A Penalty Optimization Algorithm for Eigenmode Optimization Problem Using Sensitivity Analysis (Communications in Computational Physics, 2014)
This paper investigates the eigenmode optimization problem governed bythe scalar Helmholtz equation in continuum system in which the computed eigenmodeapproaches the prescribed eigenmode in the whole domain. The first variation for theeigenmode optimization problem is evaluated by the quadratic penalty method, theadjoint variable method, and the formula based on sensitivity analysis. A penaltyoptimization algorithm is proposed, in which the density evolution is accomplishedby introducing an artificial time term and solving an additional ordinary differentialequation. The validity of the presented algorithm is confirmed by numerical results ofthe first and second eigenmode optimizations in 1D and 2D problems.