The cause for BICG´s failure to converge

In 3D analysis of moving conductor eddy current problems, the resulting global stiffness matrix is usually so large that the elimination (direct) methods become impractical due to the cost of computer resources, and an iterative type of solver has to be employed. The development of the Bi-Conjugate Gradient (BICG) method has made the solution of this problem tenable. However, the convergence of the BICG method is not guaranteed for high Peclet numbers if it is not accompanied by the use of upwinding method. In this paper, the cause of BICG´s divergence is identified for the first time as the loss of diagonal dominance when the Peclet number increases, through a careful examination of the diagonal elements in the stiffness matrix, based on an edge element formulation. This conclusion can be easily extended to node element cases by following a similar procedure. Possible remedies for this problem are proposed