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Volumn 229, Issue 13, 2010, Pages 5062-5089

Variational piecewise constant level set methods for shape optimization of a two-density drum

Author keywords

Eigenvalue; Level set methods; Piecewise constant level set method; Shape optimization; Topology optimization; Two phase

Indexed keywords

CONSTRAINED OPTIMIZATION; DROP BREAKUP; EIGENVALUES AND EIGENFUNCTIONS; ITERATIVE METHODS; LAGRANGE MULTIPLIERS; LEVEL MEASUREMENT; SHAPE OPTIMIZATION;

EID: 77952424384     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2010.03.026     Document Type: Article
Times cited : (27)

References (60)
  • 2
    • 0842290715 scopus 로고    scopus 로고
    • Structural optimization using sensitivity analysis and a level-set method
    • Allaire G., Jouve F., Toader A. Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 2004, 194:363-393.
    • (2004) J. Comput. Phys. , vol.194 , pp. 363-393
    • Allaire, G.1    Jouve, F.2    Toader, A.3
  • 4
    • 25844436983 scopus 로고    scopus 로고
    • Structural optimization using topological and shape sensitivity via a level set method
    • Allaire G., De Gournay F., Jouve F., Toader A.M. Structural optimization using topological and shape sensitivity via a level set method. Control Cybernet. 2005, 34:59-80.
    • (2005) Control Cybernet. , vol.34 , pp. 59-80
    • Allaire, G.1    De Gournay, F.2    Jouve, F.3    Toader, A.M.4
  • 7
    • 55649112883 scopus 로고    scopus 로고
    • A level-set method for computing the eigenvalues of elliptic operators defined on compact hypersurfaces
    • Brandman J. A level-set method for computing the eigenvalues of elliptic operators defined on compact hypersurfaces. J. Sci. Comput. 2008, 37:282-315.
    • (2008) J. Sci. Comput. , vol.37 , pp. 282-315
    • Brandman, J.1
  • 8
    • 0035473388 scopus 로고    scopus 로고
    • A level set method for inverse problems
    • Burger M. A level set method for inverse problems. Inverse Probl. 2001, 17:1327-1355.
    • (2001) Inverse Probl. , vol.17 , pp. 1327-1355
    • Burger, M.1
  • 9
    • 0842267881 scopus 로고    scopus 로고
    • A framework for the construction of level set methods for shape optimization and reconstruction
    • Burger M. A framework for the construction of level set methods for shape optimization and reconstruction. Interf. Free Bound. 2003, 5:301-329.
    • (2003) Interf. Free Bound. , vol.5 , pp. 301-329
    • Burger, M.1
  • 10
    • 0842312288 scopus 로고    scopus 로고
    • Incorporating topological derivatives into level set methods
    • Burger M., Hackl B., Ring W. Incorporating topological derivatives into level set methods. J. Comput. Phys. 2004, 194:344-362.
    • (2004) J. Comput. Phys. , vol.194 , pp. 344-362
    • Burger, M.1    Hackl, B.2    Ring, W.3
  • 11
    • 23844524180 scopus 로고    scopus 로고
    • A survey on level set methods for inverse problems and optimal design
    • Burger M., Osher S. A survey on level set methods for inverse problems and optimal design. Eur. J. Appl. Math. 2005, 16:263-301.
    • (2005) Eur. J. Appl. Math. , vol.16 , pp. 263-301
    • Burger, M.1    Osher, S.2
  • 12
    • 1642396916 scopus 로고    scopus 로고
    • Inverse problem techniques for the design of photonic crystals
    • Burger M., Osher S., Yablonovitch E. Inverse problem techniques for the design of photonic crystals. IEICE Trans. Electron. 2004, 87:258-265.
    • (2004) IEICE Trans. Electron. , vol.87 , pp. 258-265
    • Burger, M.1    Osher, S.2    Yablonovitch, E.3
  • 13
    • 0344550387 scopus 로고    scopus 로고
    • Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients
    • Chan T.F., Tai X.-C. Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients. J. Comput. Phys. 2003, 193:40-66.
