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Journal articles on the topic 'Maxwell's equations in time domain'

Author: Grafiati

Published: 8 February 2025

Last updated: 13 July 2025

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1

Huang, Zhi-Xiang, Wei Sha, Xian-Liang Wu, and Ming-Sheng Chen. "Decomposition methods for time-domain Maxwell's equations." International Journal for Numerical Methods in Fluids 56, no. 9 (2008): 1695–704. http://dx.doi.org/10.1002/fld.1569.

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2

Bao, Gang, Bin Hu, Peijun Li, and Jue Wang. "Analysis of time-domain Maxwell's equations in biperiodic structures." Discrete & Continuous Dynamical Systems - B 25, no. 1 (2020): 259–86. http://dx.doi.org/10.3934/dcdsb.2019181.

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3

Van, Tri, and Aihua Wood. "A Time-Domain Finite Element Method for Maxwell's Equations." SIAM Journal on Numerical Analysis 42, no. 4 (2004): 1592–609. http://dx.doi.org/10.1137/s0036142901387427.

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4

Ala, G., E. Francomano, A. Tortorici, E. Toscano, and F. Viola. "Corrective meshless particle formulations for time domain Maxwell's equations." Journal of Computational and Applied Mathematics 210, no. 1-2 (2007): 34–46. http://dx.doi.org/10.1016/j.cam.2006.10.054.

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5

Liu, Yaxing, Joon-Ho Lee, Tian Xiao, and Qing H. Liu. "A spectral-element time-domain solution of Maxwell's equations." Microwave and Optical Technology Letters 48, no. 4 (2006): 673–80. http://dx.doi.org/10.1002/mop.21440.

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6

Buchanan, W. J., and N. K. Gupta. "Maxwell's Equations in the 21st Century." International Journal of Electrical Engineering & Education 30, no. 4 (1993): 343–53. http://dx.doi.org/10.1177/002072099303000408.

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Maxwell's equations in the 21st Century The finite-difference time-domain method is a novel method for solving Maxwell's curl equations, especially when parallel-processing techniques are applied. The next generation of computers will bring a revolution by exploiting the use of parallel processing in computation to the maximum.

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7

Nevels, R., and J. Jeong. "The Time Domain Green's Function and Propagator for Maxwell's Equations." IEEE Transactions on Antennas and Propagation 52, no. 11 (2004): 3012–18. http://dx.doi.org/10.1109/tap.2004.835123.

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8

Cohen, Gary, Xavier Ferrieres, and Sébastien Pernet. "Discontinuous Galerkin methods for Maxwell's equations in the time domain." Comptes Rendus Physique 7, no. 5 (2006): 494–500. http://dx.doi.org/10.1016/j.crhy.2006.03.004.

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9

Su, Zhuo, Yongqin Yang, and Yunliang Long. "A Compact Unconditionally Stable Method for Time-Domain Maxwell's Equations." International Journal of Antennas and Propagation 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/689327.

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Higher order unconditionally stable methods are effective ways for simulating field behaviors of electromagnetic problems since they are free of Courant-Friedrich-Levy conditions. The development of accurate schemes with less computational expenditure is desirable. A compact fourth-order split-step unconditionally-stable finite-difference time-domain method (C4OSS-FDTD) is proposed in this paper. This method is based on a four-step splitting form in time which is constructed by symmetric operator and uniform splitting. The introduction of spatial compact operator can further improve its performance. Analyses of stability and numerical dispersion are carried out. Compared with noncompact counterpart, the proposed method has reduced computational expenditure while keeping the same level of accuracy. Comparisons with other compact unconditionally-stable methods are provided. Numerical dispersion and anisotropy errors are shown to be lower than those of previous compact unconditionally-stable methods.

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10

Wang, J., and Y. Long. "Long time stable compact fourth-order scheme for time domain Maxwell's equations." Electronics Letters 46, no. 14 (2010): 995. http://dx.doi.org/10.1049/el.2010.1204.

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11

Deore, Narendra, and Avijit Chatterjee. "CELL-VERTEX BASED MULTIGRID SOLUTION OF THE TIME-DOMAIN MAXWELL'S EQUATIONS." Progress In Electromagnetics Research B 23 (2010): 181–97. http://dx.doi.org/10.2528/pierb10062002.

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12

Sha, Wei, Zhixiang Huang, Mingsheng Chen, and Xianliang Wu. "Survey on Symplectic Finite-Difference Time-Domain Schemes for Maxwell's Equations." IEEE Transactions on Antennas and Propagation 56, no. 2 (2008): 493–500. http://dx.doi.org/10.1109/tap.2007.915444.

