Solution of linear steady-state eddy-current problems by complex successive overrelaxation

The paper considers two topics which arise in the application of the finite-difference successive-overrelaxation method to problems involving eddy currents induced in nonmagnetic conductors by magnetic fields varying sinusoidally with time. First, a simple 1-dimensional problem is used to determine a criterion governing the mesh length between adjacent nodes in the grid covering a conducting region. It is shown that this length should not exceed 0.2 times the skin depth of the conductor. Secondly, the important question of the convergence of the solution as a function of the accelerating or relaxation factor is considered. A method of determining the optimum accelerating factor during the course of the iterative procedure is presented.