Some recent developments in fundamental implicit FDTD schemes

Heh, Ding Yu; Tan, Eng Leong; Tay, Wei Choon

doi:10.1109/apemc.2012.6237920

Cited by 8 publications

(6 citation statements)

References 8 publications

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“…Other implicit FDTD methods (e.g., ADI-FDTD) tend to become unstable unless the time step is uniform throughout [81]. Besides electromagnetics, all the methods based on fundamental implicit schemes may also be extended readily to other branches of physics such as thermodynamics [82][83][84][85][86] and quantum mechanics [87], etc.…”

Section: Fundamental Implicit Schemes For Ss-and Lod-fdtd Methodsmentioning

confidence: 99%

Fundamental Implicit FDTD Schemes for Computational Electromagnetics and Educational Mobile Apps (Invited Review)

Tan¹

2020

PIER

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This paper presents an overview and review of the fundamental implicit finite-difference time-domain (FDTD) schemes for computational electromagnetics (CEM) and educational mobile apps. The fundamental implicit FDTD schemes are unconditionally stable and feature the most concise update procedures with matrix-operator-free right-hand sides (RHS). We review the developments of fundamental implicit schemes, which are simpler and more efficient than all previous implicit schemes having RHS matrix operators. They constitute the basis of unification for many implicit schemes including classical ones, providing insights into their interrelations along with simplifications, concise updates and efficient implementations. Based on the fundamental implicit schemes, further developments can be carried out more conveniently. Being the core CEM on mobile apps, the multiple one-dimensional (M1-D) FDTD methods are also reviewed. To simulate multiple transmission lines, stubs and coupled transmission lines efficiently, the M1-D explicit FDTD method as well as the unconditionally stable M1-D fundamental alternating direction implicit (FADI) FDTD and coupled line (CL) FDTD methods are discussed. With the unconditional stability of FADI methods, the simulations are fast-forwardable with enhanced efficiency. This is very useful for quick concept illustrations or phenomena demonstrations during interactive teaching and learning. Besides time domain, many frequency-domain methods are well-suited for further developments of useful mobile apps as well.

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Section: Fundamental Implicit Schemes For Ss-and Lod-fdtd Methodsmentioning

confidence: 99%

Fundamental Implicit FDTD Schemes for Computational Electromagnetics and Educational Mobile Apps (Invited Review)

Tan¹

2020

PIER

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“…The almost unconditionally stable ADI FDTD algorithm, which is of particular importance for large-scale problems, has also been implemented on GPUs [85]. The efficiencies of fundamental ADI FDTD and of locally onedimensional LOD FDTD on GPUs are discussed in [86]. Meshless time domain modelling of bended waveguide was numerically investigated on GPUs [87] as well.…”

Section: A Gpu Accelerationmentioning

confidence: 99%

Viability of Numerical Full-Wave Techniques in Telecommunication Channel Modelling

Novak

2020

J. commun. softw. syst. (Online)

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In telecommunication channel modelling the wavelength is small compared to the physical features of interest, therefore deterministic ray tracing techniques provide solutions that are more efficient, faster and still within time constraints than current numerical full-wave techniques. Solving fundamental Maxwell's equations is at the core of computational electrodynamics and best suited for modelling electrical field interactions with physical objects where characteristic dimensions of a computing domain is on the order of a few wavelengths in size. However, extreme communication speeds, wireless access points closer to the user and smaller pico and femto cells will require increased accuracy in predicting and planning wireless signals, testing the accuracy limits of the ray tracing methods. The increased computing capabilities and the demand for better characterization of communication channels that span smaller geographical areas make numerical full-wave techniques attractive alternative even for larger problems. The paper surveys ways of overcoming excessive time requirements of numerical full-wave techniques while providing acceptable channel modelling accuracy for the smallest radio cells and possibly wider. We identify several research paths that could lead to improved channel modelling, including numerical algorithm adaptations for large-scale problems, alternative finite-difference approaches, such as meshless methods, and dedicated parallel hardware, possibly as a realization of a dataflow machine.

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“…Recently, Tan has proposed a fundamental scheme for simply implementing the implicit FDTDs [7,8]. The advantage of the fundamental scheme is that matrix-operator-free formulations in the right-hand sides can be performed; the number of arithmetic operations is significantly reduced in the right-hand side of resultant equations.…”

Section: Introductionmentioning

confidence: 99%

Some applications of a fundamental scheme to simple implementations of the finite-difference time-domain method and the beam-propagation method

2013

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A fundamental scheme has recently been developed for simple implementations of the implicit finite diff erence time-domain (FDTD) methods based on the alternating-direction implicit and locally one-dimensional (LaD) schemes. The advantage of the fundamental scheme is that the number of arithmetic operations of the resultant equations is significantly reduced in the right-hand sides, when compared to that without the fundamental scheme. In this article, we develop a frequency-dependent LaD body-oi-revolution FDTD based on the fundamental scheme. For the assessment of the developed method, a plasmonic rod waveguide is analyzed with attention to the time step size beyond the stability limit. We also apply the fundamental scheme to a reformulation of the full-vectorial beam-propagation method for the eigenmode analysis of optical waveguides.

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Some recent developments in fundamental implicit FDTD schemes

Cited by 8 publications

References 8 publications

Fundamental Implicit FDTD Schemes for Computational Electromagnetics and Educational Mobile Apps (Invited Review)

Fundamental Implicit FDTD Schemes for Computational Electromagnetics and Educational Mobile Apps (Invited Review)

Viability of Numerical Full-Wave Techniques in Telecommunication Channel Modelling

Some applications of a fundamental scheme to simple implementations of the finite-difference time-domain method and the beam-propagation method

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