Differentiation with Respect to Domains of Boundary Integral Functionals Involving Support Functions

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-07-29 DOI:10.1007/s00245-024-10168-9

Abdesslam Boulkhemair, Abdelkrim Chakib, Azeddine Sadik

引用次数: 0

Abstract

The aim of this paper is to establish a new formula for the computation of the shape derivative of boundary integral cost functionals using Minkowski deformation of star-shaped domains by convex ones. The formula is expressed by means of the support function of the convex domain. The proof uses some geometrical tools in addition to an analysis of star-shapedness involving gauge functions. Finally, in order to illustrate this result, the formula is applied for solving an optimal shape design problem of minimizing a surface cost functional constrained to elliptic boundary value problem, using the gradient method performed by the finite element approximation.

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涉及支持函数的边界积分函数域的微分

本文的目的是利用凸域对星形域的闵科夫斯基变形，建立一个计算边界积分成本函数形状导数的新公式。该公式通过凸域的支撑函数来表示。除了涉及规函数的星形性分析之外，证明还使用了一些几何工具。最后，为了说明这一结果，利用有限元近似的梯度法，将该公式应用于解决最优形状设计问题，即最小化受椭圆边界值问题约束的表面成本函数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.