A Hybrid Crank–Nicolson FDTD Subgridding Boundary Condition for Lossy Thin-Layer Modeling

The inclusion of thin lossy material layers, such as carbon-based composites, is essential for many practical applications for modeling the propagation of electromagnetic energy through composite structures such as those found in vehicles and electronic equipment enclosures. Many existing schemes suffer problems of late time instability, inaccuracy at low frequency (LF), and/or large computational costs. This paper presents a novel technique for the modeling of thin-layer lossy materials in finite-difference time domain (FDTD) schemes, which overcomes the instability problem at low computational cost. For this, a 1-D subgrid is used for the spatial discretization of the thin-layer material. To overcome the additional time-step constraint posed by the reduction in the spatial cell size, a Crank-Nicolson time-integration scheme is used locally in the subgridded zone, and hybridized with the usual 3-D Yee-FDTD method, which is used for the rest of the computational domain. Several numerical experiments demonstrating the accuracy of this approach are shown and discussed. Results comparing the proposed technique with classical alternatives based on impedance boundary condition approaches are also presented. The new technique is shown to have better accuracy at LFs and late time stability than existing techniques with low computational cost.