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Stability Limitations in Simulation of Dynamical Systems with Multiple Time-Scales

Sadegh Rahrovani (Institutionen för tillämpad mekanik, Dynamik) ; Thomas Abrahamsson (Institutionen för tillämpad mekanik, Dynamik) ; Klas Modin (Institutionen för matematiska vetenskaper, matematik)
Conference Proceedings of the Society for Experimental Mechanics Series (2191-5644). Vol. 1 (2016), p. 93-105.
[Konferensbidrag, refereegranskat]

This paper focuses on the stability properties of a recently proposed exponential integrator particularly in simulation of highly oscillatory systems with multiple time-scales. The linear and nonlinear stability properties of the presented exponential integrator have been studied. We illustrate this with the Fermi–Pasta–Ulam (FPU) problem, a highly oscillatory nonlinear system known as a test benchmark for multi-scale time integrators. This example is also illustrative when studying the numerical resonance and algorithmic instability in the multi-time-stepping (MTS) methods, such as in exponential and/or trigonometric integration schemes, since it has no external input force and therefore no real physical resonance.

Nyckelord: Algorithmic instability; Numerical resonance; Multiple time-scale; Exponential integrator; Linear stability



Denna post skapades 2016-02-24. Senast ändrad 2016-09-28.
CPL Pubid: 232381

 

Institutioner (Chalmers)

Institutionen för tillämpad mekanik, Dynamik
Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematisk analys
Annan maskinteknik

Chalmers infrastruktur

C3SE/SNIC (Chalmers Centre for Computational Science and Engineering)