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A class of variational schemes for the hydrodynamic-electrodynamic model oflossless free-electron gas in a quasineutral background is developed forhigh-quality simulations of surface plasmon polaritons. The Lagrangian densityof lossless free-electron gas with a self-consistent electromagnetic field isestablished, and the dynamical equations with the associated constraints areobtained via a variational principle. Based on discrete exterior calculus, theaction functional of this system is discretized and minimized to obtain thediscrete dynamics. Newton-Raphson iteration and the biconjugate gradientstabilized method are equipped as a hybrid nonlinear-linear algebraic solver.Instead of discretizing the partial differential equations, the variationalschemes have better numerical properties in secular simulations, as theypreserve the discrete Lagrangian symplectic structure, gauge symmetry, andgeneral energy-momentum density. Two numerical experiments were performed. Thenumerical results reproduce characteristic dispersion relations of bulkplasmons and surface plasmon polaritons, and the numerical errors of conservedquantities in all experiments are bounded by a small value after long-termsimulations.

Variational Schemes and Geometric Simulations for a Hydrodynamic-Electrodynamic Model of Surface Plasmon Polaritons