2011/03/23 by Tao, Molei, Owhadi, Houman
#Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1103.4645
We show that symplectic and linearly-implicit integrators proposed by [Zhang and Skeel, 1997] 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, Owhadi and Marsden, 2010]). The variational formulation also allows efficient simulations of mechanical systems on Lie groups.