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Multisymplectic variational integrators for PDEs of geometrically exact beam dynamics using algorithmic differentiation
Author(s) -
Leitz Thomas,
Leyendecker Sigrid
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610364
Subject(s) - variational integrator , computation , automatic differentiation , integrator , mathematics , euler's formula , lagrangian , beam (structure) , matrix (chemical analysis) , dynamics (music) , mathematical analysis , classical mechanics , physics , algorithm , quantum mechanics , materials science , optics , composite material , acoustics , voltage
For the simulation of geometrically exact beam dynamics [4], a multisymplectic Lie‐group variational integrator [3] is derived. Based on the implementation of the discrete Lagrangian, algorithmic differentiation is used in the computation of both, the discrete Euler‐Lagrange equations, and the Jacobi matrix needed for the Newton‐Raphson iteration. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)