Further Reinterpretation of Multi-Stage Implicit FDTD Schemes

Heh, Ding Yu; Tan, Eng Leong

doi:10.1109/tap.2014.2325952

Cited by 4 publications

(4 citation statements)

References 17 publications

(35 reference statements)

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“…All these higher order methods may be simplified into their fundamental implicit schemes, which feature concise and efficient matrix-operator-free RHS in the multi-stage update procedures. Note that the multi-stage SS and ADI methods along with their temporal orders of accuracy can be interpreted based on the matrix exponential [66], which represents the exact solution to Maxwell's differential equations. Such matrix exponential interpretation is more general than the traditional Crank-Nicolson perturbation and is useful to ascertain the correct temporal order for ADI [67] and other multi-stage implicit schemes [68].…”

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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“…Equation 16can be approximated as follows: (see (17)) . To implement LOD-5 scheme, (17) will be updated in five sub-steps as follows:…”

Section: D Lod Techniquementioning

confidence: 99%

“…Recently, some implicit schemes have been proposed to remove CFL restriction, like alternating-direction-implicit (ADI) algorithm [12] and locally one-dimensional (LOD) scheme [13]. Also, there are other solutions which can be found in [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Unconditionally stable meshless method for solving 3D transient electromagnetic problems based on LOD scheme

Khakzar

Heidari

Movahhedi

2019

IET Science, Measurement & Technology

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“…The average value of the numerical phase error may also be lower than the value of the actual phase velocity which causes delay in wave propagation. Several studies have been carried out to reduce these errors . It has been shown that split‐step FDTD methods can be unconditionally stable as well as have reduced discretization errors above CFL limit .…”

Section: Introductionmentioning

confidence: 99%

Four unequal substep FDTD (4 USS‐FDTD) method with extremely low numerical dispersion error

Kuşaf

Öztoprak

2018

Int J Numerical Modelling

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A new unconditionally stable split-step FDTD method is introduced which has unequal substeps. The ratio of the unequal substeps, τ, is utilized to obtain extremely low anisotropic errors. It is shown that for any set of space step and time step values, there is a τ value which gives zero anisotropic error. Polynomials are obtained in terms of time and space step sizes for τ and the average normalized numerical phase velocity which can be used to correct for anisotropic error and the average numerical phase velocity. The 2 polynomials can be integrated into the simulation programs, so that the user gets an almost unity normalized phase velocity in all directions, for any chosen time step size and space step size. In this way, large time steps up to Nyquist rate can be used.The method is also suitable for multidomain applications, which makes the method very efficient. A further study shows that the method is very wideband, and for 1% dispersion, error bandwidth is larger than 10:1. KEYWORDS alternating direction implicit finite difference time domain (ADI-FDTD), LOD-FDTD, numerical dispersion, split-step FDTD

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Further Reinterpretation of Multi-Stage Implicit FDTD Schemes

Cited by 4 publications

References 17 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)

Unconditionally stable meshless method for solving 3D transient electromagnetic problems based on LOD scheme

Four unequal substep FDTD (4 USS‐FDTD) method with extremely low numerical dispersion error

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