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Structure analysis of higher‐order variational integrators and implementation of SUNDMAN adaptivity in time
Author(s) -
Masser Robin,
Bartelt Matthias,
Groß Michael
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610099
Subject(s) - integrator , convergence (economics) , computer science , quadrature (astronomy) , transformation (genetics) , mathematical optimization , mathematics , order (exchange) , algorithm , engineering , computer network , biochemistry , chemistry , bandwidth (computing) , finance , economics , gene , economic growth , electrical engineering
In this paper, we investigate the use of different higher‐order polynomial bases for the temporal approximation as well as various higher‐order quadrature rules. The resulting time integration schemes partially differ in their numerical properties, especially in order convergence and energy error. Further, an adaptivity of the time increment to optimize the computational effort is implemented using a time transformation according to SUNDMAN. Using an example with viscoelastic material behavior that models a bungee jumper, we show its advantages to minimize the energy error. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)