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13

Nevels, Robert, and Jaehoon Jeong. "Time Domain Coupled Field Dyadic Green Function Solution for Maxwell's Equations." IEEE Transactions on Antennas and Propagation 56, no. 8 (2008): 2761–64. http://dx.doi.org/10.1109/tap.2008.927574.

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14

Wang, Jianying, Peng Liu, and Yunliang Long. "A Compact Symplectic High-Order Scheme for Time-Domain Maxwell's Equations." IEEE Antennas and Wireless Propagation Letters 9 (2010): 371–74. http://dx.doi.org/10.1109/lawp.2010.2049470.

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15

Kim, Joonshik, and Fernando L. Teixeira. "Parallel and Explicit Finite-Element Time-Domain Method for Maxwell's Equations." IEEE Transactions on Antennas and Propagation 59, no. 6 (2011): 2350–56. http://dx.doi.org/10.1109/tap.2011.2143682.

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16

Omick, S., and S. Castillo. "Error characterization for the time-domain numerical solution of Maxwell's equations." IEEE Antennas and Propagation Magazine 36, no. 5 (1994): 58–62. http://dx.doi.org/10.1109/74.334927.

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17

Bi, Z., K. Wu, C. Wu, and J. Litva. "A new finite-difference time-domain algorithm for solving Maxwell's equations." IEEE Microwave and Guided Wave Letters 1, no. 12 (1991): 382–84. http://dx.doi.org/10.1109/75.103858.

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18

Lee, J. F. "WETD - a finite element time-domain approach for solving Maxwell's equations." IEEE Microwave and Guided Wave Letters 4, no. 1 (1994): 11–13. http://dx.doi.org/10.1109/75.267679.

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19

Bao, Gang, Ying Li, and Zhengfang Zhou. "Lp estimates of time-harmonic Maxwell's equations in a bounded domain." Journal of Differential Equations 245, no. 12 (2008): 3674–86. http://dx.doi.org/10.1016/j.jde.2008.03.004.

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20

Angulo, Luis Diaz, Jesus Alvarez, Fernando L. Teixeira, M. Fernandez Pantoja, and Salvador G. Garcia. "A Nodal Continuous-Discontinuous Galerkin Time-Domain Method for Maxwell's Equations." IEEE Transactions on Microwave Theory and Techniques 63, no. 10 (2015): 3081–93. http://dx.doi.org/10.1109/tmtt.2015.2472411.

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21

Larson, R. W., T. Rudolph, and P. H. Ng. "Special purpose computers for the time domain advance of Maxwell's equations." IEEE Transactions on Magnetics 25, no. 4 (1989): 2913–15. http://dx.doi.org/10.1109/20.34322.

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22

Dosopoulos, Stylianos, and Jin-Fa Lee. "Interior Penalty Discontinuous Galerkin Method for the Time-Domain Maxwell's Equations." IEEE Transactions on Magnetics 46, no. 8 (2010): 3512–15. http://dx.doi.org/10.1109/tmag.2010.2043235.

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23

Huang, Z. X., X. L. Wu, W. Sha, and M. S. Chen. "Optimal symplectic integrators for numerical solution of time-domain Maxwell's equations." Microwave and Optical Technology Letters 49, no. 3 (2007): 545–47. http://dx.doi.org/10.1002/mop.22193.

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24

Huang, Z. X., X. L. Wu, W. E. I. Sha, and B. Wu. "Optimized Operator-Splitting Methods in Numerical Integration of Maxwell's Equations." International Journal of Antennas and Propagation 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/956431.

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Optimized operator splitting methods for numerical integration of the time domain Maxwell's equations in computational electromagnetics (CEM) are proposed for the first time. The methods are based on splitting the time domain evolution operator of Maxwell's equations into suboperators, and corresponding time coefficients are obtained by reducing the norm of truncation terms to a minimum. The general high-order staggered finite difference is introduced for discretizing the three-dimensional curl operator in the spatial domain. The detail of the schemes and explicit iterated formulas are also included. Furthermore, new high-order Padé approximations are adopted to improve the efficiency of the proposed methods. Theoretical proof of the stability is also included. Numerical results are presented to demonstrate the effectiveness and efficiency of the schemes. It is found that the optimized schemes with coarse discretized grid and large Courant-Friedrichs-Lewy (CFL) number can obtain satisfactory numerical results, which in turn proves to be a promising method, with advantages of high accuracy, low computational resources and facility of large domain and long-time simulation. In addition, due to the generality, our optimized schemes can be extended to other science and engineering areas directly.

