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| On the Numerical Solution of Some Eikonal Equations: An Elliptic Solver Approach |
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Citation： |
Alexandre CABOUSSAT,Roland GLOWINSKI,Tsorng-Whay PAN.On the Numerical Solution of Some Eikonal Equations: An Elliptic Solver Approach[J].Chinese Annals of Mathematics B,2015,36(5):689~702 |
| Page view： 943
Net amount： 812 |
Authors： |
Alexandre CABOUSSAT; Roland GLOWINSKI;Tsorng-Whay PAN |
Foundation： |
This work was supported by the National Science Foundation
(No. DMS-0913982). |
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| Abstract： |
The steady Eikonal equation is a prototypical first-order fully
nonlinear equation. A numerical method based on elliptic solvers is
presented here to solve two different kinds of steady Eikonal
equations and compute solutions, which are maximal and minimal in
the variational sense. The approach in this paper relies on a
variational argument involving penalty, a biharmonic regularization,
and an operator-splitting-based time-discretization scheme for the
solution of an associated initial-value problem. This approach
allows the decoupling of the nonlinearities and differential
operators.
Numerical experiments are performed to validate this approach and
investigate its convergence properties from a numerical viewpoint. |
Keywords： |
Eikonal equations, Maximal solutions, Regularization methods,
Operator splitting, Finite element methods |
Classification： |
35F30, 49M20, 65K10, 65M60, 65N30 |
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