The use of time space Green’s functions in the computation of transient eddy current fields

Abstract

The utility of integral equations to solve eddy current problems has been borne out by numerous computations in the past few years, principally in sinusoidal steady-state problems. This paper attempts to examine the applicability of the integral approaches in both time and space for the more generic transient problem. The basic formulation for the time space Green’s function approach is laid out. A technique employing Gauss-Laguerre integration is employed to realize the temporal solution, while Gauss–Legendre integration is used to resolve the spatial field character. The technique is then applied to the fusion electromagnetic induction experiments (FELIX) cylinder experiments in both two and three dimensions. It is found that quite accurate solutions can be obtained using rather coarse time steps and very few unknowns; the three-dimensional field solution worked out in this context used basically only four unknowns. The solution appears to be somewhat sensitive to the choice of time step, a consequence of a numerical instability imbedded in the Green’s function near the origin.