Some computational tests for inverse conductivity problems based on vector, variational principles: The 2D case

Abstract

We focus on several direct vector, variational principles to tackle the practical recovery problem of an unknown conductivity coefficient from boundary measurements. Though the problem is classical and have received a lot of attention because of its practical significance, the variational methods we explore are not so. Despite difficulties associated with the vector nature of the problems, including lack of (quasi, poly)-convexity, experiments show remarkable performance of some of the functionals examined. Beyond the specific meaning of such computations for inverse conductivity problems, the task of approximating the optimal solutions of vector, variational problems, as in hyperelasticity models or non-linear PDE systems at the level of optimality, is also interesting on its own right.