Dispersion and Stability Analysis for TLM Unstructured Block Meshing

Abstract

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

“…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]. One should note that, as the computational domain becomes more complex and more heterogeneous, several higher order modes appear around discontinuities, leading to rapidly varying EM-fields in the spatial directions [3].…”

“…However, when dealing with heterogeneous structures, this rule of thumb can be misleading [3]. One should note that, as the computational domain becomes more complex and more heterogeneous, several higher order modes appear around discontinuities, leading to rapidly varying EM-fields in the spatial directions [3]. The correct capturing and spatial representing of these modes is crucial for the accuracy of the simulation results.…”

“…Therefore, whenever there is a discontinuity (e.g., changing in constitutive parameters) a sufficiently fine mesh in that region and its neighborhood is required [3]. The question that arise is how fine the mesh should be to ensure correct simulations.…”

“…Cross verification: by re-simulating the same problem using different numerical techniques [4]. As a general practice, one should pay attention to the three main sources of error in numerical simulations (due to discretization), namely [3]:…”

“…Geometrical discretization error: the difference between real dimensions in continues (real) domain and the ones in the discrete counterpart [3]. Numerical dispersion error: the difference in phase velocity in discrete domain and the continuous one.…”