    • (2003) J. Comput. Phys. , vol.193 , pp. 40-66
    • Chan, T.F.1    Tai, X.-C.2
  • 14
    • 2942612639 scopus 로고    scopus 로고
    • Identification of discontinuous coefficients in elliptic problems using total variation regularization
    • Chan T.F., Tai X.-C. Identification of discontinuous coefficients in elliptic problems using total variation regularization. SIAM J. Sci. Comput. 2003, 25:881-904.
    • (2003) SIAM J. Sci. Comput. , vol.25 , pp. 881-904
    • Chan, T.F.1    Tai, X.-C.2
  • 15
    • 67650443966 scopus 로고    scopus 로고
    • Level-set, penalization and Cartesian meshes: a paradigm for inverse problems and optimal design
    • Chantalat F., Bruneau C.-H., Galusinski C., Iollo A. Level-set, penalization and Cartesian meshes: a paradigm for inverse problems and optimal design. J. Comput. Phys. 2009, 228:6291-6315.
    • (2009) J. Comput. Phys. , vol.228 , pp. 6291-6315
    • Chantalat, F.1    Bruneau, C.-H.2    Galusinski, C.3    Iollo, A.4
  • 16
    • 0033330905 scopus 로고    scopus 로고
    • Maximizing band gaps in two-dimensional photonic crystals
    • Cox S.J., Dobson D.C. Maximizing band gaps in two-dimensional photonic crystals. SIAM J. Appl. Math. 1999, 59:2108-2120.
    • (1999) SIAM J. Appl. Math. , vol.59 , pp. 2108-2120
    • Cox, S.J.1    Dobson, D.C.2
  • 17
    • 0141933418 scopus 로고    scopus 로고
    • Band structure optimization of two-dimensional photonic crystals in H-polarization
    • Cox S.J., Dobson D.C. Band structure optimization of two-dimensional photonic crystals in H-polarization. J. Comput. Phys. 2000, 158:214-224.
    • (2000) J. Comput. Phys. , vol.158 , pp. 214-224
    • Cox, S.J.1    Dobson, D.C.2
  • 18
    • 2442711821 scopus 로고    scopus 로고
    • Analysis of iterative algorithms of Uzawa type for saddle point problems
    • Cui M.-R. Analysis of iterative algorithms of Uzawa type for saddle point problems. Appl. Numer. Math. 2004, 50(2):133-146.
    • (2004) Appl. Numer. Math. , vol.50 , Issue.2 , pp. 133-146
    • Cui, M.-R.1
  • 19
    • 0037337788 scopus 로고    scopus 로고
    • Shock capturing, level sets, and PDE based methods in computer vision and image processing: a review of Osher's contributions
    • Fedkiw R., Sapiro G., Shu C.-W. Shock capturing, level sets, and PDE based methods in computer vision and image processing: a review of Osher's contributions. J. Comput. Phys. 2003, 185:309-341.
    • (2003) J. Comput. Phys. , vol.185 , pp. 309-341
    • Fedkiw, R.1    Sapiro, G.2    Shu, C.-W.3
  • 21
    • 19844373682 scopus 로고    scopus 로고
    • A fast hybrid k-means level set algorithm for segmentation
    • Statistics and Mathematics
    • F. Gibou, R. Fedkiw, A fast hybrid k-means level set algorithm for segmentation, in: Proc. 4th Annu. Hawaii Int. Conf. Statistics and Mathematics, 2006, pp. 281-291.
    • (2006) Proc. 4th Annu. Hawaii Int. Conf. , pp. 281-291
    • Gibou, F.1    Fedkiw, R.2
  • 22
    • 3242878427 scopus 로고    scopus 로고
    • A multilevel, level-set method for optimizing eigenvalues in shape design problems
    • Haber E. A multilevel, level-set method for optimizing eigenvalues in shape design problems. J. Comput. Phys. 2004, 198:518-534.
    • (2004) J. Comput. Phys. , vol.198 , pp. 518-534
    • Haber, E.1
  • 23
    • 34447270283 scopus 로고    scopus 로고
    • Incorporating topological derivatives into shape derivatives based level set methods
    • He L., Kao C.-Y., Osher S. Incorporating topological derivatives into shape derivatives based level set methods. J. Comput. Phys. 2007, 225:891-909.
