Volume 1, Issue 2
A Level Set Method for Solving Free Boundary Problems Associated with Obstacles

K. Majava & X.-C. Tai

DOI:

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

Published online: 2004-01

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  • 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.

  • Keywords

Level set methods free boundary problems obstacle problem

  • AMS Subject Headings

65K10 65N22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-1-157, author = {K. Majava and X.-C. Tai}, title = {A Level Set Method for Solving Free Boundary Problems Associated with Obstacles}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2004}, volume = {1}, number = {2}, pages = {157--172}, 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.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/972.html} }
TY - JOUR T1 - A Level Set Method for Solving Free Boundary Problems Associated with Obstacles AU - K. Majava & X.-C. Tai JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 157 EP - 172 PY - 2004 DA - 2004/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/972.html KW - Level set methods KW - free boundary problems KW - obstacle problem AB - 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.
K. Majava & X.-C. Tai. (1970). A Level Set Method for Solving Free Boundary Problems Associated with Obstacles. International Journal of Numerical Analysis and Modeling. 1 (2). 157-172. doi:
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