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

Authors:
Zheng-fang Zhang;Xiao-liang Cheng
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China;Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China
Venue:
Journal of Computational Physics
Year:
2011

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Abstract

This paper investigates optimization of the least eigenvalue of -@D 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.