A boundary piecewise constant level set method for boundary control of eigenvalue optimization problems
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.
scientific article; zbMATH DE number 5842964
scientific article