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Time-Stepping and Krylov Method for large scale instability problems

Chapitre d'ouvrage scientifique
Author
BUCCI, Michele Alessandro
541882 Institut Jean Le Rond d'Alembert [DALEMBERT]
CHERUBINI, Stefania
132974 Università degli studi di Catania = University of Catania [Unict]
158937 Dipartimento di Metodologie Fisiche e Chimiche per l'Ingegneria
ccROBINET, Jean-Christophe
134975 Laboratoire de Dynamique des Fluides [DynFluid]
492366 Airbus Safran Launchers
ccLOISEAU, Jean-Christophe

URI
http://hdl.handle.net/10985/17840
DOI
10.1007/978-3-319-91494-7_2
Date
2018

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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