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25

BALL, JOHN M., YVES CAPDEBOSCQ, and BASANG TSERING-XIAO. "ON UNIQUENESS FOR TIME HARMONIC ANISOTROPIC MAXWELL'S EQUATIONS WITH PIECEWISE REGULAR COEFFICIENTS." Mathematical Models and Methods in Applied Sciences 22, no. 11 (2012): 1250036. http://dx.doi.org/10.1142/s0218202512500364.

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We are interested in the uniqueness of solutions to Maxwell's equations when the magnetic permeability μ and the permittivity ε are symmetric positive definite matrix-valued functions in ℝ3. We show that a unique continuation result for globally W1, ∞ coefficients in a smooth, bounded domain, allows one to prove that the solution is unique in the case of coefficients which are piecewise W1, ∞ with respect to a suitable countable collection of subdomains with C0 boundaries. Such suitable collections include any bounded finite collection. The proof relies on a general argument, not specific to Maxwell's equations. This result is then extended to the case when within these subdomains the permeability and permittivity are only L∞ in sets of small measure.

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26

Knoke, Tobias, Sebastian Kinnewig, Sven Beuchler, Ayhan Demircan, Uwe Morgner, and Thomas Wick. "Domain Decomposition with Neural Network Interface Approximations for time-harmonic Maxwell’s equations with different wave numbers." Selecciones Matemáticas 10, no. 01 (2023): 1–15. http://dx.doi.org/10.17268/sel.mat.2023.01.01.

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In this work, we consider the time-harmonic Maxwell's equations and their numerical solution with a domain decomposition method. As an innovative feature, we propose a feedforward neural network-enhanced approximation of the interface conditions between the subdomains. The advantage is that the interface condition can be updated without recomputing the Maxwell system at each step. The main part consists of a detailed description of the construction of the neural network for domain decomposition and the training process. To substantiate this proof of concept, we investigate a few subdomains in some numerical experiments with low frequencies. Therein the new approach is compared to a classical domain decomposition method. Moreover, we highlight current challenges of training and testing with different wave numbers and we provide information on the behaviour of the neural-network, such as convergence of the loss function, and different activation functions.

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27

Helfert, S. F. "The Method of Lines in the time domain." Advances in Radio Science 11 (July 4, 2013): 15–21. http://dx.doi.org/10.5194/ars-11-15-2013.

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Abstract. The Method of Lines (MoL) is a semi-analytical numerical algorithm that has been used in the past to solve Maxwell's equations for waveguide problems. It is mainly used in the frequency domain. In this paper it is shown how the MoL can be used to solve initial value problems in the time domain. The required expressions are derived for one-dimensional structures, where the materials may be dispersive. The algorithm is verified with numerical results for homogeneous structures, and for the concatenation of standard dielectric and left handed materials.

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28

COSTABEL, MARTIN, MONIQUE DAUGE, and CHRISTOPH SCHWAB. "EXPONENTIAL CONVERGENCE OF hp-FEM FOR MAXWELL EQUATIONS WITH WEIGHTED REGULARIZATION IN POLYGONAL DOMAINS." Mathematical Models and Methods in Applied Sciences 15, no. 04 (2005): 575–622. http://dx.doi.org/10.1142/s0218202505000480.

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The time-harmonic Maxwell equations do not have an elliptic nature by themselves. Their regularization by a divergence term is a standard tool to obtain equivalent elliptic problems. Nodal finite element discretizations of Maxwell's equations obtained from such a regularization converge to wrong solutions in any non-convex polygon. Modification of the regularization term consisting in the introduction of a weight restores the convergence of nodal FEM, providing optimal convergence rates for the h version of finite elements. We prove exponential convergence of hp FEM for the weighted regularization of Maxwell's equations in plane polygonal domains provided the hp-FE spaces satisfy a series of axioms. We verify these axioms for several specific families of hp finite element spaces.

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29

Zhang, Pan, Yanyan Hu, Yuchen Jin, Shaogui Deng, Xuqing Wu, and Jiefu Chen. "A Maxwell's Equations Based Deep Learning Method for Time Domain Electromagnetic Simulations." IEEE Journal on Multiscale and Multiphysics Computational Techniques 6 (2021): 35–40. http://dx.doi.org/10.1109/jmmct.2021.3057793.

