Asynchronous Variational Integrators
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We describe a class of asynchronous variational integrators (AVI) for nonlinear elastodynamics. The AVIs are characterized by the following distinguishing 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 principle. As a consequence of this variational structure, the algorithms conserve local energy and momenta exactly, subject to solvability of the local time steps. 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.
KeywordsLocal Energy Lagrange Equation Local Time Step Angular Momentum Balance Discrete Trajectory
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