Coarse Grid Correction for Algebraic Domain Decomposition Solvers

Louis Poirel 1 Emmanuel Agullo 1 Luc Giraud 1
1 HiePACS - High-End Parallel Algorithms for Challenging Numerical Simulations
LaBRI - Laboratoire Bordelais de Recherche en Informatique, Inria Bordeaux - Sud-Ouest
Abstract : Over the last few decades, there have been innumerable science, engineering and societal breakthroughs enabled by the development of High Performance Computing (HPC) applications, algorithms and architectures. In the context of this talk, our focus is on numerical linear algebra algorithms that appear in many large scale simulations and are often the most time consuming numerical kernel; more precisely we consider numerical schemes for the solution of large sparse systems of linear equations. In this talk, we will first cover the spectrum of the ongoing research activities of the HiePACS Inria team that ranges from dense and sparse direct solvers to novel block Krylov methods. The core of this presentation will focus on hybrid methods that hierarchically combine direct and iterative methods for the solution of large sparse systems of linear equations. These techniques inherit the advantages of each approach, namely the limited amount of memory and natural parallelization for the iterative component and the numerical robustness of the direct part. In order to perform extreme scale simulations on large distributed platforms, the number of iterations is often the main limitation of these methods since the convergence may deteriorate with the number of computational nodes. Taking into account a low-rank approximation of our problem, we are able to alleviate this penalizing numerical effect. Focusing on the distributed sparse hybrid solver MaPHyS developed in the HiePACS Inria team, we will show how the adaptation of a semi-algebraic coarse space originally proposed in the context of domain decomposition methods ensures the scalability of a distributed sparse hybrid solver.
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https://hal.inria.fr/hal-01355534
Contributor : Louis Poirel <>
Submitted on : Tuesday, August 23, 2016 - 3:24:40 PM
Last modification on : Thursday, May 9, 2019 - 11:58:12 AM

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  • HAL Id : hal-01355534, version 1

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Louis Poirel, Emmanuel Agullo, Luc Giraud. Coarse Grid Correction for Algebraic Domain Decomposition Solvers. ECCOMAS Congress 2016, Jun 2016, Hersonissos, Greece. ⟨hal-01355534⟩

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