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.
CITATION STYLE
Loiseau, J. C., Bucci, M. A., Cherubini, S., & Robinet, J. C. (2019). Time-stepping and krylov methods for large-scale instability problems. In Computational Methods in Applied Sciences (Vol. 50, pp. 33–73). Springer Netherland. https://doi.org/10.1007/978-3-319-91494-7_2
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