Robust and Efficient Approaches for High-Order Accurate Simulation of Kinetic Plasmas and Dispersive Electromagnetics

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For engineering or applied sciences, high-order accurate numerical methods hold great promise since they are potentially orders of magnitude more efficient than their low-order counterparts. However, realizing the potential payoff of high-order accurate methods in real problems, particularly for wave equations, has proven to be challenging. Consequently, widespread adoption by practitioners as been limited.

In the present talk I will highlight two aspects of our recent work developing robust and efficient high-order accurate methods. In part I of the talk I will discuss Vlasov simulation using the Eulerian-based kinetic code LOKI, which simulates plasmas in a 2+2-dimensional phase space. Perhaps the most significant computational challenge in this regime is the immense cost associated with high-dimensional phase space simulation, and we advocate the use of high-order accurate numerical schemes as a means to reduce the cost required to deliver accurate results. Part II of the talk discusses a new numerical approach for dispersive Maxwell's equations with targeted application to metamaterial design. Here, accurate and robust treatment of geometrical inclusions is the primary concern, and we use overlapping grids to address the challenge. The efficacy of the overall approach is demonstrated on a series of electromagnetic wave propagation problems, including scattering from perfect conductors as well as scattering from dielectric dispersive materials.