Mathematical and numerical analysis of a transient magnetic model with voltage drop excitations

Abstract

This paper deals with the mathematical and numerical analysis of a nonlinear 2D transient magnetic model when the source data are given in terms of the voltage drop excitations in conductors and the remanent magnetic flux for permanent magnets. The formulation consists of a distributed nonlinear magnetostatic model with time appearing as a parameter, and a circuit equation linking currents and voltage drops. This last equation is used to express the problem as an implicit ODE system whose operator involves the resolution of the distributed model. The model is spatially discretized using a finite element method and an implicit Euler scheme is employed for time discretization. We perform the mathematical analysis of the problem at both the continuous and discrete levels and obtain an error estimate that is illustrated with some numerical results.