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Volume 15, Issue 3
A Penalty Optimization Algorithm for Eigenmode Optimization Problem Using Sensitivity Analysis

Zhengfang Zhang, Weifeng Chen & Xiaoliang Cheng

DOI: 10.4208/cicp.190313.090913a

Commun. Comput. Phys., 15 (2014), pp. 776-796.

Published online: 2014-03

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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.

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@Article{CiCP-15-776, author = {Zhengfang Zhang, Weifeng Chen and Xiaoliang Cheng}, title = {A Penalty Optimization Algorithm for Eigenmode Optimization Problem Using Sensitivity Analysis}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {3}, pages = {776--796}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.190313.090913a}, url = {http://global-sci.org/intro/article_detail/cicp/7115.html} }
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 -

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.

Zhengfang Zhang, Weifeng Chen and Xiaoliang Cheng. (2014). A Penalty Optimization Algorithm for Eigenmode Optimization Problem Using Sensitivity Analysis. Communications in Computational Physics. 15 (3). 776-796. doi:10.4208/cicp.190313.090913a
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