Topological optimization and inverse problems - Jackowska-Strumiłło, Lidia; Sokołowski, Jan; Żochowski, Antoni (Computer Assisted Methods in Engineering and Science, 2023)
The topological derivative of an arbitrary shape functional is introduced in [29] for 2D elasticity. The optimality conditions for general shape optimization problems are established in [30] using the shape variations including boundary and topology variations. The topology variations result in the presence of topological derivatives in the necessary conditions for optimality. In the present paper we derive the necessary optimality conditions for a class of shape optimization problems. The topological variations of shape functionals are used for the numerical solution of inverse problems. The numerical method uses neural networks. The results of computations confirm the convergence of the method.