A Penalty-Regularization-Operator Splitting Method for the Numerical Solution of a Scalar Eikonal Equation

作     者：Alexandre CABOUSSAT Roland GLOWINSKI 

作者机构：Haute Ecole de Gestion de Genève HES-SO//University of Applied Sciences Department of Mathematics University of Houston 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2015年第36卷第5期

页      面：659-688页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by the National Science Foundation(No.DMS-0913982) 

主　　题：Eikonal equation Minimal and maximal solutions Regularization methods Penalization of equality constraints Dynamical flow Operator splitting Finite element methods 

摘      要：In this article, we discuss a numerical method for the computation of the minimal and maximal solutions of a steady scalar Eikonal equation. This method relies on a penalty treatment of the nonlinearity, a biharmonic regularization of the resulting variational problem, and the time discretization by operator-splitting of an initial value problem associated with the Euler-Lagrange equations of the regularized variational problem. A low-order finite element discretization is advocated since it is well-suited to the low regularity of the solutions. Numerical experiments show that the method sketched above can capture efficiently the extremal solutions of various two-dimensional test problems and that it has also the ability of handling easily domains with curved boundaries.