Optimisations des solveurs linéaires creux hybrides basés sur une approche par complément de Schur et décomposition de domaine

Astrid Casadei 1, 2
Abstract : In this thesis, we focus on the parallel solving of large sparse linear systems. Our main interestis on direct-iterative hybrid solvers such as HIPS, MaPHyS, PDSLIN or ShyLU, whichrely on domain decomposition and Schur complement approaches. Althrough these solvers arenot as time and space consuming as direct methods, they still suffer from serious overheads. Ina first part, we thus present the existing techniques for reducing the memory consumption, andwe present a new method which does not impact the numerical robustness of the preconditioner.This technique reduces the memory peak by doing a special scheduling of computation, allocation,and freeing tasks in particular in the Schur coupling blocks of the matrix. In a second part,we focus on the load balancing of the domain decomposition in a parallel context. This problemconsists in partitioning the adjacency graph of the matrix in as many domains as desired. Wepoint out that a good load balancing for the most expensive steps of an hybrid solver such asMaPHyS relies on the balancing of both interior nodes and interface nodes of the domains.Through, until now, graph partitioners such as MeTiS or Scotch used to optimize only thefirst criteria (i.e., the balancing of interior nodes) in the context of sparse matrix ordering. Wepropose different variations of the existing algorithms to improve the balancing of interface nodesand interior nodes simultaneously. All our changes are implemented in the Scotch partitioner.We present our results on large collection of matrices coming from real industrial cases.
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Astrid Casadei. Optimisations des solveurs linéaires creux hybrides basés sur une approche par complément de Schur et décomposition de domaine. Autre [cs.OH]. Université de Bordeaux, 2015. Français. ⟨NNT : 2015BORD0186⟩. ⟨tel-01228520⟩

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