Different implementations of material independent multi‐order nearly perfectly matched layers for <scp>EM</scp> simulations

Wu, Peng; Xie, Yongjun; Jiang, Haolin; Niu, Liqiang

doi:10.1002/mop.32495

Cited by 7 publications

(8 citation statements)

References 30 publications

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“…It can be concluded that the proposed algorithm holds the best performance from the aspect of accuracy. Such conclusion can be further demonstrated by the relative local error and relative error in the time and frequency domain, respectively 33 . The relative local error can be defined as

R_{italicdB} (t) = 20 \log_{10} [\frac{|E_{t} (t) - E_{b} (t)|}{|\max \{E_{b} (t)\}|}]

where

E_{t} (t)

is the test solution which can be obtained directly by employing different algorithms and

E_{b} (t)

is the basis for comparison.…”

Section: Numerical Results and Discussionmentioning

confidence: 92%

“…In order to maintain the stability of the algorithm, time step is chosen according to the fine mesh as

Δ t = 0.95 Δ / (2 c_{0}) = 15.8

fs. Absorption of PML regions can be reflected by the relative reflection error in the time domain, as shown in Figure 3 33 …”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…Absorption of PML regions can be reflected by the relative reflection error in the time domain, as shown in Figure 3. 33 As shown in Figure 3, CNAD and CNDG algorithms hold the worst performance due to the calculation of matrices. The proposed scheme can receive similar performance compared with FDTD and CN scheme without subgridding method.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

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ICN‐FDTD scheme with absorption boundary condition for nonuniform rotational symmetric geometrics

Dong

Liu

et al. 2022

Int J Numerical Modelling

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Based on iterated Crank–Nicolson (CN) procedure, an alternative algorithm with perfectly matched layer (PML) formulation is proposed in the body‐of‐revolution (BOR) finite‐difference time‐domain (FDTD) lattice for the simulation of rotational symmetric geometrics. For the nonuniform domain simulation, an alternative subgridding method is employed to during the simulation. The iterated CN procedure improves the efficiency through preventing the calculation of tri‐diagonal matrices. The alternative subgridding method enhances the accuracy in nonuniform domains by the calculation of subregions. Numerical example is carried out for the demonstration of effectiveness including efficiency, accuracy and absorption. Through the results, the proposed scheme shows considerable absorption and accuracy improvement in nonuniform domains. Compared with the other CN schemes, the iterated CN procedure can significantly increase the efficiency with small time steps. In conclusion, the advantages and novelty of the proposed algorithm can be described as follows: (1) The iterated CN procedure is proposed for rotational symmetric geometrics. (2) Absorption boundary condition for iterated CN is proposed in BOR‐FDTD. (3) An alternative subgridding method for iterated CN procedure is proposed in BOR‐FDTD lattice. Thus, the proposed algorithm shows potential in nonuniform rotational symmetric geometrics open region simulation.

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R_{italicdB} (t) = 20 \log_{10} [\frac{|E_{t} (t) - E_{b} (t)|}{|\max \{E_{b} (t)\}|}]

where

E_{t} (t)

is the test solution which can be obtained directly by employing different algorithms and

E_{b} (t)

is the basis for comparison.…”

Section: Numerical Results and Discussionmentioning

confidence: 92%

“…In order to maintain the stability of the algorithm, time step is chosen according to the fine mesh as

Δ t = 0.95 Δ / (2 c_{0}) = 15.8

fs. Absorption of PML regions can be reflected by the relative reflection error in the time domain, as shown in Figure 3 33 …”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Numerical Results and Discussionmentioning

confidence: 99%

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ICN‐FDTD scheme with absorption boundary condition for nonuniform rotational symmetric geometrics

Dong

Liu

et al. 2022

Int J Numerical Modelling

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“…The original higher-order formulation holds six auxiliary variables which affect the efficiency and absorption [ 32 ]. Alternative higher-order formulation with four auxiliary variables is introduced to improve the entire performance, which has been extensively employed in massive problems [ 33 , 34 , 35 , 36 ].…”

Section: Introductionmentioning

confidence: 99%

One-Step Crank-Nicolson Direct-Splitting Algorithm with Enhanced Absorption to Evaluate Low-Pressure Discharge for Satellite Sensors in Outer Space

Wang

Xie

et al. 2023

Sensors

Self Cite

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Low-pressure discharge causes air ionization resulting in performance degeneration or failure for the satellite sensors in outer space. Here, a one-step Crank--Nicolson Direct-Splitting (CNDS) algorithm is proposed to evaluate the electrical behavior of satellite sensors under the low-pressure discharge circumstance. To be more specific, the CNDS algorithm is proposed in the Lorentz medium, which can accurately analyze the ionized air and generated plasma. Higher order perfectly matched layer (PML) is modified in the Lorentz medium to efficiently terminate the unbounded lattice. It can be concluded that the proposed algorithm shows entire considerable performance in the low-pressure discharge evaluation. The proposed PML formulation behaviors enhanced absorbing performance compared with the existing algorithm. Through the experiments, it can be observed that the low-pressure discharge phenomenon causes performance variation, which shows a significant influence on the satellite sensors. Meanwhile, results show considerable agreement between the simulation and experiment results which indicates the effectiveness of the algorithm.

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“…As can be concluded that they ae based on the first order formulation whose absorption problem still exist in the low-frequency band and late-time reflections. To alleviate such condition, the higher order concept is incorporated into the PML regions for the development higher order PML regions into the simulation of GPR problems [24][25][26]. The increment of coefficients and matrices leads to the significant decrement of efficiency.…”

Section: Introductionmentioning

confidence: 99%

Computationally Efficient Locally One-Dimensional Algorithm for Open Region Ground Penetrating Radar Problem With Improved Absorption

Han²,

Xie

et al. 2021

IEEE Access

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By incorporating higher order formulation with perfectly matched layer (PML) implementation, unconditionally stable computationally efficient locally one-dimensional (LOD) algorithm with improved absorption is proposed for simulating ground penetrating radar and its open region problems in finite-difference time-domain (FDTD) algorithm. To take advantages of these methods, the proposed implementation shows characteristics of maintaining considerable accuracy, enhancing computational efficiency and improving the entire absorption. These above-mentioned advantages are illustrated through the ground penetrating radar related problem in open regions. It can be concluded from the calculation results that the proposal shows advantages of higher order formulation, PML implementation and LOD procedure which are efficient in remarkable accuracy, considerable efficiency and improved absorption with increment of CFLNs. Meanwhile, the simulation results also indicate that the proposal is an unconditionally stable procedure with the dissatisfaction of Courant-Friedrichs-Levy stability condition. INDEX TERMS Finite-difference time-domain (FDTD), Locally One-Dimensional (LOD), Perfectly matched layer (PML), Ground penetrating radar (GPR).

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Different implementations of material independent multi‐order nearly perfectly matched layers for EM simulations

Cited by 7 publications

References 30 publications

ICN‐FDTD scheme with absorption boundary condition for nonuniform rotational symmetric geometrics

ICN‐FDTD scheme with absorption boundary condition for nonuniform rotational symmetric geometrics

One-Step Crank-Nicolson Direct-Splitting Algorithm with Enhanced Absorption to Evaluate Low-Pressure Discharge for Satellite Sensors in Outer Space

Computationally Efficient Locally One-Dimensional Algorithm for Open Region Ground Penetrating Radar Problem With Improved Absorption

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