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Stochastic uncertainties in material parameters have a significant impact on the analysis of real-world electromagnetic compatibility (EMC) problems. Conventional approaches via the Monte-Carlo scheme attempt to provide viable solutions, yet at the expense of prohibitively elongated simulations and system overhead, due to the large amount of statistical implementations. The purpose of this paper is to introduce a 3-D stochastic finite-difference time-domain (S-FDTD) technique for the accurate modelling of generalised EMC applications with highly random media properties, while concurrently offering fast and economical single-run realisations.

The proposed method establishes the concept of covariant/contravariant metrics for robust tessellations of arbitrarily curved structures and derives the mean value and standard deviation of the generated fields in a single-run. Also, the critical case of geometrical and physical uncertainties is handled via an optimal parameterisation, which locally reforms the curvilinear grid. In order to pursue extra speed efficiency, code implementation is conducted through contemporary graphics processor units and parallel programming.

The curvilinear S-FDTD algorithm is proven very precise and stable, compared to existing multiple-realisation approaches, in the analysis of statistically-varying problems. Moreover, its generalised formulation allows the effective treatment of realistic structures with arbitrarily curved geometries, unlike staircase schemes. Finally, the GPU-based enhancements accomplish notably accelerated simulations that may exceed the level of 120 times. Conclusively, the featured technique can successfully attain highly accurate results with very limited system requirements.

Development of a generalised curvilinear S-FDTD methodology, based on a covariant/contravariant algorithm. Incorporation of the important geometric/physical uncertainties through a locally adaptive curved mesh. Speed advancement via modern GPU and CUDA programming which leads to reliable estimations, even for abrupt statistical media parameter fluctuations.

Important statistical variations are likely to appear in the propagation of surface plasmon polariton waves atop the surface of graphene sheets, degrading the expected performance of real-life THz applications. This paper aims to introduce an efficient numerical algorithm that is able to accurately and rapidly predict the influence of material-based uncertainties for diverse graphene configurations.

Initially, the surface conductivity of graphene is described at the far infrared spectrum and the uncertainties of its main parameters, namely, the chemical potential and the relaxation time, on the propagation properties of the surface waves are investigated, unveiling a considerable impact. Furthermore, the demanding two-dimensional material is numerically modeled as a surface boundary through a frequency-dependent finite-difference time-domain scheme, while a robust stochastic realization is accordingly developed.

The mean value and standard deviation of the propagating surface waves are extracted through a single-pass simulation in contrast to the laborious Monte Carlo technique, proving the accomplished high efficiency. Moreover, numerical results, including graphene’s surface current density and electric field distribution, indicate the notable precision, stability and convergence of the new graphene-based stochastic time-domain method in terms of the mean value and the order of magnitude of the standard deviation.

The combined uncertainties of the main parameters in graphene layers are modeled through a high-performance stochastic numerical algorithm, based on the finite-difference time-domain method. The significant accuracy of the numerical results, compared to the cumbersome Monte Carlo analysis, renders the featured technique a flexible computational tool that is able to enhance the design of graphene THz devices due to the uncertainty prediction.

Random media uncertainties exhibit a significant impact on the properties of electromagnetic fields that usually deterministic models tend to neglect. As a result, these models fail to quantify the variation in the calculated electromagnetic fields, leading to inaccurate outcomes. This paper aims to introduce an unconditionally stable finite-difference time-domain (FDTD) method for assessing two-dimensional random media uncertainties in one simulation.

The proposed technique is an extension of the stochastic FDTD (S-FDTD) scheme, which approximates the variance of a given field component using the Delta method. Specifically in this paper, the Delta method is applied to the locally one-dimensional (LOD) FDTD scheme (hence named S-LOD-FDTD), to achieve unconditional stability. The validity of this algorithm is tested by solving two-dimensional random media problems and comparing the results with other methods, such as the Monte-Carlo (MC) and the S-FDTD techniques.

This paper provides numerical results that prove the unconditional stability of the S-LOD-FDTD technique. Also, the comparison with the MC and the S-FDTD methods shows that reliable outcomes can be extracted even with larger time steps, thus making this technique more efficient than the other two aforementioned schemes.

The S-LOD-FDTD method requires the proper quantification of various correlation coefficients between the calculated fields and the electrical parameters, to achieve reliable results. This cannot be known beforehand and the only known way to calculate them is to run a fraction of MC simulations.

This paper introduces a new unconditional stable technique for measuring material uncertainties in one realization.

This paper aims to introduce an efficient time-domain formulation of adjustable accuracy for a consistent and trustworthy computation of electromagnetic field characteristics in randomly varying configurations. The developed methodology is carefully certified via comprehensive comparisons with the corresponding outcomes obtained by the Monte Carlo approach.

The presented methodology uses higher-order approximations of Taylor series expansions of stochastic multivariable functions for the rapid estimation of the electromagnetic field component mean value and confidence intervals of their variance. Toward this objective, new time-update equations for the mean value and the variance of the involved electromagnetic field are elaborately derived.

The featured technique presents an efficient alternative to the excessively resource-consuming Monte Carlo finite-difference time-domain (MC–FDTD) implementation, which requires an unduly number of realizations to achieve a satisfying convergence. The higher-order stochastic algorithm retrieves accurately the statistical properties of all electromagnetic field in a single simulation, presenting promising accuracy, stability and convergence.

The adjustable-accuracy higher-order scheme introduces a new framework for the derivation of the stochastic explicit time-update equations and precisely computes the required confidence intervals for the electromagnetic field variance instead of the variance itself, which can be deemed a key advantage over existing schemes. This fully controllable formulation results in significantly more accurate calculations of the electromagnetic field variance, especially for larger fluctuations of the involved electromagnetic media parameters.