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30

Joon-Ho Lee, Jiefu Chen, and Qing Huo Liu. "A 3-D Discontinuous Spectral Element Time-Domain Method for Maxwell's Equations." IEEE Transactions on Antennas and Propagation 57, no. 9 (2009): 2666–74. http://dx.doi.org/10.1109/tap.2009.2027731.

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31

Nickisch, L. J., and P. M. Franke. "Finite-difference time-domain solution of Maxwell's equations for the dispersive ionosphere." IEEE Antennas and Propagation Magazine 34, no. 5 (1992): 33–39. http://dx.doi.org/10.1109/74.163808.

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32

El Bouajaji, M., B. Thierry, X. Antoine, and C. Geuzaine. "A quasi-optimal domain decomposition algorithm for the time-harmonic Maxwell's equations." Journal of Computational Physics 294 (August 2015): 38–57. http://dx.doi.org/10.1016/j.jcp.2015.03.041.

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33

Winges, Johan, and Thomas Rylander. "Higher-order brick-tetrahedron hybrid method for Maxwell's equations in time domain." Journal of Computational Physics 321 (September 2016): 698–707. http://dx.doi.org/10.1016/j.jcp.2016.05.063.

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34

Zhong, Shuangying, and Song Liu. "The Force-Gradient Symplectic Finite-Difference Time-Domain Scheme for Maxwell's Equations." IEEE Transactions on Antennas and Propagation 63, no. 2 (2015): 834–38. http://dx.doi.org/10.1109/tap.2014.2381255.

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35

Palaniswamy, Sampath, William F. Hall, and Vijaya Shankar. "Numerical solution to Maxwell's equations in the time domain on nonuniform grids." Radio Science 31, no. 4 (1996): 905–12. http://dx.doi.org/10.1029/96rs00783.

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36

Lee, Robert L., and Niel K. Madsen. "A mixed finite element formulation for Maxwell's equations in the time domain." Journal of Computational Physics 85, no. 2 (1989): 503. http://dx.doi.org/10.1016/0021-9991(89)90168-x.

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37

Lee, Robert L., and Niel K. Madsen. "A mixed finite element formulation for Maxwell's equations in the time domain." Journal of Computational Physics 88, no. 2 (1990): 284–304. http://dx.doi.org/10.1016/0021-9991(90)90181-y.

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38

Niegemann, Jens, Lasha Tkeshelashvili, and Kurt Busch. "Higher-Order Time-Domain Simulations of Maxwell's Equations Using Krylov-Subspace Methods." Journal of Computational and Theoretical Nanoscience 4, no. 3 (2007): 627–34. http://dx.doi.org/10.1166/jctn.2007.027.

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39

Lovetri, Joe, and George I. Costache. "Efficient implementation issues of finite difference time-domain codes for Maxwell's equations." International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 6, no. 3 (1993): 195–206. http://dx.doi.org/10.1002/jnm.1660060304.

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40

Meagher, Timothy, Bin Jiang, and Peng Jiang. "An enhanced finite difference time domain method for two dimensional Maxwell's equations." Numerical Methods for Partial Differential Equations 36, no. 5 (2020): 1129–44. http://dx.doi.org/10.1002/num.22467.

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41

Huang, Zhi-Xiang, Wei Sha, Xian-Liang Wu, and Ming-Sheng Chen. "A novel high-order time-domain scheme for three-dimensional Maxwell's equations." Microwave and Optical Technology Letters 48, no. 6 (2006): 1123–25. http://dx.doi.org/10.1002/mop.21563.

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42

Bouquet, A., C. Dedeban, and S. Piperno. "Discontinuous Galerkin time‐domain solution of Maxwell's equations on locally refined grids with fictitious domains." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 29, no. 3 (2010): 578–601. http://dx.doi.org/10.1108/03321641011028206.

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43

DOUGLAS, JIM, JUAN E. SANTOS, and DONGWOO SHEEN. "A NONCONFORMING MIXED FINITE ELEMENT METHOD FOR MAXWELL'S EQUATIONS." Mathematical Models and Methods in Applied Sciences 10, no. 04 (2000): 593–613. http://dx.doi.org/10.1142/s021820250000032x.

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We present a nonconforming mixed finite element scheme for the approximate solution of the time-harmonic Maxwell's equations in a three-dimensional, bounded domain with absorbing boundary conditions on artificial boundaries. The numerical procedures are employed to solve the direct problem in magnetotellurics consisting in determining a scattered electromagnetic field in a model of the earth having bounded conductivity anomalies of arbitrary shapes. A domain-decomposition iterative algorithm which is naturally parallelizable and is based on a hybridization of the mixed method allows the solution of large three-dimensional models. Convergence of the approximation by the mixed method is proved, as well as the convergence of the iteration.

