A COMPACT UPWIND SECOND ORDER SCHEME FOR THE EIKONAL EQUATION

作     者：J.-D. Benamou Songting Luo Hongkai Zhao 

作者机构：INRIA INRIA B.P. 105 78153 Le Chesnay Cedex France Department of Mathematics Michigan State University East Lansing MI 48824 USA Department of Mathematics University of California Irvine CA 92697 USA 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2010年第28卷第4期

页      面：489-516页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070102[理学-计算数学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：partially supported by ONR Grant N00014-02-1-0090 ARO MURI Grant W911NF-07-1-0185 NSF Grant DMS0811254 

主　　题：Eikonal equation Upwind scheme Hamilton-Jacobi Viscosity Solution Sweeping method. 

摘      要：We present a compact upwind second order scheme for computing the viscosity solution of the Eikonal equation. This new scheme is based on： 1. the numerical observation that classical first order monotone upwind schemes for the Eikonal equation yield numerical upwind gradient which is also first order accurate up to singularities; 2. a remark that partial information on the second derivatives of the solution is known and given in the structure of the Eikonal equation and can be used to reduce the size of the stencil. We implement the second order scheme as a correction to the well known sweeping method but it should be applicable to any first order monotone upwind scheme. Care is needed to choose the appropriate stencils to avoid instabilities.