Numerical solution of boundary value problems for the eikonal equation in an anisotropic medium
This work provides a numerical approach for solving eikonal equations in anisotropic media, which is relevant for applications like wave propagation, but the contribution appears incremental.
The paper addresses the numerical solution of boundary value problems for the eikonal equation in anisotropic media by solving a singularly perturbed diffusion-reaction problem. Numerical examples for a 2D case are presented, but no concrete performance numbers are given.
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.