    • (2007) J. Comput. Phys. , vol.225 , pp. 891-909
    • He, L.1    Kao, C.-Y.2    Osher, S.3
  • 24
    • 2542438832 scopus 로고    scopus 로고
    • A second order shape optimization approach for image segmentation
    • Hintermüller M., Ring W. A second order shape optimization approach for image segmentation. SIAM J. Appl. Math. 2003, 64:442-467.
    • (2003) SIAM J. Appl. Math. , vol.64 , pp. 442-467
    • Hintermüller, M.1    Ring, W.2
  • 25
    • 0034503787 scopus 로고    scopus 로고
    • Weighted ENO schemes for Hamilton-Jacobi equations
    • Jiang G., Peng D. Weighted ENO schemes for Hamilton-Jacobi equations. SIAM J. Sci. Comput. 1999, 21:2126-2143.
    • (1999) SIAM J. Sci. Comput. , vol.21 , pp. 2126-2143
    • Jiang, G.1    Peng, D.2
  • 26
    • 0002501641 scopus 로고    scopus 로고
    • Sequential and parallel splitting methods for bilinear control problems in Hilbert spaces
    • Kunisch K., Tai X.-C. Sequential and parallel splitting methods for bilinear control problems in Hilbert spaces. SIAM J. Numer. Anal. 1997, 34:91-118.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 91-118
    • Kunisch, K.1    Tai, X.-C.2
  • 27
    • 0037275743 scopus 로고    scopus 로고
    • On the relation between constraint regularization, level sets, and shape optimization
    • Leitão A., Scherzer O. On the relation between constraint regularization, level sets, and shape optimization. Inverse Probl. 2003, 19:1-11.
    • (2003) Inverse Probl. , vol.19 , pp. 1-11
    • Leitão, A.1    Scherzer, O.2
  • 28
    • 85190205932 scopus 로고    scopus 로고
    • Piecewise constant level set method to interface problems, UCLA CAM Report 06-05
    • H. Li, X.-C. Tai, Piecewise constant level set method to interface problems, UCLA CAM Report 06-05, 2006.
    • (2006)
    • Li, H.1    Tai, X.-C.2
  • 30
    • 33646013275 scopus 로고    scopus 로고
    • A binary level set model and some applications to Mumford-Shah image segmentation
    • Lie J., Lysaker M., Tai X.-C. A binary level set model and some applications to Mumford-Shah image segmentation. IEEE Trans. Image Process. 2006, 15:1171-1181.
    • (2006) IEEE Trans. Image Process. , vol.15 , pp. 1171-1181
    • Lie, J.1    Lysaker, M.2    Tai, X.-C.3
  • 31
    • 33746291689 scopus 로고    scopus 로고
    • A variant of the level set method and applications to image segmentation
    • Lie J., Lysaker M., Tai X.-C. A variant of the level set method and applications to image segmentation. Math. Comput. 2006, 75:1155-1174.
    • (2006) Math. Comput. , vol.75 , pp. 1155-1174
    • Lie, J.1    Lysaker, M.2    Tai, X.-C.3
  • 32
    • 60149087611 scopus 로고    scopus 로고
    • Design of piezoelectric actuators using a multiphase level set method of piecewise constants
    • Luo Z., Tong L., Luo J., Wei P., Wang M.Y. Design of piezoelectric actuators using a multiphase level set method of piecewise constants. J. Comput. Phys. 2009, 228:2643-2659.
    • (2009) J. Comput. Phys. , vol.228 , pp. 2643-2659
    • Luo, Z.1    Tong, L.2    Luo, J.3    Wei, P.4    Wang, M.Y.5
  • 33
    • 38049120696 scopus 로고    scopus 로고
    • A binary level set model for elliptic inverse problems with discontinuous coefficients
    • Nielsen L.K., Tai X.-C., Aanonsen S.I., Espedal M. A binary level set model for elliptic inverse problems with discontinuous coefficients. Int. J. Numer. Anal. Model. 2007, 4:74-99.
