TY - JOUR
T1 - A Penalty Optimization Algorithm for Eigenmode Optimization Problem Using Sensitivity Analysis
AU - Zhengfang Zhang, Weifeng Chen & Xiaoliang Cheng
JO - Communications in Computational Physics
VL - 3
SP - 776
EP - 796
PY - 2014
DA - 2014/03
SN - 15
DO - http://doi.org/10.4208/cicp.190313.090913a
UR - https://global-sci.org/intro/article_detail/cicp/7115.html
KW - 
AB - <p style="text-align: justify;">This paper investigates the eigenmode optimization problem governed by
the scalar Helmholtz equation in continuum system in which the computed eigenmode
approaches the prescribed eigenmode in the whole domain. The first variation for the
eigenmode optimization problem is evaluated by the quadratic penalty method, the
adjoint variable method, and the formula based on sensitivity analysis. A penalty
optimization algorithm is proposed, in which the density evolution is accomplished
by introducing an artificial time term and solving an additional ordinary differential
equation. The validity of the presented algorithm is confirmed by numerical results of
the first and second eigenmode optimizations in 1<em>D</em> and 2<em>D</em> problems.</p>