Quadratic Complex Rational Function Research Articles

Numerical Stability of Modified Lorentz FDTD Unified From Various Dispersion Models.

The finite-difference time-domain (FDTD) method has been widely used to analyze electromagnetic wave propagation in complex dispersive media. Until now, there are many reported dispersion models including Debye, Drude, Lorentz, complex-conjugate pole-residue (CCPR), quadratic complex rational function (QCRF), and modified Lorentz (mLor). The mLor FDTD is promising since the mLor dispersion model can simply unify other dispersion models. To fully utilize the unified mLor FDTD method, it is of great importance to investigate its numerical stability in the aspects of the original dispersion model parameters. In this work, the numerical stability of the mLor FDTD formulation unified from the aforementioned dispersion models is comprehensively studied. It is found out that the numerical stability conditions of the original model-based FDTD method are equivalent to its unified mLor FDTD counterparts. However, when unifying the mLor FDTD formulation for the QCRF model, a proper Courant number should be used. Otherwise, its unified mLor FDTD simulation may suffer from numerical instability, different from other dispersion models. Numerical examples are performed to validate our investigations.

Dispersive FDTD Scheme and Surface Impedance Boundary Condition for Modeling Pulse Propagation in Very Lossy Medium

A dispersive surface impedance boundary condition (SIBC) is implemented in a dispersive finite-difference time-domain (FDTD) scheme to model pulse propagation and scattering from an aquifer, which has high permittivity and high conductivity. A quadratic complex rational function (QCRF) is adopted to model the dispersive media over a wide frequency band for implementing the dispersive FDTD scheme. The proposed method is demonstrated by simulating the operation of ground-penetrating radar (GPR) in detecting water table. Group delay and pulse-broadening parameter (PBP) are defined to analyze the deformation of pulses propagating in a dispersive lossy medium.

Comprehensive Study on Numerical Aspects of Modified Lorentz Model-Based Dispersive FDTD Formulations

Finite-difference time domain (FDTD) has been widely used to analyze electromagnetic wave interaction with dispersive media. It is of great necessity to incorporate a dispersion model into FDTD formulation for electromagnetic wave analysis of dispersive media. Recently, it was reported that the modified Lorentz model can cover Debye, Drude, Lorentz, critical point, and quadratic complex rational function models. In this work, it is illustrated that the modified Lorentz model can also cover the complex-conjugate pole-residue model which is one of the most popular dispersion models. Modified Lorentz-based dispersive FDTD has not been thoroughly studied, especially for numerical aspects. In this work, we investigate auxiliary differential equation (ADE)-FDTD formulations for the modified Lorentz model based on electric flux density (D), current (J), or polarization (P). We perform a comprehensive study on memory requirement, the number of arithmetic operations, numerical stability, and numerical permittivity for the above three ADE-FDTD formulations. In addition, the bilinear transformation (BT) is incorporated into modified Lorentz-based FDTD formulations and it will be shown that the utilization of the BT can lead to better performance in terms of numerical stability and numerical accuracy. Numerical examples are used to demonstrate our work.

Newmark-FDTD Formulation for Modified Lorentz Dispersive Medium and Its Equivalence to Auxiliary Differential Equation-FDTD with Bilinear Transformation

The finite-difference time-domain (FDTD) method has been popularly utilized to analyze the electromagnetic (EM) wave propagation in dispersive media. Various dispersion models were introduced to consider the frequency-dependent permittivity, including Debye, Drude, Lorentz, quadratic complex rational function, complex-conjugate pole-residue, and critical point models. The Newmark-FDTD method was recently proposed for the EM analysis of dispersive media and it was shown that the proposed Newmark-FDTD method can give higher stability and better accuracy compared to the conventional auxiliary differential equation- (ADE-) FDTD method. In this work, we extend the Newmark-FDTD method to modified Lorentz medium, which can simply unify aforementioned dispersion models. Moreover, it is found that the ADE-FDTD formulation based on the bilinear transformation is exactly the same as the Newmark-FDTD formulation which can have higher stability and better accuracy compared to the conventional ADE-FDTD. Numerical stability, numerical permittivity, and numerical examples are employed to validate our work.

Accurate and Efficient Finite-Difference Time-Domain Simulation Compared With CCPR Model for Complex Dispersive Media

Recently, it has received a great deal of attention to analyze the electromagnetic wave problems in dispersive media by using the finite-difference time-domain (FDTD) method. Accordingly, it is of great importance to employ a proper dispersion model which can fit the frequency-dependent permittivity of a medium considered. The reported dispersion models include Debye, Drude, Lorentz, modified Lorentz, quadratic complex rational function, complex-conjugate pole-residue (CCPR) models. The CCPR dispersion model has advantage over other dispersion models in the fact that accurate CCPR dispersion parameters can be simply extracted by using the powerful and robust vector fitting tool which has been widely used in the circuit theory. However, the arithmetic operation of CCPR-based FDTD implementation is involved with complex-valued numbers and thus its numerical computation is not efficient. In this work, we propose an accurate and efficient FDTD simulation for complex dispersive media. In specific, an accurate CCPR dispersion model is simply obtained using the vector fitting tool and then the CCPR dispersion model is converted to the modified Lorentz dispersion model which leads to the arithmetic operation of only real-valued numbers in its FDTD implementation. Numerical examples are used to illustrate the accuracy and efficiency of our dispersive FDTD simulation.

