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Eikonal Equation and the WKB Approximation
1986In this chapter we describe briefly the methods adopted to arrive at the solutions of the wave equation in one dimension by well known eikonal approximations [1], successive applications of the Liouville transformations [2], and the elegant matrix formalism developed in the monograph by Froman and Froman [3].
Richard Bellman, Ramabhadra Vasudevan
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The eikonal equation in a moving medium
Proceedings of the IEEE, 1967The eikonal equation as derived by Sommerfeld and Runge has been extended to include the case of moving media under the condition where (v/c) ≪ 1 (v is the velocity of the medium, c is the speed of light in vacuum). Using the Hamilton Jacobi formalism, the equivalent system of linear equations was determined which can be used for ray tracing. An exmple
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A numerical approach to the eikonal equation
Nonlinear Analysis: Theory, Methods & Applications, 2001Omata, S., Kinami, S.
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Improved Characteristic Fast Marching Method for the Generalized Eikonal Equation in a Moving Medium
Journal of Scientific Computing, 2019M. Ho, Ju-Hyok Ri, Sin-Bom Kim
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Fast sweeping method for the factored eikonal equation
Journal of Computational Physics, 2009Sergey Fomel +2 more
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A parallel fast sweeping method for the Eikonal equation
Journal of Computational Physics, 2013Frédéric Gibou, Chohong Min
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A Regularizing Property of the 2D-Eikonal Equation
Communications in Partial Differential Equations, 2015Camillo De Lellis, Radu Ignat
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