A level set approach to optimal homogenized coefficients

CMES - Computer Modeling in Engineering and Sciences

Volumn 4, Issue 1, 2003, Pages 21-30

  Sheen, Dongwoo ^a   Seo, Sangwon ^a   Cho, Jinwoo ^a  

^a Seoul National University   (South Korea)

Author keywords

Homogenization; Level set; Locally fitted mesh; Reconstruction

Indexed keywords

APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; FINITE ELEMENT METHOD; MICROSTRUCTURE; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; SET THEORY; THEOREM PROVING; VISCOSITY;

LEVEL SET METHOD; LOCALLY FITTED MESH; OPTIMAL HOMOGENIZED COEFFICIENTS; STEADY DIFFUSION EQUATION;

COMPUTER SIMULATION;

EID: 0242317241     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. Allaire, G.; Kohn, R. V. (1993): Optimal design for minimum weight and compliance in plane stress using extremal microstructure. Eur. J. Mech, A/Solids, vol. 12, no. 6, pp. 839-878.
2. Bendsoe, M. P. (1995): Optimization of Structural Topology, Shape, and Material. Springer-Verlag, Berlin Heidelberg.
3. Bendsoe, M. P; Soares, C. A. M. (Eds): Topology Design of Structures. Proceedings of the NATO Advanced Research Workshop held in Sesimbra, June 20-26, 1992, Dordrecht, 1993. Kluwer Academic Publishers.
4. Börgers, C. (1990): A triangulation algorithm for fast elliptic solvers based on domain imbedding. IAM J. Numer. Anal., vol. 27, pp. 1187-1196.
5. Chang, Y. C.; Hou, T. Y.; Merriman, B,.; Osher, S. (1996): A level set formulation of Eulerian interface capturing methods for incompressible fluid flows. J. Comput. Phys., vol. 124, pp. 449-464.
6. Crandall, M. G.; Lions, P. L. (1984): Two approximations of solutions of Hamilton-Jacobi equations. Math. Comp., vol. 43, pp. 1-19.
7. De Giorgi, E.; Colombini, E. F.; Pinccini, L. C. (1972): Frontiere orientate di misura minima e questioni collegate. Pubblicazione della classe di scienze della Scuola Normale.
8. Grisvard, P. (1985): Elliptic Problems in Nonsmooth Domains. Pitman.
9. Haslinger, J.; Dvořák, J. (1995): Optimal composite material design. RAIRO Mathematical Modelling and Numerical Analysis, vol. 29, pp. 657-686.
10. Hornung, U.(Ed): Homogenization and Porous Media, volume 6 of Interdisciplinary Applied Mathematics. Springer-Verlag, New York.
11. Malladi, R.; Sethian, J. A.; Vemuri, B. C. (1995): Shape modeling with front propagation: A level set approach. IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 17, no. 2, pp. 158-175.
12. Osher, S.; Sethian, J. A. (1988): Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulation. J. Comput. Phys., vol. 79, pp. 23-49.
13. Sanchez-Palencia, E. (1980): Non-Homogeneous Media and Vibration Theory, volume 127 of Lecture Notes in Physics. Springer-Verlag.
14. Santosa, F. (1996): A level-set approach for inverse problems involving obstacles. ESAIM: Control, Optimization and Calculus of variations, vol. 1, pp. 17-33.
15. Sethian, J. A. (1996): Level Set Methods. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge.
16. Sokolowski, J.; Zolesio, J. P. (1992): Introduction to Shape Optimization: Shape Sensitivity Analysis. Springer-Verlag, Berlin Heidelberg.
17. Struwe, M. (1990): Variational Methods, Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems. Springer-Verlag, Berlin Heidelberg.
18. Sussman, M.; Smereka, P.; Osher, S. (1994): A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys., vol. 114, pp. 146-159.
19. Suzuki, K.; Kikuchi, N. (1991): A homogenization method for shape and topology optimization. Comput. Methods Appl. Mech. Engrg., vol. 93, pp. 291-318.
20. Zhu, J.; Sethian, J. (1992): Projection methods coupled to level set interface techniques. J. Comput. Phys., vol. 102, pp. 128-138.