2024/03/29 by Mejdi Azaïez, Azaiez, M., Anna Doubova +7
Mathematics · Engineering · Computer Science · #Numerical methods in inverse problems #Topology Optimization in Engineering #Advanced Mathematical Modeling in Engineering
paper · pdf · doi:10.48550/arxiv.2403.20181
We analyze an optimization problem of the conductivity in a composite material arising in a heat conduction energy storage problem. The model is described by the heat equation that specifies the heat exchange between two types of materials with different conductive properties with Dirichlet-Neumann boundary conditions on the external part of the domain, and on the interface characterized by the resisting coefficient between the highly conductive material and the less conductive material. The main purpose of the paper is to compute a shape gradient of an optimization functional in order to accurately determine the optimal location of the conductive material using a classical shape optimization strategy. We also present some numerical experiments to illustrate the efficiency of the proposed method.