Abstract
We propose a stochastic hybrid implicit–explicit finite-difference time-domain method (S-HIE-FDTD) to compute the mean and variance of the electromagnetic (EM) fields using a single simulation, given those of the conductivity and permittivity in the computation domain. The mean and variance field update equations underlying the proposed method are derived from the field update equations of the “traditional” deterministic HIE-FDTD. The Courant–Friedrichs–Lewy condition of the S-HIE-FDTD depends on the spatial discretization sizes only in two dimensions; therefore, for computation domains with fine geometric features only in the remaining dimension, it uses a time step size that is larger than that of fully explicit schemes. Indeed, numerical results demonstrate that the proposed method is faster than the previously developed stochastic FDTD in computing the mean and variance of the EM fields in two different problems: wave propagation through a multilayer human tissue and transmission through a frequency selective surface.
Highlights
INTRODUCTIONThe statistical electromagnetic (EM) analysis [1] is indispensable in various fields of engineering and physics, including, but not limited to, bioelectromagnetics [2]–[4], atmospheric wave propagation [5], remote sensing [6], [7], and integrated circuit design [8], where materials’ electrical properties are not deterministically known (often due to measurement limitations) and/or scatterer and antenna dimensions
The statistical electromagnetic (EM) analysis [1] is indispensable in various fields of engineering and physics, including, but not limited to, bioelectromagnetics [2]–[4], atmospheric wave propagation [5], remote sensing [6], [7], and integrated circuit design [8], where materials’ electrical properties are not deterministically known and/or scatterer and antenna dimensionsManuscript received September 5, 2019; revised February 29, 2020; accepted March 30, 2020
We develop a stochastic hybrid implicit– explicit FDTD (S-HIE-FDTD) to efficiently compute the mean and variance of the EM fields given those of the conductivity and permittivity in a simulation with fine geometric features in one or
Summary
The statistical electromagnetic (EM) analysis [1] is indispensable in various fields of engineering and physics, including, but not limited to, bioelectromagnetics [2]–[4], atmospheric wave propagation [5], remote sensing [6], [7], and integrated circuit design [8], where materials’ electrical properties are not deterministically known (often due to measurement limitations) and/or scatterer and antenna dimensions. They might unnecessarily increase the overall computational cost for problems involving structures with fine geometric features only in one or two dimensions (e.g., radiation from patch antennas, transmission through thin layers, and scattering in a layered medium) To address this shortcoming, several FDTD schemes, such as weakly conditionally stable (WCS) method [18], [19] and hybrid implicit–explicit method [20]–[23], have been developed. The overall computational cost of these schemes is expected to be lower than that of the fully explicit or fully implicit FDTD methods when analyzing structures with fine geometric features only in one or two dimensions In this communication, we develop a stochastic hybrid implicit– explicit FDTD (S-HIE-FDTD) to efficiently compute the mean and variance of the EM fields given those of the conductivity and permittivity in a simulation with fine geometric features in one or. The numerical results demonstrate that the S-HIE-FDTD is more efficient than the S-FDTD in the statistical analysis of wave propagation through a multilayer biological tissue and transmission through a frequency selective surface (FSS)
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