Level-set, penalization and cartesian meshes: A paradigm for inverse problems and optimal design

Journal of Computational Physics

Volumn 228, Issue 17, 2009, Pages 6291-6315

  Chantalat, Frédéric ^a   Bruneau, Charles Henri ^a   Galusinski, Cédric ^b   Iollo, Angelo ^a  

^a UNIVERSITÉ BORDEAUX 1   (France)

^b UNIVERSITÉ DE TOULON   (France)

Author keywords

Domain penalization; Inverse problem; Level set; Optimal design

Indexed keywords

NUMERICAL METHODS; OPTIMAL SYSTEMS; SHAPE OPTIMIZATION;

BODY-FITTED GRIDS; CARTESIAN MESH; DOMAIN PENALIZATION; INVERSE OPTIMIZATION; LEVEL SET; LEVEL SET METHOD; NONPARAMETRICS; OPTIMAL DESIGN; PENALISATION; SHAPE OPTIMIZATION PROBLEM;

INVERSE PROBLEMS;

EID: 67650443966     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.05.017     Document Type: Article

References (21)

1. Dorn O., Miller E.L., and Rappaport C.M. A shape reconstruction method for electromagnetic tomograpy using adjoint fields and level sets. Inverse Probl. 16 (2000) 1119-1156
2. Francini E., Höft T., and Santosa F. An inverse problem in nondestructive evaluation of spot-welds. Inverse Probl. 22 (2006) 645-661
3. Angot Ph., Bruneau Ch.-H., and Fabrie P. A penalization method to take into account obstacles in incompressible viscous flows. Numer. Math. 81 (1999)
4. Osher S., and Sethian J.A. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79 (1988) 12-49
5. Céa J. Conception optimale ou identification de formes calcul rapide de la dérivé directionnelle de la fonction cot. Math. Model. Numer. Anal. 20 3 (1986) 371-402
6. J Osher S., and Santosa F. Level set methods for optimization problems involving geometry and constraints. I. Frequencies of a two-density inhomogeneous drum. J. Comput. Phys. 171 (2001) 272-288
7. Sethian J.A. Evolution and application of level-set and fastmarching methods for advancing fronts. J. Comput. Phys. 169 (2001) 503-555
8. Sethian J.A. A fast marching level set method for monotonically advancing fronts. Proc. Natl. Acad. Sci. USA 93 (1996) 1591-1593
9. Allaire G., De Gournay F., Jouve F., and Toader A.-M. Structural optimization using topological and shape sensitivity via a level set method. Contr. Cybernet. 34 (2005) 59-80
10. Céa J., Garreau S., Guillaume P., and Masmoudi M. The shape and topological optimizations connection. Comput. Method Appl. Mech. Eng. 188 4 (2000) 713-726
11. Eschenauer H., Kobelev H., and Schumacher A. A bubble method for topology and shape optimization of structures. Struct. Optim. 8 (1994) 142-151
12. Sokolowski J., and Zochowski A. On the topological derivative in shape optimization. SIAM J. Contr. Optim. 37 (1999) 1251-1272
13. Jiang G.-S., and Shu C.-W. Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126 (1996) 202-228
14. Saad Y., and Schultz M.H. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. J. Sci. Stat. Comput. 7 (1986) 856-869
15. Protas B., Bewley T.R., and Hagen G. A computational framework for the regularization of adjoint analysis in multiscale PDE systems. J. Comput. Phys. 195 (2004) 49-89
16. Burger M., Hackl B., and Ring W. Incorporating topological derivatives into level set methods. J. Comput. Phys. 194 (2004) 344-362
17. Bruneau C.-H., and Fabrie P. Effective downstream boundary conditions for incompressible Navier-Stokes equations. Int. J. Numer. Method Fluid 19 (1994) 693-705
18. Pironneau O. On optimum profiles in Stokes flow. J. Fluid Mech. 59 (1973) 117-128
19. Harlow F.H., and Welch J.E. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluid 8 (1965) 2182-2189
20. Bruneau C.-H., and Saad M. The 2D-lid driven cavity problem revisited. Comput. Fluid 35 (2006) 326-348
21. Koobus B., Marco N., and Dervieux A. An additive multilevel preconditioning method. J. Sci. Comput. 12 3 (1997) 233-251