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Limitations of computing time savings in variational multirate integrations
Author(s) -
Gail Tobias,
Leyendecker Sigrid,
OberBlöbaum Sina
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410015
Subject(s) - macro , convergence (economics) , computer science , grid , relation (database) , mathematics , mathematical optimization , geometry , database , economics , programming language , economic growth
For systems that contain slow and fast dynamics, variational multirate integration schemes are used. These schemes split the system into parts which are simulated using a time grid consisting of micro and macro nodes. This leads to computing time savings, however not unlimited, for a certain number of micro steps per macro step the computing time is minimal. To find a relation between this minimum computing time and the number of variables in the system, the computing time for the Fermi‐Pasta‐Ulam problem (FPU) is measured for different numbers of masses and different numbers of micro steps. In addition, the numerical convergence of the variational multirate integration is shown for the FPU. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)