Multiple One-Dimensional FDTD Method for Coupled Transmission Lines and Stability Condition

Yang, Zaifeng; Tan, Eng Leong

doi:10.1109/lmwc.2016.2615021

Cited by 16 publications

(12 citation statements)

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“…For coupled transmission lines, the EM fields are governed by alternative differential equations, which are different from the usual Maxwell's equations and can be written as [103,104],…”

Section: M1-d Fadi Cl-fdtd Methods For Coupled Transmission Linesmentioning

confidence: 99%

“…W cl is the 4×4 coupled line (CL) system matrix, and E x1 , H y1 are the EM fields along line 1, while E x2 , H y2 are those along line 2. s , m and µ s , µ m are the self and mutual permittivities and permeabilities, respectively, which can be expressed in terms of CL even-and odd-mode characteristic impedances (Z 0e , Z 0o ), phase velocities (v e , v o ) and effective permittivities ( e eff , o eff ) [105][106][107]. Equations (29a)-(29b) can be solved using the M1-D CL-FDTD method [103,104], which could bypass the fine mesh for line width and spacing of coupled transmission lines. However, due to the stability constraint of such explicit method for CL, there is a time step limit that is usually more restrictive than that for the single uncoupled TL.…”

Section: M1-d Fadi Cl-fdtd Methods For Coupled Transmission Linesmentioning

confidence: 99%

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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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“…For coupled transmission lines, the EM fields are governed by alternative differential equations, which are different from the usual Maxwell's equations and can be written as [103,104],…”

Section: M1-d Fadi Cl-fdtd Methods For Coupled Transmission Linesmentioning

confidence: 99%

Section: M1-d Fadi Cl-fdtd Methods For Coupled Transmission Linesmentioning

confidence: 99%

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

Tan¹

2020

PIER

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“…The media parameters are selected such that there is sufficient inhomogeneity contrast in the mutual permittivities and permeabilities between the two media. The time step is specified as CFLN = ∆t/∆t CF L , where ∆t CF L is the CFL time step in [4]. Fig.…”

Section: B Two-media Reduced-matrix Stability Analysismentioning

confidence: 99%

“…To overcome the inefficiency of the 3-D FDTD methods, the multiple onedimensional (M1-D) FDTD method has been proposed for simulation of EM wave propagation in multiple transmission lines and stubs [3]. It has been extended to incorporate coupled transmission lines [4]. However, the time step is still constrained by its own Courant-Friedrichs-Lewy (CFL) stability condition.…”

Section: Introductionmentioning

confidence: 99%

Multiple LOD-FDTD Method for Inhomogeneous Coupled Transmission Lines and Stability Analyses

Heh

Tan

2020

IEEE Trans. Antennas Propagat.

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A multiple locally one-dimensional (MLOD) finitedifference time-domain (FDTD) method for inhomogeneous coupled transmission lines and stability analyses are presented. The method is aptly called the MLOD coupled line (CL)-FDTD method. Various split matrices are proposed, and the corresponding update equations are formulated and discussed. All the proposed split matrices yield implicit electric field update equations with tridiagonal or block tridiagonal matrices on the left-hand sides. For more efficiency, the block tridiagonal matrices for implicit electric field may be reformulated and replaced by tridiagonal matrices for implicit magnetic field. The stability analysis is first performed using the von Neumann method in the Fourier domain. It is shown that the von Neumann method alone may not be sufficient to ascertain stability for inhomogeneous media. To include media inhomogeneity, the twomedia reduced-matrix stability analysis is proposed. It allows us to analyze efficiently the key stability characteristics in inhomogeneous media, and is useful for quick detection of any potential instability that is not apparent via the von Neumann method. The stability characteristics with variation of media parameters are also investigated and discussed. Numerical results are provided to validate the stability and accuracy of the proposed MLOD CL-FDTD method with various split matrices.

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“…To reduce the required computing resources, the multiple one-dimensional (M1-D) explicit FDTD method has been proposed in [9] for coupled transmission lines. The coupled line parameters are incorporated directly into the M1-D method based on even-and odd-mode approach, which requires only discretization along the propagation direction z.…”

Section: Manuscript Receivedmentioning

confidence: 99%

Multiple 1-D Fundamental ADI-FDTD Method for Coupled Transmission Lines on Mobile Devices

Tan

Heh

2019

IEEE J. Multiscale Multiphys. Comput. Tech.

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This paper presents the multiple one-dimensional (M1-D) fundamental alternating direction implicit (FADI) finitedifference time-domain (FDTD) method for coupled transmission lines on mobile devices. The method is aptly called the M1-D FADI coupled line (CL)-FDTD method. It is based on the fundamental implicit scheme, which features matrix operatorfree right-hand sides (RHS). The formulations of the M1-D FADI CL-FDTD method and update equations are provided. Various sets of split matrices including those with self symmetry, mutual symmetry and self-mutual separation are proposed and discussed. Their stability analyses are performed using the Fourier amplification matrix formulated in fundamental form, which is simpler with only one inverse term each without RHS operator. It is found that the sets of split matrices with self symmetry are unconditionally stable, while those with mutual symmetry and self-mutual separation are not. Using two auxiliary quadratic polynomials along with single necessary and sufficient condition, the analytical proof of unconditional stability is made more convenient and concise. The efficiency of both stable sets of split matrices with self symmetry is discussed based on the number of RHS terms and floating-point operations (flops) count. Numerical results are presented to validate the accuracy of the proposed method at time step larger than the stability limit. Several EM simulations of coupled line structures are demonstrated on mobile devices. The CPU time incurred on various platforms is provided for M1-D FADI CL-FDTD method using both sets of split matrices with self symmetry. Using mobile devices, the EM simulations can be performed efficiently and ubiquitously anytime, anywhere.

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Multiple One-Dimensional FDTD Method for Coupled Transmission Lines and Stability Condition

Cited by 16 publications

References 1 publication

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)

Multiple LOD-FDTD Method for Inhomogeneous Coupled Transmission Lines and Stability Analyses

Multiple 1-D Fundamental ADI-FDTD Method for Coupled Transmission Lines on Mobile Devices

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