A new H-splitting decoupled scheme for a transient eddy current problem over an unbounded domain

A new H-splitting decoupled scheme by using Finite Element Method and Natural Boundary Reduction is suggested to approximate a transient eddy current problem over an unbounded domain containing a simply connected conductor. It is based on solving a vector potential only in the conducting domain and a scalar potential over the whole space. As distinguished from the traditional fully discrete coupled scheme in which both vector and scalar unknowns are solved in an equation system at every time step, our computing scheme deals with them in two different equation systems respectively and thus decreases the total storage amount of non-zero entries of coefficient matrix and computational costs. In this paper, two error estimates of our scheme in finite time are obtained.