    • (2007) Int. J. Numer. Anal. Model. , vol.4 , pp. 74-99
    • Nielsen, L.K.1    Tai, X.-C.2    Aanonsen, S.I.3    Espedal, M.4
  • 35
    • 0000653947 scopus 로고    scopus 로고
    • Level set methods: an overview and some recent results
    • Osher S., Fedkiw R. Level set methods: an overview and some recent results. J. Comput. Phys. 2001, 169:463-502.
    • (2001) J. Comput. Phys. , vol.169 , pp. 463-502
    • Osher, S.1    Fedkiw, R.2
  • 37
    • 0000653948 scopus 로고    scopus 로고
    • Level set methods for optimization problems involving geometry and constraints I. Frequencies of a two-density inhomogeneous drum
    • Osher S., Santosa F. Level set methods for optimization problems involving geometry and constraints I. Frequencies of a two-density inhomogeneous drum. J. Comput. Phys. 2001, 171:272-288.
    • (2001) J. Comput. Phys. , vol.171 , pp. 272-288
    • Osher, S.1    Santosa, F.2
  • 38
    • 44749084234 scopus 로고
    • Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations
    • Osher S., Sethian J.A. Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 1988, 79:12-49.
    • (1988) J. Comput. Phys. , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.A.2
  • 39
    • 0026204106 scopus 로고
    • High-order essentially non-oscillatory schemes for Hamilton-Jacobi equations
    • Osher S., Shu C.-W. High-order essentially non-oscillatory schemes for Hamilton-Jacobi equations. SIAM J. Numer. Anal. 1991, 28:907-922.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 907-922
    • Osher, S.1    Shu, C.-W.2
  • 40
    • 3142698698 scopus 로고    scopus 로고
    • A simple mesh generator in matlab
    • Persson P.-O., Strang G. A simple mesh generator in matlab. SIAM Rev. 2004, 46:329-345.
    • (2004) SIAM Rev. , vol.46 , pp. 329-345
    • Persson, P.-O.1    Strang, G.2
  • 43
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • Rudin L., Osher S., Fatemi E. Nonlinear total variation based noise removal algorithms. Physica D 1992, 60:259-268.
    • (1992) Physica D , vol.60 , pp. 259-268
    • Rudin, L.1    Osher, S.2    Fatemi, E.3
  • 45
  • 46
    • 0001176192 scopus 로고    scopus 로고
    • Structural boundary design via level set method and immersed interface methods
    • Sethian J.A., Wiegmann A. Structural boundary design via level set method and immersed interface methods. J. Comput. Phys. 2000, 163:489-528.
    • (2000) J. Comput. Phys. , vol.163 , pp. 489-528
    • Sethian, J.A.1    Wiegmann, A.2
  • 47
    • 0032681559 scopus 로고    scopus 로고
    • On the topological derivative in shape optimization
    • Sokołowski J., Żochowski A. On the topological derivative in shape optimization. SIAM J. Control Optim. 1999, 37:1251-1272.
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 1251-1272
    • Sokołowski, J.1    Zochowski, A.2
  • 49
    • 85190203645 scopus 로고    scopus 로고
    • A fast algorithm for level set based optimization, UCLA CAM Report 02-68
    • B. Song, T.F. Chan, A fast algorithm for level set based optimization, UCLA CAM Report 02-68, 2002.
    • (2002)
    • Song, B.1    Chan, T.F.2
  • 50
    • 28144444111 scopus 로고
    • A level set approach for computing solutions to incompressible two-phase flow
    • Sussman M., Smereka P., Osher S. A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 1994, 114:146-159.
    • (1994) J. Comput. Phys. , vol.114 , pp. 146-159
    • Sussman, M.1    Smereka, P.2    Osher, S.3
  • 51
    • 24644508476 scopus 로고    scopus 로고
    • A survey on multiple level set methods with applications for identifying piecewise constant functions
    • Tai X.-C., Chan T.F. A survey on multiple level set methods with applications for identifying piecewise constant functions. Int. J. Numer. Anal. Model. 2004, 1:25-48.
