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A Stable and Efficient Direct time Integration of the Vector Wave Equation in the finite-element time-domain method for Dispersive Media

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2015年第1期63卷 314-321页

作者： Akbarzadeh-Sharbaf, Ali Giannacopoulos, Dennis D. McGill Univ Dept Elect & Comp Engn Montreal PQ H3A 0E9 Canada

The finite-element time-domain (FETD) solution of the vector wave equation (VWE) is directly extended to doubly dispersive media using the bilinear transform approach. The proposed formulation is quite general and flexible in the sense of material dispersion model in contrast to limitations of existing convolutional-based approaches. In addition, it can be implemented in a very straightforward and efficient manner. A stability analysis is performed that demonstrates the unconditional stability of the original formulation is preserved in the dispersive case. However, in order to avoid the well-known late-time instabilities that arise in this formulation, an alternative formulation is considered and extended to the dispersive case with the same approach. Several numerical examples are simulated to verify the validity and accuracy of the proposed formulations. The late-time stability of the alternative formulation is tested through a numerical example with 20 million time steps. The solution is completely free from late-time growth.

关键词： Dispersive media finite-element time-domain method

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A NOVEL finite element time domain method FOR NONLINEAR MAXWELL'S EQUATIONS BASED ON THE PARAMETRIC QUADRATIC PROGRAMMING method

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MICROWAVE AND OPTICAL TECHNOLOGY LETTERS 2015年第7期57卷 1640-1645页

作者： Zhu, Bao Yang, Hongwei Chen, Jiefu Dalian Univ Technol Sch Mat Sci & Engn Dalian 116023 Liaoning Peoples R China Beijing Univ Technol Coll Appl Sci Beijing 100124 Peoples R China Weatherford Int Advantage R&D Ctr Houston TX 77060 USA

A finite-element time-domain method is developed for Maxwell's equations with nonlinear media. Compared with conventional nonlinear numerical methods, the proposed scheme is not based on iterations, but using the quadratic programming method. The nonlinear constitutive relations are treated as a series of linear complementary problems, thus, this scheme presents very good convergence behavior in computation. Numerical results demonstrate the validity of the proposed method. (c) 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 57:1640-1645, 2015

关键词： nonlinear electromagnetism finite-element time-domain method linear complementarity problem parametric variational principle

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Hybrid method for transient responses of transmission line in an apertured enclosure based on FETD method and transmission line equations

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IET SCIENCE MEASUREMENT & TECHNOLOGY 2020年第9期14卷 685-695页

作者： Gong, Yanfei Jiang, Luhang Beijing Informat Sci & Technol Univ Minist Educ Optoelect Measurement Technol & Instr Key Lab 35 Beisihuan Middle Rd Beijing Peoples R China North China Elect Power Univ Sch Elect & Elect Engn 2 Beinong Rd Beijing Peoples R China

A hybrid method combining the finite-element time-domain (FETD) method and transmission line (TL) equations (FETD-TL) is presented for evaluating the transient responses of a lossy TL in an apertured rectangular enclosure excited by electromagnetic pulses. First, the electric fields in the enclosure without the TL are calculated based on the Bethe's small holes theory and the mirror procedure. Then, the enclosure's electric fields are introduced into the second-order TL equation for current as the equivalent distributed sources. The transient currents induced on the TL are obtained by solving the second-order TL equation for current based on the FETD method with a single iteration variable. Finally, the transient voltages induced on the TL are computed by discretising the first-order TL equation. Compared with the method based on finite-difference time-domain (FDTD) method and TL (FDTD-TL) via several examples, the proposed hybrid method is proved to be correct and effective, which possesses much higher convenience and efficiency than FDTD-TL method in dealing with TL model terminated by complex lumped parametric networks.

关键词： transmission line theory lumped parameter networks transient response electromagnetic pulse finite element analysis finite difference time-domain analysis iterative methods complex lumped parametric networks single iteration variable equivalent distributed sources Bethe small holes theory finite-element time-domain method apertured enclosure FDTD-TL method hybrid method finite-difference time-domain method first-order TL equation transient voltages FETD method transient currents second-order TL equation apertured rectangular enclosure transient responses transmission line equations

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Research and application of the FETD method for the EM transient response of MTLs excited by HEMP

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IET SCIENCE MEASUREMENT & TECHNOLOGY 2019年第6期13卷 803-811页

作者： Gong, Yanfei Hao, Jianhong Jiang, Luhang Liu, Qiang Zhou, Haijing North China Elect Power Univ Dept Elect & Elect Engn 2 Beinong Rd Beijing Peoples R China Inst Appl Phys & Computat Math Dept Software Ctr 2 Fenghao East Rd Beijing Peoples R China

