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Stochastic geometrically exact beam: Continuous-time geometric principles and variational discretizations
Minghang Du, François Gay-Balmaz, Tianzhi Li, and Donghua Shi

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This work presents variational principles for the dynamics of the stochastic geometrically exact beam, in both continuous- and discrete-time settings. The resulting two structure-preserving stochastic geometric integrators are shown to be stochastic extensions of the well-known deterministic staggered leapfrog scheme for the wave equation, and also stochastic extensions of Yee's scheme for spatially one-dimensional computational electromagnetism. Numerical results are shown to demonstrate the effectiveness of the proposed approaches.