Open Access
Issue
ESAIM: M2AN
Volume 57, Number 2, March-April 2023
Page(s) 841 - 864
DOI https://doi.org/10.1051/m2an/2022084
Published online 30 March 2023
  1. S.M. Rytov, Y.A. Kravtsov and V.I. Tatarskii, Principles of Statistical Radiophysics: Elements and Random Fields 3. Springer, Berlin (1989). [Google Scholar]
  2. G.N. Ord, A stochastic model of Maxwell’s equations in 1+1 dimensions. Int. J. Theor. Phys. 35 (1996) 263–266. [CrossRef] [Google Scholar]
  3. T. Horsin, I. Stratis and A. Yannacopoulos, On the approximate controllability of the stochastic Maxwell equations.s IMA J. Math. Control Inf. 27 (2010) 103–118. [CrossRef] [Google Scholar]
  4. K.B. Liaskos, I.G. Stratis and A.N. Yannacopoulos, Stochastic integrodifferential equations in Hilbert spaces with applications in electromagnetics. J. Integral Equ. App. 22 (2010) 559–590. [Google Scholar]
  5. P. Benner and J. Schneider, Uncertainty quantification for Maxwell’s equations using stochastic collocation and model order reduction. Int. J. Uncertainty Quantif. 5 (2015) 195–208. [CrossRef] [MathSciNet] [Google Scholar]
  6. C. Jung, Evolution of probability distribution in time for solutions of hyperbolic equations. J. Sci. Comput. 41 (2009) 13–48. [CrossRef] [MathSciNet] [Google Scholar]
  7. C. Jung, B. kwon, A. Mahalov and T. Nguyen, Maxwell solutions in media with multiple random interfaces. Int. J. Numer. Anal. Model. 11 (2014) 194–213. [Google Scholar]
  8. J. Li, Z. Fang and G. Lin, Regularity analysis of metamaterial Maxwell’s equations with random coefficients and initial conditions. Comput. Methods Appl. Mech. Eng. 335 (2018) 24–51. [CrossRef] [Google Scholar]
  9. J. Hong, L. Ji, L. Zhang and J. Cai, An energy-conserving method for stochastic Maxwell equations with multiplicative noise. J. Comput. Phys. 351 (2017) 216–229. [CrossRef] [MathSciNet] [Google Scholar]
  10. D. Cohen, J. Cui, J. Hong and L. Sun, Exponential integrators for stochastic Maxwell’s equations driven by Itô noise. J. Comput. Phys. 410 (2020) 109382. [CrossRef] [MathSciNet] [Google Scholar]
  11. C. Chen, J. Hong and J. Ji, Mean-square convergence of a semidiscrete scheme for stochastic Maxwell equations. SIAM J. Numer. Anal. 57 (2019) 728–750. [CrossRef] [MathSciNet] [Google Scholar]
  12. L. Zhang, C. Chen, J. Hong and L. Ji, A review on stochastic multi-symplectic methods for stochastic Maxwell equations. Commun. Appl. Math. Comput. 1 (2019) 467–501. [CrossRef] [MathSciNet] [Google Scholar]
  13. J. Hong, B. Hou and L. Sun, Energy-preserving fully-discrete schemes for nonlinear stochastic wave equations with multiplicative noise. J. Comput. Phys. 451 (2022) 110829. [CrossRef] [Google Scholar]
  14. Y. Li, S. Wu and Y. Xing, Finite element approximations of a class of nonlinear stochastic wave equation with multiplicative noise. J. Sci. Comput. 91 (2022) 53. [CrossRef] [Google Scholar]
  15. W.H. Reed and T. Hill, Triangular mesh methods for the neutron transport equation. Technical report, , Los Alamos Scientific Lab, N. Mex. (USA) (1973). [Google Scholar]
  16. B. Cockburn, S. Hou and C.-W. Shu, The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case. Math. Comput. 54 (1990) 545–581. [Google Scholar]
  17. B. Cockburn and G. Karniadakis and C.-W. Shu, The development of discontinuous galerkin methods, in Discontinuous Galerkin Methods: Theory, Computation and Applications, in Discontinuous Galerkin Methods: Theory, Computation and Applications. Lecture Notes in Computational Science and Engineering, Part I: Overview, edited by B. Cockburn, G. Karniadakis, C.-W. Shu, Vol 11, Springer (2000) 3–50. [Google Scholar]
  18. B. Cockburn, S.-Y. Lin and C.-W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one dimensional systems. J. Comput. Phys. 84 (1989) 90–113. [Google Scholar]
  19. B. Cockburn and C.-W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework. Math. Comput. 52 (1989) 411–435. [Google Scholar]
  20. Y. Cheng, C.-S. Chou, F. Li and Y. Xing, L2 stable discontinuous Galerkin methods for one-dimensional two-way wave equations. Math. Comput. 86 (2017) 121–155. [Google Scholar]
  21. Z. Sun and Y. Xing, Optimal error estimates of discontinuous Galerkin methods with generalized fluxes for wave equations on unstructured meshes. Math. Comput. 90 (2021) 1741–1772. [CrossRef] [Google Scholar]
  22. Y. Li, C.-W. Shu and S. Tang, A discontinuous Galerkin method for stochastic conservation laws. SIAM J. Sci. Comput. 42 (2020) A54–A86. [Google Scholar]
  23. J. Sun, Y. Xing and C.-W. Shu, Multi-symplectic discontinuous Galerkin methods for the stochastic Maxwell equations with additive noise. J. Comput. Phys. 461 (2022) 111199. [CrossRef] [Google Scholar]
  24. C. Chen, A symplectic discontinuous Galerkin full discretization for stochastic Maxwell equations. SIAM J. Numer. Anal. 59 (2021) 2197–2217. [CrossRef] [MathSciNet] [Google Scholar]
  25. X. Meng, C.-W. Shu and B. Wu, Optimal error estimates for discontinuous Galerkin methods based on upwind-biased fluxes for linear hyperbolic equations. Math. Comput. 85 (2016) 1225–1261. [Google Scholar]
  26. P. Kloeden and E. Platen, in Numerical Solution of Stochastic Differential Equations. Applications in Mathematics, Stochastic Modelling and Applied Probability. 3rd ed., Vol 23, Springer-Verlag, Berlin (1999). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you