A finite difference time domain scheme for transient eddy current problems

In this paper, we present a general explicit finite difference time domain (FDTD) algorithm for transient electromagnetic problems at low frequencies. A detailed theoretical analysis is given, based on a nonstandard finite difference scheme, which is studied in terms of stability and consistency. The study reveals a whole class of finite difference diffusion schemes with different properties. Some of the existing methods are special cases of this general framework and an optimal algorithm is proposed. The application of finite difference methods to eddy current problems requires the introduction of a hybrid methodology, which combines the explicit differencing scheme for the diffusion equation with a boundary element method (BEM) for the open regions. The resulting algorithm involves a simple time stepping iteration, without any system solution, thus being remarkably robust.