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

Abstract

The inclusion of thin lossy, material layers, such as carbon based composites, is essential for many practical applications 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, and/or large computational costs. This work presents a novel technique for the modeling of thin-layer lossy materials in FDTD schemes which overcomes the instability problem at low computational cost. For this, a 1D-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 3D 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 low frequencies, and late time stability than existing techniques with low computational cost.

From Microscopic to Macroscopic Description of Composite Thin Panels: A Road Map for Their Simulation in Time Domain

“…We can incorporate their behavior into numerical methods by means of NIBCs, as described in [10], or by the novel SGBCs introduced by Cabello et al [14], [15]. The latter approach has proven to exhibit a superior late time stability compared with the NIBC method.…”

“…This fact introduces an added difficulty that has attracted a lot of research efforts since the original works of [21] and [22]. 3) The ε eff can now be found from (14) and (15); however, the assumption of a nonmagnetic material releases us from solving the branch problem, since ε eff can be directly found by…”

“…The SGBC method introduced in [14] was born as a robustly stable subcell alternative of NIBC to find the tangential electric fields at each side of the thin slab, as a function of the magnetic fields in the adjacent host medium. It combines two methods: 1) a CNTD method in 1-D, to find the transversal EM solution within the slab, which is finely meshed to account for the fields variation inside and 2) the usual 3D Yee-FDTD method to solve the exterior problem coarsely discretized according to the desired resolution.…”

“…To overcome these limitations, in [14], we proposed a novel technique based on a robustly stable subgridding boundary condition (SGBC), which does not present the late-time instabilities of NIBC. The method was based on a hybrid implicitexplicit (HIE) combination of the classical FDTD with a Crank-Nicolson time-domain (CNTD) unconditionally stable method.…”

“…The method was based on a hybrid implicitexplicit (HIE) combination of the classical FDTD with a Crank-Nicolson time-domain (CNTD) unconditionally stable method. However, the formulation presented in [14] required to know the multilayer interior structure of the thin panel, in terms of its bulk conductivity and the thickness of each layer. As a consequence, that approach could not be used to model arbitrarily dispersive thin-panels, and it has been extended to this end.…”