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arXiv · 1802.06203

Numerical solution of boundary value problems for the eikonal equation in an anisotropic medium

Alexander G. Churbanov·Petr N. Vabishchevich
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Abstract

A Dirichlet problem is considered for the eikonal equation in an anisotropic medium. The nonlinear boundary value problem (BVP) formulated in the present work is the limit of the diffusion-reaction problem with a reaction parameter tending to infinity. To solve numerically the singularly perturbed diffusion-reaction problem, monotone approximations are employed. Numerical examples are presented for a two-dimensional BVP for the eikonal equation in an anisotropic medium. The standard piecewise-linear finite-element approximation in space is used in computations.

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Alexander G. Churbanov, Petr N. Vabishchevich. 2018-02-17. Numerical solution of boundary value problems for the eikonal equation in an anisotropic medium. https://arxiv.org/abs/1802.06203

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