THE CAUSE FOR BICGS FAILURE TO CONVERGE

In 3D analysis of moving conductor eddy current problems, the resultin g global stiffness matrix is usually so large that the elimination (di rect) 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 th is problem tenable. However, the convergence of the BICG method is not guaranteed for high Peclet numbers if it is not accompanied by the us e of upwinding method. In this paper, the cause of BICG's divergence i s identified for the first time as the loss of diagonal dominance when the Peclet number increases, through a careful examination of the dia gonal elements in the stiffness matrix, based on an edge element formu lation. This conclusion can be easily extended to node element cases b y following a similar procedure. Possible remedies for this problem ar e proposed.