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 ...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.展开更多
基金supported by the National Science Foundation(No.DMS-0913982)
文摘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.