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44

Park, Jong Hyuk, and John C. Strikwerda. "The Domain Decomposition Method for Maxwell's Equations in Time Domain Simulations with Dispersive Metallic Media." SIAM Journal on Scientific Computing 32, no. 2 (2010): 684–702. http://dx.doi.org/10.1137/070705374.

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45

Yee, K. S., and J. S. Chen. "The finite-difference time-domain (FDTD) and the finite-volume time-domain (FVTD) methods in solving Maxwell's equations." IEEE Transactions on Antennas and Propagation 45, no. 3 (1997): 354–63. http://dx.doi.org/10.1109/8.558651.

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46

Sheu, Tony W. H., S. Z. Wang, J. H. Li, and Matthew R. Smith. "Simulation of Maxwell's Equations on GPU Using a High-Order Error-Minimized Scheme." Communications in Computational Physics 21, no. 4 (2017): 1039–64. http://dx.doi.org/10.4208/cicp.oa-2016-0079.

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AbstractIn this study an explicit Finite Difference Method (FDM) based scheme is developed to solve the Maxwell's equations in time domain for a lossless medium. This manuscript focuses on two unique aspects – the three dimensional time-accurate discretization of the hyperbolic system of Maxwell equations in three-point non-staggered grid stencil and it's application to parallel computing through the use of Graphics Processing Units (GPU). The proposed temporal scheme is symplectic, thus permitting conservation of all Hamiltonians in the Maxwell equation. Moreover, to enable accurate predictions over large time frames, a phase velocity preserving scheme is developed for treatment of the spatial derivative terms. As a result, the chosen time increment and grid spacing can be optimally coupled. An additional theoretical investigation into this pairing is also shown. Finally, the application of the proposed scheme to parallel computing using one Nvidia K20 Tesla GPU card is demonstrated. For the benchmarks performed, the parallel speedup when compared to a single core of an Intel i7-4820K CPU is approximately 190x.

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47

Yu, Mengjun, and Kun Li. "A data-driven reduced-order modeling approach for parameterized time-domain Maxwell's equations." Networks and Heterogeneous Media 19, no. 3 (2024): 1309–35. http://dx.doi.org/10.3934/nhm.2024056.

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<p>This paper proposed a data-driven non-intrusive model order reduction (NIMOR) approach for parameterized time-domain Maxwell's equations. The NIMOR method consisted of fully decoupled offline and online stages. Initially, the high-fidelity (HF) solutions for some training time and parameter sets were obtained by using a discontinuous Galerkin time-domain (DGTD) method. Subsequently, a two-step or nested proper orthogonal decomposition (POD) technique was used to generate the reduced basis (RB) functions and the corresponding projection coefficients within the RB space. The high-order dynamic mode decomposition (HODMD) method leveraged these corresponding coefficients to predict the projection coefficients at all training parameters over a time region beyond the training domain. Instead of direct regression and interpolating new parameters, the predicted projection coefficients were reorganized into a three-dimensional tensor, which was then decomposed into time- and parameter-dependent components through the canonical polyadic decomposition (CPD) method. Gaussian process regression (GPR) was then used to approximate the relationship between the time/parameter values and the above components. Finally, the reduced-order solutions at new time/parameter values were quickly obtained through a linear combination of the POD modes and the approximated projection coefficients. Numerical experiments were presented to evaluate the performance of the method in the case of plane wave scattering.</p>

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48

Jin, Jian-Ming, Mohammad Zunoubi, Kalyan C. Donepudi, and Weng C. Chew. "Frequency-domain and time-domain finite-element solution of Maxwell's equations using spectral Lanczos decomposition method." Computer Methods in Applied Mechanics and Engineering 169, no. 3-4 (1999): 279–96. http://dx.doi.org/10.1016/s0045-7825(98)00158-3.

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49

Zunoubi, M., Jian-Ming Jin, and Weng Cho Chew. "Spectral Lanczos decomposition method for time domain and frequency domain finite-element solution of Maxwell's equations." Electronics Letters 34, no. 4 (1998): 346. http://dx.doi.org/10.1049/el:19980333.

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50

Tiwari, Apurva, and Avijit Chatterjee. "Divergence Error Based p-adaptive Discontinuous Galerkin Solution of Time-domain Maxwell's Equations." Progress In Electromagnetics Research B 96 (2022): 153–72. http://dx.doi.org/10.2528/pierb22080403.

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