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Communication avoiding iterative solvers and preconditioners

The cost of moving data in an algorithm can surpass by several orders of magnitude the cost of performing arithmetics, and this gap has been steadily and exponentially growing over time. This talk will review work performed in the recent years on a new class of algorithms for numerical linear algebra that drastically reduce the communication cost with respect to classic algorithms, or even provably minimize it in several cases. We focus in particular on enlarged Krylov subspace methods and preconditioners based on low rank corrections for solving large sparse linear systems of equations on massively parallel computers. We also discuss several associated computational kernels as computing a low rank approximation of a sparse matrix. The efficiency of the proposed methods is tested on matrices arising from linear elasticity problems as well as convection diffusion problems with highly heterogeneous coefficients.

CMAP UMR 7641 École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex France, Tél: +33 1 69 33 46 23 Fax: +33 1 69 33 46 46