A boundary piecewise constant level set method for boundary control of eigenvalue optimization problems

作者：Zhang, Zheng-fang^*; Cheng, Xiao-liang

来源：Journal of Computational Physics, 2011, 230(2): 458-473.

DOI：10.1016/j.jcp.2010.10.005

• Boundary piecewise constant level set method
• Eigenvalue optimization problem
• Finite element method

This paper investigates optimization of the least eigenvalue of -Delta with the constraint of one-dimension Hausdorff measure of Dirichlet boundary. We propose the boundary piecewise constant level set (BPCLS) method based on the regularity technique to combine two types of boundary conditions into a single Robin boundary condition. We derive the first variation of the least eigenvalue w.r.t. the BPCLS function and propose a penalty BPCLS algorithm and an augmented Lagrangian BPCLS algorithm. Numerical results are reported for experiments on ellipse and L-shape domains.

• 出版日期2011-1-20
• 单位浙江大学