Finite-Difference Time-Domain Modeling for Electromagnetic Wave Analysis of Human Voxel Model at Millimeter-Wave Frequencies

The finite-difference time-domain (FDTD) modeling of a human voxel model at millimeter-wave (mmWave) frequencies is presented. It is very important to develop the proper geometrical and electrical modeling of a human voxel model suitable for accurate electromagnetic (EM) analysis. Although there are many human phantom models available, their voxel resolution is too poor to use for the FDTD study of EM wave interaction with human tissues. In this paper, we develop a proper human voxel model suitable for mmWave FDTD analysis using the voxel resolution enhancement technique and the image smoothing technique. The former can improve the resolution of the human voxel model and the latter can alleviate staircasing boundaries of the human voxel model. Quadratic complex rational function is employed for the electrical modeling of human tissues in the frequency range of 6–100 GHz. Massage passing interface-based parallel processing is also applied to dramatically speed up FDTD calculations. Numerical examples are used to illustrate the validity of the mmWave FDTD simulator developed here for bio electromagnetics studies.

Stability Considerations for the Direct FDTD Implementation of the Dispersive Quadratic Complex Rational Function Models

In this communication, detailed stability considerations for the direct finite difference time domain implementation of the dispersive quadratic complex rational function models are investigated. It is shown that the time step stability limit of this numerical scheme is more restrictive than the previously published constrain. In addition, it is found that by using high spatial resolution, the stability limit tends to retain the classical Courant–Friedrichs–Lewy constrain. Numerical examples are included to verify these results.

Simulation of Randomly Textured Tandem Silicon Solar Cells Using Quadratic Complex Rational Function Approach Along with Artificial Neural Network

Simulation of Randomly Textured Tandem Silicon Solar Cells Using Quadratic Complex Rational Function Approach Along with Artificial Neural Network

Parallel Dispersive FDTD Method Based on the Quadratic Complex Rational Function

Recently, the quadratic complex rational function (QCRF) function was proposed for accurate finite-difference time-domain (FDTD) dispersive modeling. First, this letter discusses two implementations of QCRF-FDTD to a zeroth-order temporal derivative term and it is observed that the numerical accuracy of the double averaging implementation is better than that of the direct implementation. Second, this work presents a fast QCRF-FDTD algorithm by employing a parallel processing algorithm. The proposed parallel QCRF-FDTD is validated in terms of the speedup fact and the computational accuracy. Finally, we analyze the shielding effectiveness of large-scale concrete structures by using our parallel QCRF-FDTD.

Three-dimensional efficient dispersive alternating-direction-implicit finite-difference time-domain algorithm using a quadratic complex rational function.

Efficient unconditionally stable FDTD method is developed for the electromagnetic analysis of dispersive media. Toward this purpose, a quadratic complex rational function (QCRF) dispersion model is applied to the alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method. The 3-D update equations of QCRF-ADI-FDTD are derived using Maxwell's curl equations and the constitutive relation. The periodic boundary condition of QCRF-ADI-FDTD is discussed in detail. A 3-D numerical example shows that the time-step size can be increased by the proposed QCRF-ADI-FDTD beyond the Courant-Friedrich-Levy (CFL) number, without numerical instability. It is observed that, for refined computational cells, the computational time of QCRF-ADI-FDTD is reduced to 28.08 % of QCRF-FDTD, while the L2 relative error norm of a field distribution is 6.92 %.

Accurate FDTD modelling for dispersive media using rational function and particle swarm optimisation

This article presents an accurate finite-difference time domain (FDTD) dispersive modelling suitable for complex dispersive media. A quadratic complex rational function (QCRF) is used to characterise their dispersive relations. To obtain accurate coefficients of QCRF, in this work, we use an analytical approach and a particle swarm optimisation (PSO) simultaneously. In specific, an analytical approach is used to obtain the QCRF matrix-solving equation and PSO is applied to adjust a weighting function of this equation. Numerical examples are used to illustrate the validity of the proposed FDTD dispersion model.

On the Numerical Stability of Finite-Difference Time-Domain for Wave Propagation in Dispersive Media Using Quadratic Complex Rational Function

Recently, based on a quadratic complex rational function, a simple and accurate finite-difference time-domain algorithm was introduced for the study of electromagnetic wave propagation in dispersive media. It is of great necessity to investigate the numerical stability of the quadratic complex rational function–finite-difference time-domain to fully utilize this finite-difference time-domain algorithm. In this work, using the von Neumann method with the Routh–Hurwitz criterion, the numerical stability conditions of the quadratic complex rational function–finite-difference time-domain are investigated. It is shown that the numerical stability conditions of the quadratic complex rational function–finite-difference time-domain are not same as those of the conventional finite-difference time-domain schemes.

