各向异性介质中eikonal方程边值问题的数值解法
Numerical solution of boundary value problems for the eikonal equation in an anisotropic medium
AI总结：
研究各向异性介质中eikonal方程的Dirichlet问题，采用单调逼近法求解奇异摄动扩散-反应问题，给出二维边值问题的数值例子。
摘要：
本文考虑了各向异性介质中eikonal方程的Dirichlet问题。本文提出的非线性边值问题（BVP）是扩散-反应问题在反应参数趋于无穷大时的极限。为数值求解奇异摄动的扩散-反应问题，采用单调逼近法。给出了各向异性介质中二维eikonal方程边值问题的数值例子。计算中使用标准的分段线性有限元逼近。
英文摘要：
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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