|
|
| |
| y-Regularization-Operator Splitting Method for the NumericalSolution of a Scalar Eikonal Equation |
| |
Citation： |
Alexandre CABOUSSAT,Roland GLOWINSKI.y-Regularization-Operator Splitting Method for the NumericalSolution of a Scalar Eikonal Equation[J].Chinese Annals of Mathematics B,2015,36(5):659~688 |
| Page view： 1560
Net amount： 801 |
Authors： |
Alexandre CABOUSSAT; Roland GLOWINSKI |
Foundation： |
This work was supported by the National Science Foundation
(No.DMS-0913982). |
|
|
| Abstract： |
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. |
Keywords： |
Eikonal equation, Minimal and maximal solutions, Regularization
methods, Penalization of equality constraints, Dynamical flow,
Operator splitting, Finite element methods |
Classification： |
65N30, 65K10, 65M60, 49M20, 35F30 |
|
|
Download PDF Full-Text
|
|
|
|
