Int. J. Numer. Anal. Mod., 1 (2004), pp. 157-172.


A level set method for solving free boundary problems associated with obstacles

Kirsi Majava 1, Xue-Cheng Tai 2

1 Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35 (Agora), FI-40014 University of Jyväskylä, Finland
2 Department of Mathematics, University of Bergen, Johannes Brunsgate 12, N-5009 Bergen, Norway

Received by the editors February 1, 2004.
Abstract

A level set method is proposed for solving free boundary problems coming from contact with obstacles. Two different approaches are described and applied for solving an unilateral obstacle problem. The cost functionals coming from the new approach are nonsmooth. For solving the nonsmooth minimization problems, two methods are applied: firstly, a proximal bundle method, which is a method for solving general nonsmooth optimization problems. Secondly, a gradient method is proposed for solving the regularized problems. Numerical experiments are included to verify the convergence of the methods and the quality of the results.

AMS subject classifications: 65K10, 65N22
Key words: Level set methods, free boundary problems, obstacle problem
Email: majkir@mit.jyu.fi (K. Majava), tai@mi.uib.no (X.-C. Tai)
 

The Global Science Journal