Asynchronous variational integrators

A. Lew, J. E. Marsden, M. Ortiz, M. West

Research output: Contribution to journalReview articlepeer-review

Abstract

We describe a new class of asynchronous variational integrators (AVI) for nonlinear elastodynamics. The AVIs are distinguished by the following attributes: (i) The algorithms permit the selection of independent time steps in each element, and the local time steps need not bear an integral relation to each other; (ii) the algorithms derive from a spacetime form of a discrete version of Hamilton's variational principle. As a consequence of this variational structure, the algorithms conserve local momenta and a local discrete multisymplectic structure exactly. To guide the development of the discretizations, a spacetime multisymplectic formulation of elastodynamics is presented. The variational principle used incorporates both configuration and spacetime reference variations. This allows a unified treatment of all the conservation properties of the system. A discrete version of reference configuration is also considered, providing a natural definition of a discrete energy. The possibilities for discrete energy conservation are evaluated. Numerical tests reveal that, even when local energy balance is not enforced exactly, the global and local energy behavior of the AVIs is quite remarkable, a property which can probably be traced to the symplectic nature of the algorithm.

Original languageEnglish (US)
Pages (from-to)85-146
Number of pages62
JournalArchive for Rational Mechanics and Analysis
Volume167
Issue number2
DOIs
StatePublished - Apr 2003
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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