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Variational and linearly implicit integrators, with applications

Tao, Molei and Owhadi, Houman (2016) Variational and linearly implicit integrators, with applications. IMA Journal of Numerical Analysis, 36 (1). pp. 80-107. ISSN 0272-4979.

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We show that symplectic and linearly implicit integrators proposed by Zhang & Skeel (1997, Cheap implicit symplectic integrators. Appl. Numer. Math., 25, 297–302) are variational linearizations of Newmark methods. When used in conjunction with penalty methods (i.e., methods that replace constraints by stiff potentials), these integrators permit coarse time-stepping of holonomically constrained mechanical systems and bypass the resolution of nonlinear systems. Although penalty methods are widely employed, an explicit link to Lagrange multiplier approaches appears to be lacking; such a link is now provided (in the context of two-scale flow convergence (Tao, M., Owhadi, H. & Marsden, J. E. (2010) Nonintrusive and structure-preserving multiscale integration of stiff ODEs, SDEs and Hamiltonian systems with hidden slow dynamics via flow averaging. Multiscale Model. Simul., 8, 1269–1324). The variational formulation also allows efficient simulations of mechanical systems on Lie groups.

Item Type:Article
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Owhadi, Houman0000-0002-5677-1600
Additional Information:© 2015 The authors. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. Received January 16, 2013. Revision received August 25, 2014. First published online: February 3, 2015.
Subject Keywords:variational integrators; symplectic and linearly implicit; coarse time-stepping; constrained dynamics; mechanical system on Lie group
Issue or Number:1
Record Number:CaltechAUTHORS:20160317-083434102
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Official Citation:Molei Tao and Houman Owhadi Variational and linearly implicit integrators, with applications IMA J Numer Anal (2016) 36 (1): 80-107 first published online February 3, 2015 doi:10.1093/imanum/dru064
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65413
Deposited By: Tony Diaz
Deposited On:17 Mar 2016 20:01
Last Modified:03 Oct 2019 09:47

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