On the Numerical Accuracy of Finite-Difference Time-Domain Dispersive Modeling Based on a Complex Quadratic Rational Function

Recently, based on a quadratic complex rational function, an attractive finite-difference time-domain algorithm was suggested for dispersive modeling of complex media because it is accurate and easy to implement. To fully utilize the quadratic complex rational function finite-difference time-domain, it is essential to investigate its numerical errors based on an exact mathematical approach. Toward this purpose, the exact expression of the numerical permittivity is first derived. From this numerical permittivity, the numerical dispersion, numerical dissipation, and numerical anisotropy inherent to the quadratic complex rational function finite-difference time-domain are examined. Numerical examples illustrate that the numerical errors of the quadratic complex rational function finite-difference time-domain is almost same as those of the nondispersive finite-difference time-domain.

Time domain simulation of tandem silicon solar cells with optimal textured light trapping enabled by the quadratic complex rational function.

Amorphous silicon/crystalline silicon (a-Si/c-Si) micromorph tandem cells, with best confirmed efficiency of 12.3%, have yet to fully approach their theoretical performance limits. In this work, we consider a strategy for improving the light trapping and charge collection of a-Si/c-Si micromorph tandem cells using random texturing with adjustable short-range correlations and long-range periodicity. In order to consider the full-spectrum absorption of a-Si and c-Si, a novel dispersion model known as a quadratic complex rational function (QCRF) is applied to photovoltaic materials (e.g., a-Si, c-Si and silver). It has the advantage of accurately modeling experimental semiconductor dielectric values over the entire relevant solar bandwidth from 300-1000 nm in a single simulation. This wide-band dispersion model is then used to model a silicon tandem cell stack (ITO/a-Si:H/c-Si:H/silver), as two parameters are varied: maximum texturing height h and correlation parameter f. Even without any other light trapping methods, our front texturing method demonstrates 12.37% stabilized cell efficiency and 12.79 mA/cm² in a 2 μm-thick active layer.

Accurate FDTD Dispersive Modeling for Concrete Materials

This work presents an accurate finite-difference time-domain (FDTD) dispersive modeling of concrete materials with different water/cement ratios in 50 MHz to 1 GHz. A quadratic complex rational function (QCRF) is employed for dispersive modeling of the relative permittivity of concrete materials. To improve the curve fitting of the QCRF model, the Newton iterative method is applied to determine a weighting factor. Numerical examples validate the accuracy of the proposed dispersive FDTD modeling.

FDTD Dispersive Modeling of Human Tissues Based on Quadratic Complex Rational Function

We propose a dispersive finite-difference time domain (FDTD) suitable for the electromagnetic analysis of human tissues. The dispersion relation of biological tissues is characterized by a quadratic complex rational function (QCRF) that leads to an accurate FDTD algorithm in 400 MHz-3 GHz. QCRF coefficients are extracted by applying the complex-curve fitting technique, without initial guess. Numerical examples are used to illustrate the computational accuracy and stability of QCRF-based FDTD.

정확하고 효율적인 인체 FDTD 분산 모델링

본 논문에서는 인체의 전자파 해석을 위해 유한 차분 시간 영역법(FDTD: Finite-Difference Time-Domain)에 적합한 분산 모델링을 제안한다. 주파수에 따라 전기적 특성이 변하는 인체의 분산 특성을 정확하고 효율적으로 모델링을 하기 위해 상대 유전율을 2차 복소수 분수 함수식(QCRF: Quadratic Complex Rational Function)으로 표현하였다. WLSM(Weight Least Square Method) 기반의 복소수 커브 피팅법을 적용하여 인체 조직에 대한 QCRF 계수들을 추출하였으며, QCRF 분산 모델을 FDTD에 적용하는 방법을 논의하였다. 본 논문에서 제안한 QCRF 기반의 인체 분산 모델이 Gabriel의 측정 데이터와 일치하며, FDTD 적용시 Cole-Cole 분산 모델보다 계산 효율이 뛰어남을 확인하였다. 단일 주파수와 광대역 주파수 신호를 입력원으로 한 모의 실험을 통하여 QCRF 기반의 FDTD 분산 알고리즘의 검증 및 분석을 마무리하였다. We propose a dispersive finite-difference time domain(FDTD) algorithm suitable for the electromagnetic analysis of the human body. In this work, the dispersion relation of the human body is modeled by a quadratic complex rational function(QCRF), which leads to an accurate and efficient FDTD algorithm. Coefficients(involved in QCRF) for various human tissues are extracted by applying a weighted least square method(WLSM), referred to as the complex-curve fitting technique. We also presents the FDTD formulation for the QCRF-based dispersive model in detail. The QCRFbased dispersive model is significantly accurate and its FDTD implementation is more efficient than the counterpart of the Cole-Cole model. Numerical examples are used to show the validity of the proposed FDTD algorithm.