A novel finite element time domain method for nonlinear Maxwell's equations based on the parametric quadratic programming method

ABSTRACT 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 tr...

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Published in:	Microwave and optical technology letters Vol. 57; no. 7; pp. 1640 - 1645
Main Authors:	Zhu, Bao, Yang, Hongwei, Chen, Jiefu
Format:	Journal Article
Language:	English
Published:	New York Blackwell Publishing Ltd 01.07.2015 Wiley Subscription Services, Inc
Subjects:	Convergence Finite element method finite-element time-domain method linear complementarity problem Mathematical analysis Mathematical models Maxwell's equations Microwaves nonlinear electromagnetism Nonlinearity parametric variational principle Quadratic programming
ISSN:	0895-2477, 1098-2760
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Abstract	ABSTRACT 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. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 57:1640–1645, 2015
AbstractList	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. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 57:1640–1645, 2015 ABSTRACT 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. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 57:1640–1645, 2015 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. copyright 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 57:1640-1645, 2015
Author	Chen, Jiefu Zhu, Bao Yang, Hongwei
Author_xml	– sequence: 1 givenname: Bao surname: Zhu fullname: Zhu, Bao organization: School of Materials Science and Engineering, Dalian University of Technology, Liaoning, 116023, Dalian, China – sequence: 2 givenname: Hongwei surname: Yang fullname: Yang, Hongwei organization: College of Applied Sciences, Beijing University of Technology, 100124, Beijing, China – sequence: 3 givenname: Jiefu surname: Chen fullname: Chen, Jiefu email: chenjiefu@gmail.com organization: Advantage R&D Center, Weatherford International, TX, 77060, Houston
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References_xml	– reference: R.W. Cottle, J. Pang, and J.S. Pang, The linear complementarity problem, MA Academic Press, Boston, 1992. – reference: N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984), 373-395. – reference: M. Kojima, S. Mizuno, and A. Yoshise, A polynomial-time algorithm for a class of linear complementarity problems, Math Program 44 (1989), 1-26. – reference: C.E. Lemke and J.T. Howson, Equilibrium points of bimatrix games, SIAM J Appl Math 12 (1964), 413-423. – reference: M.C. Ferris and J.S. Pang, Engineering and economic applications of complementarity problems," SIAM Rev 39 (1997), 669-713. – reference: S.J. Wright, Primal-dual interior-point methods, SIAM, Philadelphia, PA, 1997. – reference: O.L. Mangasarian, Solution of symmetric linear complementarity problems by iterative methods, J Optim Theory Appl 22 (1977), 465-485. – reference: A. Fischer, A special Newton-type optimization method, Optimization 24 (1992), 269-284. – reference: R. Ziolkowski, Full-wave vector Maxwell equation modeling of the self-focusing of ultrashort optical pulses in a nonlinear kerr medium exhibiting a finite response time, J Opt Soc Am B 10 (1993), 186-198. – reference: A.S. Nagra and R.A. York, FDTD analysis of wave propagation in nonlinear absorbing and gain media, IEEE Trans Antennas Propag 46 (1998), 334-340. – reference: J. Chen, and Q.H. Liu, A non-spurious vector spectral element method for Maxwell's equations, Prog Electromagn Res 96 (2009), 205-215. – reference: R.M. Joseph and A. Taflove, FDTD Maxwell's equations models for nonlinear electrodynamics and optics, IEEE Trans Antennas Propag 45 (1997), 364-376. – reference: H.W. Zhang, S.Y. He, and X.S. 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Snippet	ABSTRACT A finite‐element time‐domain method is developed for Maxwell's equations with nonlinear media. Compared with conventional nonlinear numerical methods,... A finite‐element time‐domain method is developed for Maxwell's equations with nonlinear media. Compared with conventional nonlinear numerical methods, the... A finite-element time-domain method is developed for Maxwell's equations with nonlinear media. Compared with conventional nonlinear numerical methods, the...
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SubjectTerms	Convergence Finite element method finite-element time-domain method linear complementarity problem Mathematical analysis Mathematical models Maxwell's equations Microwaves nonlinear electromagnetism Nonlinearity parametric variational principle Quadratic programming
Title	A novel finite element time domain method for nonlinear Maxwell's equations based on the parametric quadratic programming method
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