Abdelkrim Chakib , Ibrahim Khalil , Azeddine Sadik
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引用次数: 0
Abstract
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.
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.