An efficient field-to-line coupling model in the time domain is developed combining the second-order decoupled multiconductor transmission lines (MTLs) equations and the finite-element time-domain (FETD) method for evaluating the electromagnetic (EM) transient response of MTLs over a lossy ground excited by a high-altitude EM pulse (HEMP). First, the incident HEMP electric fields on the lines are calculated as equivalent distributed sources introduced into the MTLs equations. Then, the discrete FETD equations for the lines against the HEMP, in which the effect of frequency-dependent parameters caused by the ground impedance is considered, are derived using the FETD method with current as the single iteration variable. Finally, the transient currents induced on the lines are obtained by assembling all the discrete FETD equations into the global FETD equation, and the transient induced voltages on the lines are calculated by discretising the coupled equations with respect to current and voltage. The proposed model is successfully compared with the finite-difference time-domain method via several examples. It is then employed to analyse the effect of various parameters on the transient currents including the polarisation and the incident angles of the HEMP, the conductivity, and the relative permittivity of the soil.

关键词： permittivity transmission line theory transient response time-domain analysis multiconductor transmission lines finite element analysis electrical conductivity frequency-dependent parameters ground impedance FETD method discrete FETD equations global FETD equation coupled equations efficient field-to-line coupling model finite-element time-domain method lossy ground high-altitude EM pulse incident HEMP electric fields equivalent distributed sources MTL equations EM transient currents second-order decoupled multiconductor transmission line equations electromagnetic transient response single iteration variable transient induced voltages electrical conductivity relative permittivity soil

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Spectral-Prism element for Multi-Scale Layered Package-Chip Co-Simulations Using the Discontinuous Galerkin time-domain method

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ELECTROMAGNETICS 2014年第3-4期34卷 270-285页

作者： Tobon, Luis E. Ren, Qiang Liu, Qing Huo Duke Univ Dept Elect & Comp Engn Durham NC 27708 USA Pontificia Univ Javeriana Cali Dept Elect Engn & Comp Sci Bogota Colombia

A new kind of prism element with a triangular base is presented for discretization of multi-scale layered structures within the discontinuous Galerkin time-domain framework. Mixed-order curl-conforming vector basis functions are used in the triangular bases of the prismatic element. The height of the prism adopts spectral basis functions based on Gauss-Lobatto-Legendre polynomials, with an arbitrary order of interpolation. This method combines the flexibility of triangles with the accuracy of spectral elements for layered structures. Eigenvalues obtained show better results than traditional finite elements using tetrahedrons and hexahedrons. For transient analysis, the implicit Crank-Nicholson method is implemented for sequential sub-domains. This kind of arrangement of sub-domains produces a block tridiagonal linear system, thus allowing a block Thomas algorithm to solve the system efficiently. A package-to-chip example shows the efficacy of this method.

关键词： multi-layer structure spectral-prism element finite-element time-domain method discontinuous Galerkin multi-scale problems

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Complex frequency shifted-perfectly matched layer for the finite-element time-domain method

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AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS 2009年第1期63卷 72-77页

作者： Movahhedi, Masoud Abdipour, Abdolali Shahid Bahonar Univ Dept Elect Engn Kerman Iran Amirkabir Univ Technol Tehran Polytech Dept Elect Engn Tehran Iran

We present a new formulation to implement the complex frequency shifted-perfectly matched layer (CFS-PML) for boundary truncation in three-dimensional vector finite-element time-domain method applied to the vector wave equation. It is shown that the proposed method is highly absorptive to evanescent modes, when computing the wave interaction of elongated structures or sharp corners, and can improve the performance of the boundary truncation, significantly. The impact of the CFS-PML parameters on the reflection error is investigated and optimal choices of these parameters are derived. (C) 2007 Elsevier GmbH. All rights reserved.

关键词： Complex frequency shifted-perfectly matched layer (CFS-PML) finite-element time-domain method Vector wave equation

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APPLICATION OF THE MULTILEVEL COMPRESSED BLOCK DECOMPOSITION TO ELECTROMAGNETIC PROBLEMS ANALYSIS BASED ON FETD method

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MICROWAVE AND OPTICAL TECHNOLOGY LETTERS 2014年第3期56卷 654-660页

作者： Ding, Dazhi Z. Niu, Rongxin X. Jiang, Zhaoneng N. Chen, Rushan S. Nanjing Univ Sci & Technol Dept Commun Engn Nanjing Jiangsu Peoples R China

