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A Stochastic Collocation Methods to 1D Maxwell's Equations with Uncertainty

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DOI: 10.23977/jemm.2022.070304 | Downloads: 15 | Views: 173

Author(s)

Lizheng Cheng 1, Hongping Li 1

Affiliation(s)

1 Changsha Normal University, Changsha, China

Corresponding Author

Hongping Li

ABSTRACT

In this paper, a stochastic collocation method is considered for one-dimensional Maxwell equations with uncertainty. The random inputs of model problem comes from the dielectric constant, magnetic permeability, and the initial and boundary conditions. We first prove the regularity of the solution of one-dimensional Maxwell equations. Then the convergence of our numerical approach is verified. Further some relevant numerical examples are implemented to support the analysis.

KEYWORDS

Maxwell equations, convergence analysis, stochastic collocation methods, regularity

CITE THIS PAPER

Lizheng Cheng, Hongping Li, A Stochastic Collocation Methods to 1D Maxwell's Equations with Uncertainty. Journal of Engineering Mechanics and Machinery (2022) Vol. 7: 17-26. DOI: http://dx.doi.org/10.23977/jemm.2022.070304.

REFERENCES

[1] Canuto, C., Hussaini, M.Y., Quarteroni, A. and Zang, T. A. Spectral Methods Fundamentals in Single Domains, Springer-Verlag, 2006.
[2] Fishman, G. Monte Carlo: Concepts, Algorithms, and Applications. Springer, New York (1996).
[3] Fox, B. Strategies for Quasi-Monte Carlo. Kluwer Academic, Dordrecht (1999).
[4] Gottlieb, D., Xiu, D. Galerkin method for wave equations with uncertain coefficients. Commun. Comput. Phys. 3, 505-518 (2008).
[5] Tang, T., Zhou, T. Convergence analysis for stochastic collocation methods to scalar hyperbolic equations with a random wave speed. Commun. Comput. Phys. 8, 226-248 (2010).
[6] Lizheng, C., Bo, W., Ziqing, X. A stochastic Galerkin method for Maxwell equations with uncertainty. Acta Mathematica Scientia, 2020, 40 (4): 1091-1104.
[7] Wiener, N. The homogeneous chaos. Am. J. Math. 60, 897-936 (1938).
[8] Xiu, D. Fast numerical methods for stochastic computations: A review. Commun. Comput. Phys. 5, 242-272 (2009).
[9] Xiu, D., Karniadakis, G.E. Modeling uncertainty in flow simulations via generalized polynomial chaos. J. Comput. Phys. 187, 137-167 (2003).

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