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

K. Majava & X.-C. Tai

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 a 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 a 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, free boundary problems, 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 a 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 and X.-C. Tai. (2004). 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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