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A Penalty Optimization Algorithm for Eigenmode Optimization Problem Using Sensitivity Analysis

Published online by Cambridge University Press:  03 June 2015

Zhengfang Zhang ,
Weifeng Chen  and
Xiaoliang Cheng
Zhengfang Zhang*
Affiliation:
College of Science, Hangzhou Dianzi University, Hangzhou 310018, P.R. China
Weifeng Chen
Affiliation:
School of Information, Zhejiang University of Finance and Economics, Hangzhou 310018, P.R. China
Xiaoliang Cheng
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, P.R. China
*
Corresponding author.Email:zhengfangzhang@hdu.edu.cn
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Abstract

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 1D and 2D problems.

Keywords

35Q6049R0565F1565F1890C31Sensitivity analysiseigenmode optimization problemfinite element methodpenalty method
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 3 , March 2014 , pp. 776 - 796
Copyright
Copyright © Global Science Press Limited 2014

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