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Chapitre D'ouvrage Année : 2018

Time-Stepping and Krylov Method for large scale instability problems

Résumé

With the ever increasing computational power available and the development of high-performances computing, investigating the properties of realistic very large-scale nonlinear dynamical systems has become reachable. It must be noted however that the memory capabilities of computers increase at a slower rate than their computational capabilities. Consequently, the traditional matrix-forming approaches wherein the Jacobian matrix of the system considered is explicitly assembled become rapidly intractable. Over the past two decades, so-called matrix-free approaches have emerged as an efficient alternative. The aim of this chapter is thus to provide an overview of well-grounded matrix-free methods for fixed points computations and linear stability analyses of very large-scale nonlinear dynamical systems.
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Dates et versions

hal-02445571 , version 1 (20-01-2020)

Identifiants

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Jean-Christophe Loiseau, M. A. Bucci, S. Cherubini, Jean-Christophe Robinet. Time-Stepping and Krylov Method for large scale instability problems. Computational modelling of bifurcations and instabilities in fluid dynamics, Springer, pp.33-73, 2018, 9783319914947. ⟨10.1007/978-3-319-91494-7_2⟩. ⟨hal-02445571⟩
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