On the topological gradient method for an inverse problem resolution

IF 3.2 1区数学 Q1 MATHEMATICS

Advances in Nonlinear Analysis Pub Date : 2023-01-01 DOI:10.1515/anona-2023-0109

Mohamed Abdelwahed, Nejmeddine Chorfi

引用次数: 0

Abstract

Abstract In this work, we consider the topological gradient method to deal with an inverse problem associated with three-dimensional Stokes equations. The problem consists in detecting unknown point forces acting on fluid from measurements on the boundary of the domain. We present an asymptotic expansion of the considered cost function using the topological sensitivity analysis method. A detection algorithm is then presented using the developed formula. Some numerical tests are presented to show the efficiency of the presented algorithm.

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关于拓扑梯度法求解一个逆问题

在这项工作中，我们考虑了拓扑梯度方法来处理与三维Stokes方程相关的逆问题。问题在于从区域边界的测量中检测作用在流体上的未知点力。我们用拓扑灵敏度分析法给出了所考虑的代价函数的渐近展开式。然后利用所开发的公式提出了一种检测算法。通过数值实验验证了该算法的有效性。

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

Advances in Nonlinear Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

6.00

自引率

9.50%

发文量

审稿时长

30 weeks

期刊介绍： Advances in Nonlinear Analysis (ANONA) aims to publish selected research contributions devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The Journal focuses on papers that address significant problems in pure and applied nonlinear analysis. ANONA seeks to present the most significant advances in this field to a wide readership, including researchers and graduate students in mathematics, physics, and engineering.