An Efficient Implementation of the Stretched Coordinate Perfectly Matched Layer

Li, Jianxiong; Dai, Jufeng

doi:10.1109/lmwc.2007.895690

Cited by 14 publications

(20 citation statements)

References 7 publications

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“…Subsequently, we employ a memory-minimized algorithm [23] to reduce memory requirement. It is seen from (11) that the order of jω in the rational polynomial function is lower in comparison with the SO-FDTD method introduced in [22] (for example, the order N = 4 and M = 6 in [22], N = 2 and M = 3 in this paper), which is advantageous for reducing the memory storage when adopting the memory-minimized algorithm.…”

Section: Derivation Of the Improved So-fdtd Formulationsmentioning

confidence: 99%

“…When EM-wave propagates through uniform magnetized plasma plate with a magnetic declination angle θ between 0 • and 90 • , there are two kinds of eigen waves in this case, which are both elliptically polarized waves. One is called first type wave (I-wave) where the "+" sign is taken in Equation (23), and the other is second type wave (II-wave) where the "−" sign is taken in Equation (23). Suppose θ is set to 45 • and 65 • , the reflection coefficient and transmission coefficient vs. frequency for I-wave and II-wave computed using the improved SO-FDTD and kDB-SO-FDTD methods are compared to the exact solutions in Figures 4 and 5.…”

Section: Numerical Verificationmentioning

confidence: 99%

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Improved Shift-Operator FDTD Method for Anisotropic Magnetized Cold Plasmas With Arbitrary Magnetic Field Declination

Yin¹,

Hou²,

dVdvNioONAp³

et al. 2012

PIER B

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Abstract-In this paper, a recently improved SO-FDTD (shiftoperator finite difference time-domain) method is proposed and applied to the numerical analysis of the anisotropic magnetized plasma with arbitrary magnetic declination. By using the constitutive relation between polarized current density vector J and electric vector E and bringing the shift operators, the difference iteration equations of field components for Maxwell equations are derived in detail. Furthermore, the memory requirement is decreased significantly through incorporating a memory-minimized algorithm into the FDTD iterative cycles.The reflection and transmission coefficients of electromagnetic wave through a magnetized plasma layer are calculated by using this method. It is shown that the new method not only improves accuracy but also produces speed and memory advantages over the SO-FDTD method in kDB coordinates system proposed in the recent reference. In addition, the recursion formulae of the improved SO-FDTD method are deduced and programmed easily and they involve no complex variables, so the computations for the magnetized plasma become very simple.

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Section: Derivation Of the Improved So-fdtd Formulationsmentioning

confidence: 99%

Section: Numerical Verificationmentioning

confidence: 99%

Improved Shift-Operator FDTD Method for Anisotropic Magnetized Cold Plasmas With Arbitrary Magnetic Field Declination

Yin¹,

Hou²,

dVdvNioONAp³

et al. 2012

PIER B

View full text Add to dashboard Cite

show abstract

“…Even if memory requirements, proposed by Li and Dai [4], [5], are saved significantly as compared with those in published papers [2], [3], they can only produce results as accurate as those in [2] and [3].…”

mentioning

confidence: 99%

“…To the best of our knowledge, however, the various SC-PML algorithms are not effective at attenuating the evanescent waves in [2]- [5]. In order to get over this limitation, the complex frequency shifted perfectly matched layer (CFS-PML) [6] has been presented and attracted overwhelming attention due to the fact that the CFS-PML is very efficient in terms of absorbing the low-frequency evanescent waves and decreasing late-time reflections.…”

mentioning

confidence: 99%

“…However, several unsplit-field-based implementations of the SC-PML algorithms have been proposed due to the fact that the split-field implementations of the PML require more memory and computational time. The convolutional perfectly matched layer (CPML) [10] is based upon applying the convolution theorem to the SC-PML equations, while the ADE-PML [3], [5] is based upon incorporating the ADE method into the SC-PML formulations. Other SC-PML implementations were presented based upon the -transform methods [2], [4] which have been incorporated into the FDTD algorithms.…”

mentioning

confidence: 99%

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Direct <formula formulatype="inline"><tex Notation="TeX">$Z$</tex></formula>-Transform Implementation of the CFS-PML Based on Memory-Minimized Method

Feng

Yue

Liu

2015

IEEE Trans. Microwave Theory Techn.

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Efficient and unsplit-field-based stretched coordinate perfectly matched layer (PML) formulations with the complex frequency-shifted (CFS) scheme that combine the memory-minimized method (Tri-M) and the direct -transform (DZT) method are proposed to truncate the finite-difference time-domain lattices. The proposed algorithm takes advantage of the minimized memory of the Tri-M method, the optimal accuracy of the DZT method, and the capacity of the PML for attenuating evanescent waves and reducing late-time reflections. Three 3-D numerical simulations have been carried out to validate the proposed formulations. Index Terms-Complex frequency-shifted perfectly matched layer (CFS-PML), direct -transform (DZT) method, finite difference time domain (FDTD), memory-minimized method (Tri-M).

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Implicit Approximate Crank–Nicolson Theory for Anisotropic Ferrite Structure Simulation with Enhanced Absorption

Xie

Jiang

et al. 2021

Advcd Theory and Sims

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To simulate ferrite structures with anisotropic characteristics efficiently, an unconditionally stable implementation is proposed by incorporating the approximate Crank–Nicolson (CN) theory and a complex‐frequency‐shifted perfectly matched layer (CFS‐PML) formulation in the finite‐difference time‐domain lattice. More specifically, the proposed implementation combines the CN approximate factorization splitting procedure with bilinear transformation in the z‐domain within the CFS‐PML regions. To simulate the unique anisotropic characteristic of the ferrite structure, the auxiliary differential equation (ADE) method, which is modified at the integer time step, is introduced during the formulation. Numerical examples are presented to demonstrate the effectiveness and efficiency theoretically and experimentally. According to the results, it can be concluded that the proposed scheme takes full advantage of the approximate CN theory, CFS‐PML formulation, and modified ADE method in terms of the considerable computational accuracy, outstanding absorbing performance, and remarkable efficiency. Moreover, it can be demonstrated that the proposed algorithm can maintain its stability with the dissatisfaction of the Courant–Friedrichs–Lewy condition.

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An Efficient Implementation of the Stretched Coordinate Perfectly Matched Layer

Cited by 14 publications

References 7 publications

Improved Shift-Operator FDTD Method for Anisotropic Magnetized Cold Plasmas With Arbitrary Magnetic Field Declination

Improved Shift-Operator FDTD Method for Anisotropic Magnetized Cold Plasmas With Arbitrary Magnetic Field Declination

Direct <formula formulatype="inline"><tex Notation="TeX">$Z$</tex></formula>-Transform Implementation of the CFS-PML Based on Memory-Minimized Method

Implicit Approximate Crank–Nicolson Theory for Anisotropic Ferrite Structure Simulation with Enhanced Absorption

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