Stability and Dispersion Analysis of a TLM Unified Approach for Dispersive Anisotropic Media

Dispersion and Stability Analysis for TLM Unstructured Block Meshing

“…The numerical dispersion analysis generally stems from the study of plane waves propagating in an infinite mesh with homogeneous media properties [25], [29]- [34]. The outcome of this study is a mathematical relationship linking the frequency, mesh size, time step, constitutive parameters of the medium, and the direction of propagation [25], [29], [32]- [34]. The general procedure consists of modeling the eigenvalue problem that governs the temporal field updates and spatial propagation in the Hilbert space [25], [32]- [34].…”

“…Therefore, the heterogeneity and the complexity of media do not have any impact on the subgridding TLM algorithm accuracy. Note that, in all previously mentioned techniques, the computational domain is supposed to operate at one global time step corresponding to the smallest Courant-Friedrichs-Lewy (CFL) time step limit [25]. Many attempts to use a local time step (namely, a time step that corresponds to the CFL limit in the block with a specific mesh size) have failed because of instability that often takes place after a few hundreds/thousands of iterations, depending on the application [14], [26].…”

“…Second, the time step will correspond to the maximum CFL limit in every subdomain. Therefore, minimum numerical dispersion is guaranteed [2], [25].…”

Numerical Dosimetry at 5G-Bands Using Time-Domain Methods and the Impact of Discretization and Uncertainty in Tissues Constitutive Parameters

“…Traditionally, in Computational Electromagnetics (CEM) Time-Domain methods it is recommended to use a mesh-size of less than 10 , or ten cells per wavelength at most, to ensure a negligible level of numerical dispersion [1] [2]. This limit was derived for a plane wave propagating in a homogeneous medium discretized into a structured homogenous mesh (cubic uniform cells) [1] [2]. However, when dealing with heterogeneous structures, this rule of thumb can be misleading [3].…”

“…Limit 1: numerical dispersion error To ensure a negligible numerical dispersion error per cell, the mesh-size should respect the condition [1] [2]:…”