Identification of the B-H curve from external measurements using complementary formulations

This paper deals with theoretical and numerical problems related with the i nverse problem of the reconstruction of the first piece of the piecewise af fine approximation of the B-H nonlinear characteristic starting from the kn owledge of measured flux-current relationship. The reconstruction of the fi rst piece of the characteristic is critical, as highlighted in novel approa ches reconstructing the whole characteristic without relying on the common assumption that the driving system produces a uniformly distributed magneti c field inside the specimen. In this paper a proof will be given of the uni queness of the solution of the inverse problem based on elementary analysis arguments and a numerical procedure that, by means of the use of complemen tary formulations, allows one to compute and control the reconstruction err or due to the numerical formulation. The paper is organized as follows: a b rief discussion of the problem is reported in Section 1, the numerical form ulation and the error bounds are reported in Section 2, the uniqueness of t he inverse problem is addressed in Section 3 and numerical tramples are rep orted in Section 4. (C) 2000 Elsevier Science B.V. All rights reserved.