Optimize vibration frequencies of a two-density drum:  Piecewise Constant Level Set Method       

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         minimize 1st eigenvalue                               2nd eigenvalue       

Irregular design regions:  Disk,  Annula

References:

[1] S. Osher, F. Santosa, 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

[2] S. Zhu, Q. Wu, C. Liu, Variational piecewise constant level set methods for shape optimization of a two-density drum. J. Comput. Phys. 229 (2010) 5062–5089

[3] 朱升峰，最优形状设计问题数值方法的研究，博士论文，浙江大学，2011