Numerical solution of boundary value problems for the eikonal equation in an anisotropic medium
Numerical Analysis
2018-02-20 v1 Numerical Analysis
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.
Cite
@article{arxiv.1802.06203,
title = {Numerical solution of boundary value problems for the eikonal equation in an anisotropic medium},
author = {Alexander G. Churbanov and Petr N. Vabishchevich},
journal= {arXiv preprint arXiv:1802.06203},
year = {2018}
}
Comments
20 pages, 18 figures