Review of Computational Approaches to Optimization Problems in Inhomogeneous Rods and Plates  

作　　者：Weitao Chen Chiu-Yen Kao 

机构地区：[1]Department of Mathematics,University of California at Riverside,900 University Ave,Riverside,CA,92521,USA [2]Department of Mathematical Sciences,Claremont McKenna College,850 Columbia Ave,Claremont,CA,91711,USA

出　　处：《Communications on Applied Mathematics and Computation》2024年第1期236-256,共21页应用数学与计算数学学报（英文）

基　　金：supported by the DMS-1853701;supported in part by the DMS-2208373.

摘　　要：In this paper,we review computational approaches to optimization problems of inhomogeneous rods and plates.We consider both the optimization of eigenvalues and the localization of eigenfunctions.These problems are motivated by physical problems including the determination of the extremum of the fundamental vibration frequency and the localization of the vibration displacement.We demonstrate how an iterative rearrangement approach and a gradient descent approach with projection can successfully solve these optimization problems under different boundary conditions with different densities given.

关 键 词：Inhomogeneous rods and plates Bi-Laplacian Optimization of eigenvalues Localization of eigenfunctions REARRANGEMENT 

分 类 号：O17[理学—数学]