Min max method, shape, topological derivatives, averaged Lagrangian, homogenization, two scale convergence, Helmholtz equation
Optimization and Control
2022-11-17 v3 Numerical Analysis
Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2210.08220,
title = {Min max method, shape, topological derivatives, averaged Lagrangian, homogenization, two scale convergence, Helmholtz equation},
author = {Mame Gor Ngom and Ibrahima Faye and Diaraf Seck},
journal= {arXiv preprint arXiv:2210.08220},
year = {2022}
}