In this article, the multilevel compressed block decomposition algorithm (MLCBD) is introduced to provide a data-sparse way to approximate the inverse of the sparse coefficient matrix produced by the finite-element time-domain (FETD) method which is dense originally. Once the approximate inverse is obtained, the FETD method can be computed explicitly at each time step. The accuracy of this approximation is controllable related to the different choices of the MLCBD parameters. A modification algorithm is proposed to efficiently improve the accuracy of the approximate solution computed by the MLCBD-based direct method. Numerical experiments are performed to demonstrate the accuracy and efficiency of the proposed method. ? 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:654–660, 2014

关键词： finite-element time-domain method multilevel compressed block decomposition algorithm electromagnetic problems

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finite-element time-domain Solution of the Vector Wave Equation in Doubly Dispersive Media Using Mobius Transformation Technique

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2013年第8期61卷 4158-4166页

作者： Akbarzadeh-Sharbaf, Ali Giannacopoulos, Dennis D. McGill Univ Dept Elect & Comp Engn Montreal PQ H3A 0E9 Canada

Several finite-element time-domain (FETD) formulations to model inhomogeneous and electrically/magnetically/doubly dispersive materials based on the second-order vector wave equation discretized by the Newmark-beta scheme are developed. In contrast to the existing formulations, which employ recursive convolution (RC) approaches, we use a Mobius transformation method to derive our new formulations. Hence, the obtained equations are not only simpler in form and easier to derive and implement, but also do not suffer from the intrinsic limitations of the RC methods in modeling arbitrary high-order media. To obtain the formulations, we first demonstrate that the update equation for the electric field strength {e} in the mixed Crank-Nicolson (CN) FETD formulation, which is based on expanding the electric and magnetic field in terms of the edge and face elements in space and discretizing the resultant first-order differential equations using Crank-Nicolson scheme in time, is equivalent to the unconditionally stable (US) second-order vector wave equation for the same variable ({e}) discretized by the Newmark-beta method with beta = 1/4. In addition, we show that the update equation for the magnetic flux density {b} in CN-FETD is the same as the second-order vector wave equation for {b} on the dual grid discretized again by a similar Newmark-beta method. Subsequently, thanks to the mixed FETD formulation properties, we derive update equations for the constitutive relations using a Mobius transformation method separately. In addition, we use the shown equivalence to derive formulations based on the vector wave equation. Finally, several numerical examples are solved to validate the developed formulations.

关键词： Dispersive media finite-element time-domain method

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Analysis of photonic crystals using the hybrid finite-element/finite-difference time domain technique based on the discontinuous Galerkin method

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INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN ENGINEERING 2012年第5期92卷 495-506页

作者： Zhu, Bao Chen, Jiefu Zhong, Wanxie Liu, Qing Huo Dalian Univ Technol Dept Engn Mech State Key Lab Struct Anal Ind Equipment Dalian 116023 Liaoning Peoples R China Weatherford Int Ltd Advantage Res & Dev Ctr Houston TX 77060 USA Duke Univ Dept Elect & Comp Engn Durham NC 27708 USA

Two-dimensional photonic crystal structures are analyzed by a recently developed hybrid technique combining the finite-element time-domain (FETD) method and the finite-difference time-domain (FDTD) method. This hybrid FETD/FDTD method uses the discontinuous Galerkin method as framework for domain decomposition. To the best of our knowledge, this is the first hybrid FETD/FDTD method that allows non-conformal meshes between different FETD and FDTD subdomains. It is also highly parallelizable. These properties are very suitable for the computation of periodic structures with curved surfaces. Numerical examples for the computation of the scattering parameters of two-dimensional photonic bandgap structures are presented as applications of the hybrid FETD/FDTD method. Numerical results demonstrate the efficiency and accuracy of the proposed hybrid method. Copyright (c) 2012 John Wiley & Sons, Ltd.

关键词： finite-element time-domain method finite-difference time-domain method discontinuous Galerkin method domain decomposition non-conformal mesh photonic bandgap structures

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Scattered field FETD modeling of oblique plane wave incidence from a circular PEC cylinder: TMz polarization

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MICROWAVE AND OPTICAL TECHNOLOGY LETTERS 2013年第7期55卷 1516-1520页

作者： Bavelis, Konstantinos Mias, Christos Univ Warwick Sch Engn Coventry CV4 7AL W Midlands England

Oblique TMz polarized plane wave scattering from a perfectly electrically conducting cylinder of circular cross-section is modeled using a finite-element time-domain formulation in terms of the scattered electric field using a modal nonreflecting boundary condition and both nonperiodic and periodic formulations.(c) 2013 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:15161520, 2013;View this article online at ***. DOI 10.1002/mop.27614

关键词： finite-element time-domain method cylinder oblique scattering TM polarization

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