Accurate, time-domain, electromagnetic simulation of embedded dielectric interfaces in Neptune

摘要

Summary form only given. Dielectric materials play an important role in many classes of electromagnetic device, but present unique challenges to simulate accurately using time-domain Electromagnetic Particle-in-Cell (EM-PIC) codes. Results for previously published embedded boundary (or `cut-cell') algorithms typically do not exhibit true 2nd-order convergence with respect to grid cell size when curved interfaces must be resolved, particularly when the ratio of dielectric constants across an interface is large. We demonstrate here a new algorithm for time-domain simulation of structures that successfully addresses this challenge and provides accurate results in a broad range of geometries. In our method, we first derive a general, yet concise, tensor formula for the effective average permittivity inside a small region that spans a dielectric interface, such as a ceramic surface in vacuum. This formula is a simple function of the permittivity tensors each side of the interface and the vector locally normal to the interface. The effective permittivity is generally tensor-valued even when the dielectrics are isotropic, due to the orientation dependence imposed by the surface. By applying this formula cell by cell to an interface embedded in a fixed Cartesian grid, we derive a matrix representation for the material response that is more accurate than the stair-step representation. We demonstrated this method previously for frequency domain eigenmode solutions of Maxwell's equations 1. We present new results for a time-domain algorithm based on our embedded boundary dielectric model. Time domain solution using this method presents additional challenges when compared to frequency domain solutions. Firstly, the time-domain scheme must be stable and, secondly, the solution must be able to compute the inverse-permittivity to effectively update the electric field equations in the conventional EM-PIC model. We present our solution that satisfies these constraints, and that we have implemented for the GPU-based EM-PIC algorithm in Neptune.