Min max method, shape, topological derivatives, averaged Lagrangian, homogenization, two scale convergence, Helmholtz equation

2022/10/15 by Mame Gor Ngom, Ngom, Mame Gor, Ibrahima Faye +3
Engineering · #Composite Structure Analysis and Optimization #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Soil, Finite Element Methods #Topology Optimization in Engineering

paper · pdf · doi:10.48550/arxiv.2210.08220

openalex publication_date 2022/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we perform a rigourous version of shape and topological derivatives for optimizations problems under constraint Helmoltz problems. A shape and topological optimization problem is formulated by introducing cost functional. We derive first by considering the lagradian method the shape derivative of the functional. It is also proven a topological derivative with the same approach. An application to several unconstrained shape functions arising from differential geometry are also given.

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