Volume 18, Issue 2 (June 2022)                   IJEEE 2022, 18(2): 141-154 | Back to browse issues page

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Hosseini K. CFL Stability Conditions for the FDTD Method in Bounded Inhomogeneous Anisotropic Media. IJEEE 2022; 18 (2) :141-154
URL: http://ijeee.iust.ac.ir/article-1-2398-en.html
CFL Stability Conditions for the FDTD Method in Bounded Inhomogeneous Anisotropic Media
Keyhan Hosseini
Abstract:   (1740 Views)
Anisotropic media appear regularly in electromagnetic wave engineering. The finite-difference time-domain (FDTD) method is a robust technique to model such media. However, the value of the time step in the FDTD algorithm is bounded by the Courant-Friedrichs-Lewy (CFL) condition. In this paper, a simple analytical approach is developed using the Gershgorin circle theorem to derive a point-wise closed-form relation for the CFL condition in bounded inhomogeneous anisotropic media. The proposed technique includes objects of arbitrary shapes with straight, tilted, or curved interfaces located in a computational space with uniform or adaptive gridding schemes. Both axial and non-axial anisotropies are considered in the analysis. The proposed method is able to investigate the effect of boundaries and interfaces on the stability of the algorithm. It is shown that in the presence of an interface between two anisotropic media, the von-Neumann criterion is not able to predict the stability bound for specific ranges of the permittivity tensor components and unit cell aspect ratios. Exploiting the proposed closed-form formulations, it is possible to tune the CFL time step and avoid the temporal instability by the wise selection of the gridding scheme especially in curved boundaries where subcell modelings such as Yu-Mittra formalism are applicable. Some illustrative examples are provided to verify the method by comparing the results with those of the eigenvalue analysis and time-domain simulations.
Keywords: Anisotropic Media , Curved Boundaries , Finite Difference Time Domain (FDTD) Method , Gershgorin Circle Theorem , Inhomogeneous Media , Stability
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  • A closed-form relation is derived for the CFL condition in bounded inhomogeneous anisotropic media.
  • The proposed theory can take into account the effect of straight, tilted or curved boundaries on the stability of the FDTD time ma
  • It is shown that for some ranges of permittivities and unit cell aspect ratios, the von-Neumann criterion is not able to predict the CFL time step.

Type of Study: Research Paper | Subject: Computational Electromagnetics
Received: 2022/01/19 | Revised: 2024/05/13 | Accepted: 2022/02/19
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© 2022 by the authors. Licensee IUST, Tehran, Iran. This is an open access journal distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license.