关于形状优化双拉普拉卡特征值问题的数值求解

IF 4.4 2区 数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Abdelkrim Chakib , Ibrahim Khalil , Azeddine Sadik
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引用次数: 0

摘要

本文涉及体积受限屈曲和夹紧板双拉普拉卡特征值问题的一些形状优化模型的数值解析。我们提出了一种使用拉格朗日函数、哈达玛形状导数和梯度法结合有限元离散化的数值方法,以确定这两个问题前十个特征值的最小值。我们还对一些商函数的最大化进行了数值研究,从而获得了这些谱商问题的最佳可能上限,并在数值上建立了一些猜想。我们针对不同的成本函数提供了数值示例和说明。所获得的数值结果表明了所提出方法的效率和实用性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On numerical resolution of shape optimization bi-Laplacian eigenvalue problems
In this paper, we deal with the numerical resolution of some shape optimization models for the volume-constrained buckling and clamped plate bi-Laplacian eigenvalues problems. We propose a numerical method using the Lagrangian functional, Hadamard’s shape derivative and the gradient method combined with the finite elements discretization, to determine the minimizers for the first ten eigenvalues for both problems. We investigate also numerically the maximization of some quotient functionals, which allows us to obtain the optimal possible upper bounds of these spectral quotient problems and establish numerically some conjectures. Numerical examples and illustrations are provided for different and various cost functionals. The obtained numerical results show the efficiency and practical suitability of the proposed approaches.
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来源期刊
Mathematics and Computers in Simulation
Mathematics and Computers in Simulation 数学-计算机:跨学科应用
CiteScore
8.90
自引率
4.30%
发文量
335
审稿时长
54 days
期刊介绍: The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles. Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO. Topics covered by the journal include mathematical tools in: •The foundations of systems modelling •Numerical analysis and the development of algorithms for simulation They also include considerations about computer hardware for simulation and about special software and compilers. The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research. The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.
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