Optimization method based on bio-inspired approach for solving a robin inverse problem

Abstract

In this paper, we are interested in solving an inverse problem of reconstructing an unknown Robin coefficient. It consists to identify the Robin parameter from some additional measurement in the accessible part of the boundary. This problem is knowing as an ill-posed problem in the Hadamard sense and require regularisation methods to be solved. To this end, we formulate the inverse problem into an optimization problem, where we consider the given data as a control, in addition to a regularizing term known as Thikhonov regularization. Then, we investigate the particle swarm optimization as a stochastic approach, in combination with a finite element method (FEM) to solve the optimization problem. The numerical results indicate that our approach yields accurate, convergent, and stable solutions for the considered Robin inverse problem in irregular 2D domain.