Advanced algorithms for inverse problems

Abstract: – This paper presents some theoretical and numerical problems that arise in inverse problems in electromagnetic devices. The principal objective of the paper is to describe some computational aspects for inverse problems in coupled electromagnetic and thermal fields. We develop the necessary conditions for optimality using Lagrange multipliers. The state equations are mathematical models for magnetic field in case of time-harmonic Maxwell equations in vector magnetic potential formulation for axisymmetric fields. The model for the heat transfer is the heat conduction equation. The state and co-state equations are discretised by the finite element method using domain decomposition techniques for the analysis domain. The analysis domain is divided into two overlapping subdomains for the two coupled-fields considering physical significance of the pseudo-boundary of the two subdomains