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Acebron, J. A. & Ribeiro, M. A. (2016). A Monte Carlo method for solving the one-dimensional telegraph equations with boundary conditions. Journal of Computational Physics. 305, 29-43
J. A. Torres and M. A. Ribeiro, "A Monte Carlo method for solving the one-dimensional telegraph equations with boundary conditions", in Journal of Computational Physics, vol. 305, pp. 29-43, 2016
@article{torres2016_1714953815135, author = "Acebron, J. A. and Ribeiro, M. A.", title = "A Monte Carlo method for solving the one-dimensional telegraph equations with boundary conditions", journal = "Journal of Computational Physics", year = "2016", volume = "305", number = "", doi = "10.1016/j.jcp.2015.10.027", pages = "29-43", url = "http://www.sciencedirect.com/science/article/pii/S0021999115006919" }
TY - JOUR TI - A Monte Carlo method for solving the one-dimensional telegraph equations with boundary conditions T2 - Journal of Computational Physics VL - 305 AU - Acebron, J. A. AU - Ribeiro, M. A. PY - 2016 SP - 29-43 SN - 0021-9991 DO - 10.1016/j.jcp.2015.10.027 UR - http://www.sciencedirect.com/science/article/pii/S0021999115006919 AB - A Monte Carlo algorithm is derived to solve the one-dimensional telegraph equations in a bounded domain subject to resistive and non-resistive boundary conditions. The proposed numerical scheme is more efficient than the classical Kac's theory because it does not require the discretization of time. The algorithm has been validated by comparing the results obtained with theory and the Finite-difference time domain (FDTD) method for a typical two-wire transmission line terminated at both ends with general boundary conditions. We have also tested transmission line heterogeneities to account for wave propagation in multiple media. The algorithm is inherently parallel, since it is based on Monte Carlo simulations, and does not suffer from the numerical dispersion and dissipation issues that arise in finite difference-based numerical schemes on a lossy medium. This allowed us to develop an efficient numerical method, capable of outperforming the classical FDTD method for large scale problems and high frequency signals. ER -