    • (2004) Int. J. Numer. Anal. Model. , vol.1 , pp. 25-48
    • Tai, X.-C.1    Chan, T.F.2
  • 52
    • 33846621880 scopus 로고    scopus 로고
    • Image segmentation using some piecewise constant level set methods with MBO type of projection
    • Tai X.-C., Christiansen O. Image segmentation using some piecewise constant level set methods with MBO type of projection. Int. J. Comp. Vis. 2007, 73:61-76.
    • (2007) Int. J. Comp. Vis. , vol.73 , pp. 61-76
    • Tai, X.-C.1    Christiansen, O.2
  • 53
    • 34147142049 scopus 로고    scopus 로고
    • A piecewise constant level set method for elliptic inverse problems
    • Tai X.-C., Li H. A piecewise constant level set method for elliptic inverse problems. Appl. Numer. Math. 2007, 57:686-696.
    • (2007) Appl. Numer. Math. , vol.57 , pp. 686-696
    • Tai, X.-C.1    Li, H.2
  • 54
    • 85190190362 scopus 로고    scopus 로고
    • Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model, UCLA CAM Report 09-05
    • X.-C. Tai, C. Wu, Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model, UCLA CAM Report 09-05, 2009.
    • (2009)
    • Tai, X.-C.1    Wu, C.2
  • 55
    • 77952430538 scopus 로고    scopus 로고
    • Fast sweeping algorithms for a class of Hamilton-Jacobi equations
    • Tsai Y.-H.R., Cheng L.-T., Osher S., Zhao H.-K. Fast sweeping algorithms for a class of Hamilton-Jacobi equations. J. Comput. Phys. 1996, 127:179-195.
    • (1996) J. Comput. Phys. , vol.127 , pp. 179-195
    • Tsai, Y.-H.R.1    Cheng, L.-T.2    Osher, S.3    Zhao, H.-K.4
  • 56
    • 33846252014 scopus 로고    scopus 로고
    • An extended level set method for shape and topology optimization
    • Wang S.Y., Lim K.M., Khoo B.C., Wang M.Y. An extended level set method for shape and topology optimization. J. Comput. Phys. 2007, 221:395-421.
    • (2007) J. Comput. Phys. , vol.221 , pp. 395-421
    • Wang, S.Y.1    Lim, K.M.2    Khoo, B.C.3    Wang, M.Y.4
  • 57
    • 0037414968 scopus 로고    scopus 로고
    • A level set method for structural topology optimization
    • Wang M.Y., Wang X., Guo D. A level set method for structural topology optimization. Comput. Meth. Appl. Mech. Eng. 2003, 192:227-246.
    • (2003) Comput. Meth. Appl. Mech. Eng. , vol.192 , pp. 227-246
    • Wang, M.Y.1    Wang, X.2    Guo, D.3
  • 58
    • 64049088299 scopus 로고    scopus 로고
    • Piecewise constant level set method for structural topology optimization
    • Wei P., Wang M.Y. Piecewise constant level set method for structural topology optimization. Int. J. Numer. Meth. Eng. 2009, 78:379-402.
    • (2009) Int. J. Numer. Meth. Eng. , vol.78 , pp. 379-402
    • Wei, P.1    Wang, M.Y.2
  • 59
    • 0030210970 scopus 로고    scopus 로고
    • A variational level set approach to multiphase motion
    • Zhao H.-K., Chan T.F., Merriman B., Osher S. A variational level set approach to multiphase motion. J. Comput. Phys. 1996, 127:179-195.
    • (1996) J. Comput. Phys. , vol.127 , pp. 179-195
    • Zhao, H.-K.1    Chan, T.F.2    Merriman, B.3    Osher, S.4
  • 60
    • 54249147959 scopus 로고    scopus 로고
    • A variational level set method for the topology optimization of steady-state Navier-Stokes flow
    • Zhou S., Li Q. A variational level set method for the topology optimization of steady-state Navier-Stokes flow. J. Comput. Phys. 2008, 227:10178-10195.
    • (2008) J. Comput. Phys. , vol.227 , pp. 10178-10195
    • Zhou, S.1    Li, Q.2


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