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International Journal of Computer Mathematics Volume 88, 2011 - Issue 1
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Section B

Greedy algorithms for eigenvalue optimization problems in shape design of two-density inhomogeneous materials

Zheng-Fang Zhang Department of Mathematics, Zhejiang University, Hangzhou, 310027, China
,
Ke-Wei Liang Department of Mathematics, Zhejiang University, Hangzhou, 310027, ChinaCorrespondence[email protected]
&
Xiao-Liang Cheng Department of Mathematics, Zhejiang University, Hangzhou, 310027, China
Pages 183-195 | Received 20 Mar 2009, Accepted 25 Sep 2009, Published online: 26 Nov 2010

References

  • Allaire , G. , Aubry , S. and Jouve , F. 2001 . Eigenfrequency optimization in optimal design . Comp. Meth. Appl. Mech. Eng. , 190 ( 2 ) : 3565 – 3579 .
  • Bendsoe , M. P. 1997 . Optimization of Structural Topology, Shape and Material , Berlin : Springer-Verlag .
  • Bendsoe , M. P. and Mota Soares , C. A. 1993 . Topology Design of Structures , Dordrecht : Kluwer Academic .
  • Haber , E. 2004 . A multilevel, level-set method for optimizing eigenvalues in shape design problems . J. Comput. Phys. , 198 : 518 – 534 .
  • Janczewski , R. 2009 . Greedy T-colorings of graphs . Discrete Math. , 309 : 1685 – 1690 .
  • Lewis , A. S. 2003 . The mathematics of eigenvalue optimization . Math. Program. , 97 : 155 – 176 .
  • Osher , S. and Santosa , F. 2001 . Level set methods for optimization problems involving geometry and constraints I: Frequencies of a two-density inhomogeneous drum . J. Comput. Phys. , 171 : 272 – 288 .
  • Osher , S. and Sethian , J. 1988 . Front propagation with curvature-dependent speed: Algorithms based on Hamilton–Jacobi formulations . J. Comput. Phys. , 79 : 12 – 49 .
  • Overton , M. L. 1992 . Large-scale optimization of eigenvalues . SIAM J. Optim. , 2 : 88 – 120 .
  • Pedrosa , R. 2006 . Stability of optimal composite membranes , SP, Brazil : International Research Experience for Students (IRES)-Campinas .
  • Rozvany , G. I.N. 1997 . Topology Optimization in Structural Methanics , New York : Springer-Verlag .
  • Rudin , L. , Osher , S. and Fatemi , E. 1992 . Nonlinear total variation based noise removal algorithms . Physica D , 60 : 259 – 268 .
  • Shapiro , A. and Fan , M. K.H. 1995 . On eigenvalue optimization . SIAM J. Optim. , 5 : 552 – 569 .
  • Shenmaier , V. V. 2004 . A greedy algorithm for maximizing a linear objective function . Discrete Appl. Math. , 135 : 267 – 279 .
  • The Mathworks Inc . 2004 . Matlab User's Guide , Natick, MA : The Mathworks Inc . Version 7
  • Zhao , H. , Chan , T. , Merriman , B. and Osher , S. 1996 . A variational level set approach to multiphase motion . J. Comput. Phys. , 127 : 179 – 195 .

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