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

International Journal of Numerical Analysis and Modeling

Volumn 1, Issue 2, 2004, Pages 157-171

  Majava, Kirsi ^a   Tai, Xue Cheng ^b  

^a UNIVERSITY OF JYVÄSKYLÄ   (Finland)

^b UNIVERSITY OF BERGEN   (Norway)

Author keywords

Free boundary problems; Level set methods; Obstacle problem

Indexed keywords

EID: 85011878303     PISSN: 17055105     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. T. F. Chan and X. C. Tai. Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients. Journal of Comput. Phys., 193:40–66, 2003.
2. T. F. Chan and L. A. Vese. Image segmentation using level sets and the piecewise constant mumford-shah model. Technical report, CAM Report 00-14, UCLA, Math. Depart., April 2000. revised December 2000.
3. E. T. Chung, T. F. Chan, and X.-C. Tai. A level set method for eletrical impedance tomography. UCLA, CAM-report 03-64, 2003.
4. F. H. Clarke. Optimization and Nonsmooth Analysis. John Wiley & Sons, New York, 1983.
5. R. Glowinski. Numerical methods for nonlinear variational problems. Springer-Verlag, 1984.
6. J. E. Kelley. The cutting plane method for solving convex programs. Journal of the SIAM, 8:703–712, 1960.
7. K. C. Kiwiel. Methods of Descent for Nondifferentiable Optimization. Lecture Notes in Mathematics 1133. Springer-Verlag, Berlin-Heidelberg, 1985.
8. K. C. Kiwiel. A method for solving certain quadratic programming problems arising in nonsmooth optimization. IMA J. Numer. Anal., 6:137–152, 1986.
9. K. C. Kiwiel. Proximity control in bundle methods for convex nondifferentiable optimization. Math. Program., 46:105–122, 1990.
10. M. M. Mäkelä and P. Neittaanmäki. Nonsmooth Optimization. Analysis and Algorithms with Applications to Optimal Control. World Scientific, Singapore, 1992.
11. S. Osher and R. Fedkiw. Level set methods and dynamic implicit surfaces, volume 153 of Applied Mathematical Sciences. Springer-Verlag, New York, 2003.
12. S. Osher and R. P. Fedkiw. Level set methods: an overview and some recent results. J. Comput. Phys., 169(2):463–502, 2001.
13. S. Osher and F. Santosa. Level set methods for optimization problems involving geometry and constraints. I. Frequencies of a two-density inhomogeneous drum. J. Comput. Phys., 171(1):272–288, 2001.
14. S. Osher and J. A. Sethian. Fronts propagating with curvature dependent speed: Algorithms based on hamilton-jacobi formulations. J. Comput. Phys., 79:12–49, 1988.
15. F. Santosa. A level-set approach for inverse problems involving obstacles. ESAIM Contrôle Optim. Calc. Var., 1:17–33 (electronic), 1995/96.
16. H. Schramm and J. Zowe. A version of the bundle idea for minimizing a nonsmooth function: conceptual idea, convergence analysis, numerical results. SIAM J. Optim., 2(1):121–152, 1992.
17. J. A. Sethian. Level set methods and fast marching methods, volume 3 of Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge, second edition, 1999. Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science.
18. J. A. Sethian and J. Strain. Crystal growth and dendritic solidification. J. Comput. Phys., 98(2):231–253, 1992.
19. X.-C. Tai. Rate of convergence for some constraint decomposition methods for nonlinear variational inequalities. Numer. Math., 93(4):755–786, 2003.