Output error behavior for discretizations of ergodic, chaotic systems of ordinary differential equations
Name
5.0112998.pdf
Size
3.4 MB
Format
Adobe PDF
Checksum (MD5)
f2d07410b7be5e0737021e658207d92c
Author(s)
Frontin, Cory V.
Darmofal, David L.
Date Issued
October 2022
Publisher
AIP Publishing
Citation
Frontin, Cory V. and Darmofal, David L. 2022. "Output error behavior for discretizations of ergodic, chaotic systems of ordinary differential equations." 34 (10).
Version
Final published version
Abstract
The use of numerical simulation for prediction of characteristics of chaotic dynamical systems inherently involves unpredictable processes. In this work, we develop a model for the expected error in the simulation of ergodic, chaotic ordinary differential equation (ODE) systems, which allows for discretization and statistical effects due to unpredictability. Using this model, we then generate a framework for understanding the relationship between the sampling cost of a simulation and the expected error in the result and explore the implications of the various parameters of simulations. Finally, we generalize the framework to consider the total cost—including unsampled spin-up timesteps—of simulations and consider the implications of parallel computational environments to give a realistic model of the relationship between wall-clock time and the expected error in simulation of a chaotic ODE system.
Subjects
Condensed Matter Physics
Fluid Flow and Transfer Processes
Mechanics of Materials
Computational Mechanics
Mechanical Engineering
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1063/5.0112998
