An efficient numerical procedure for the computation of steady state harmonic currents in flat plates

In this paper we present a fast iterative method for the numerical solution of an integro-differential boundary value problem arising from the study of harmonic eddy currents in a square plate. The approximate solution is a piecewise bilinear spline function and the equation is discretized by Galerkin's method. If we denote by
N
the number of unknowns in our approximate solution then the number of operations required to obtain the solution is
O(N(\log N)^{2})
.