cs.DC]

Maxime Barrault, Bruno Lathuilière, Pierre Ramet, Jean Roman. Efficient Parallel Resolution of The Simplified Transport Equations in Mixed-Dual Formulation. Journal of Computational Physics, 2011, 230 (5), pp.2004-2020. ⟨10.1016/j.jcp.2010.11.047⟩. ⟨hal-00547406⟩