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Time-Stepping and Krylov Methods for Large-Scale Instability Problems

  • J.-Ch. Loiseau
  • M. A. Bucci
  • S. Cherubini
  • J.-Ch. RobinetEmail author
Chapter
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 50)

Abstract

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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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • J.-Ch. Loiseau
    • 1
  • M. A. Bucci
    • 1
  • S. Cherubini
    • 2
  • J.-Ch. Robinet
    • 1
    Email author
  1. 1.Laboratoire DynFluidArts et Métiers ParisTechParisFrance
  2. 2.DMMM, Politecnico di BariBariItaly

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