Advances in Finite-Difference Time-Domain Methods and Applications

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (30 November 2021) | Viewed by 5471

Special Issue Editors


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Guest Editor
Department of Electrical and Computer Engineering, University of Western Macedonia, 50131 Kozani, Greece
Interests: FDTD methods; high-order algorithms; GPU computing; dispersion-relation-preserving schemes; computational electromagnetics; uncertainty quantification

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Co-Guest Editor
Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
Interests: electromagnetic compatibility (EMC); EMC principles and systems; standardization of EMC systems; electromagnetic interference (ΕΜΙ) and shielding; anechoic chambers and measurement technology; EMC circuit models; management and utilization of the electromagnetic spectrum; development of computational techniques for EMC/ΕΜΙ problems; applications of specialized materials in EMC/EMI structures; wireless power transfer

Special Issue Information

Dear Colleagues,

Thanks to its advantageous properties and flexibility in modeling time-dependent problems, the finite-difference time-domain (FDTD) method is one of the numerical techniques currently playing a prominent role in the area of Computational Electromagnetics (and other disciplines as well, such as Acoustics and Geophysics). Although the main idea has remained the same since its introduction (i.e., solution of Maxwell’s equations via finite-difference approximations on a dual staggerred grid), the capabilities of the FDTD method have been expanded throughout the years, new features have been added, generalizations have been proposed, and modifications have been devised. In fact, this is still an ongoing process, as the constantly increasing complexity of electromagnetic devices imposes stricter requirements on the corresponding computational models, both in terms of reliability and efficiency. Technological advances are commonly associated with applications involving diverse phenomena, unexplored interactions, and non-trivial material responses, whose consistent prediction is of vital importance. In this context, traditional computational approaches are necessary to live up to these emerging challenges.

The purpose of this Special Issue is to report on novel advances and findings regarding FDTD methods and pertinent applications in the area of Computational Electromagnetics and other scientific disciplines. The main topics of interest include (but are not limited to):

  • discretization schemes for curvilinear and unstructured grids;
  • dispersion-relation-preserving and optimized schemes;
  • space-time mesh refinement techniques;
  • modeling of complex material responses;
  • higher-order extensions;
  • unconditionally stable and implicit–explicit formulations;
  • absorbing and surface-boundary conditions;
  • overlapping and non-conforming grids;
  • stochastic methods;
  • subcell modeling and thin-wire formulations;
  • reduced-order models;
  • hybridization with other computational methods;
  • parallelization strategies;
  • advanced applications of the FDTD method (e.g., complex problems where specific capabilities of the FDTD method are utilized); and
  • novel applications of the FDTD methods.

Assoc. Prof. Dr. Theodoros Zygiridis
Prof. Dr. Nikolaos Kantartzis
Guest Editors

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Keywords

  • finite-difference time-domain methods
  • hybrid techniques
  • higher-order methods
  • stability
  • material modeling
  • CPU and GPU parallelization
  • uncertainty quantification
  • numerical dispersion
  • model order reduction
  • mesh refinement
  • FDTD applications

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Published Papers (2 papers)

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11 pages, 482 KiB  
Article
Accurate Time-Domain Modeling of Arbitrarily Shaped Graphene Layers Utilizing Unstructured Triangular Grids
by Stamatios Amanatiadis, Theodoros Zygiridis and Nikolaos Kantartzis
Axioms 2022, 11(2), 44; https://doi.org/10.3390/axioms11020044 - 22 Jan 2022
Cited by 1 | Viewed by 2359
Abstract
The accurate modeling of curved graphene layers for time-domain electromagnetic simulations is discussed in the present work. Initially, the advanced properties of graphene are presented, focusing on the propagation of strongly confined surface plasmon polariton waves at the far-infrared regime. Then, the implementation [...] Read more.
The accurate modeling of curved graphene layers for time-domain electromagnetic simulations is discussed in the present work. Initially, the advanced properties of graphene are presented, focusing on the propagation of strongly confined surface plasmon polariton waves at the far-infrared regime. Then, the implementation of an unstructured triangular grid was examined, based on the Delaunay triangulation method. The electric-field components were placed at the edges of the triangles, while two different techniques were proposed for the sampling of the magnetic ones. Specifically, the first one suggests that the magnetic component is placed at the triangle’s circumcenter providing more accurate results, although instability may occur for nonacute triangles. On the other hand, the magnetic field was sampled at the triangle’s centroid, considering the second technique, ensuring the algorithm’s stability, but further approximations were required, leading to a slight accuracy reduction. Moreover, the updating equations in the time-domain were extracted via an appropriate approximation of Maxwell equations in their integral form. Finally, graphene was introduced in the computational domain as an equivalent surface current density, whose location matches the corresponding electric components. The validity of our methodology was successfully performed via the comparison of graphene surface wave propagation properties to their theoretical values, whereas the global error determination indicates the minimal triangle dimensions. Additionally, an instructive setup comprising a circular graphene scatterer was analyzed thoroughly, to reveal our technique’s advantages compared to the conventional staircase discretization. Full article
(This article belongs to the Special Issue Advances in Finite-Difference Time-Domain Methods and Applications)
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18 pages, 1709 KiB  
Tutorial
From Time-Collocated to Leapfrog Fundamental Schemes for ADI and CDI FDTD Methods
by Eng Leong Tan
Axioms 2022, 11(1), 23; https://doi.org/10.3390/axioms11010023 - 7 Jan 2022
Cited by 9 | Viewed by 2072
Abstract
The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence implicit (CDI) FDTD method. In this paper, the formulations from time-collocated to leapfrog fundamental schemes are presented for ADI and CDI FDTD methods. [...] Read more.
The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence implicit (CDI) FDTD method. In this paper, the formulations from time-collocated to leapfrog fundamental schemes are presented for ADI and CDI FDTD methods. For the ADI FDTD method, the time-collocated fundamental schemes are implemented using implicit E-E and E-H update procedures, which comprise simple and concise right-hand sides (RHS) in their update equations. From the fundamental implicit E-H scheme, the leapfrog ADI FDTD method is formulated in conventional form, whose RHS are simplified into the leapfrog fundamental scheme with reduced operations and improved efficiency. For the CDI FDTD method, the time-collocated fundamental scheme is presented based on locally one-dimensional (LOD) FDTD method with complying divergence. The formulations from time-collocated to leapfrog schemes are provided, which result in the leapfrog fundamental scheme for CDI FDTD method. Based on their fundamental forms, further insights are given into the relations of leapfrog fundamental schemes for ADI and CDI FDTD methods. The time-collocated fundamental schemes require considerably fewer operations than all conventional ADI, LOD and leapfrog ADI FDTD methods, while the leapfrog fundamental schemes for ADI and CDI FDTD methods constitute the most efficient implicit FDTD schemes to date. Full article
(This article belongs to the Special Issue Advances in Finite-Difference Time-Domain Methods and Applications)
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