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We explain the Lorentz resonances in plasmonic crystals that consist of two-dimensional nano-dielectric inclusions as the interaction between resonant material properties and geometric resonances of electrostatic nature. One example of such plasmonic crystals are graphene nanosheets that are periodically arranged within a non-magnetic bulk dielectric. We identify local geometric resonances on the length scale of the small-scale period. From a materials perspective, the graphene surface exhibits a dispersive surface conductance captured by the Drude model. Together these phenomena conspire to generate Lorentz resonances at frequencies controlled by the surface geometry and the surface conductance. The Lorentz resonances found in the frequency response of the effective dielectric tensor of the bulk metamaterial are shown to be given by an explicit formula, in which material properties and geometric resonances are decoupled. This formula is rigorous and obtained directly from corrector fields describing local electrostatic fields inside the heterogeneous structure. Our analytical findings can serve as an efficient computational tool to describe the general frequency dependence of periodic optical devices. As a concrete example, we investigate two prototypical geometries composed of nanotubes and nanoribbons.more » « less
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We discuss the efficient implementation of a high-performance second-order collocation-type finite-element scheme for solving the compressible Euler equations of gas dynamics on unstructured meshes. The solver is based on the convex-limiting technique introduced by Guermond et al. (SIAM J. Sci. Comput. 40, A3211–A3239, 2018). As such, it is invariant-domain preserving ; i.e., the solver maintains important physical invariants and is guaranteed to be stable without the use of ad hoc tuning parameters. This stability comes at the expense of a significantly more involved algorithmic structure that renders conventional high-performance discretizations challenging. We develop an algorithmic design that allows SIMD vectorization of the compute kernel, identify the main ingredients for a good node-level performance, and report excellent weak and strong scaling of a hybrid thread/MPI parallelization.more » « less
