Modelization of a split in a ferromagnetic body by an equivalent boundary condition: Part I

Abstract

We study the influence of a thin split over the dynamic evolution of a ferromagnetic body. A naive numerical simulation would require a huge number of cells to model the split. To avoid this problem, we introduce an equivalent boundary condition which is obtained by a Taylor expansion in the thickness of the split. We prove the existence of solutions to this new problem and then rigorously establish the convergence of the expansion.