Automatic Determination of Acceleration Factor Based on Residual and Functional in Shifted ICCG Method for 3-D Electromagnetic Field Analyses

This paper describes new strategy for determining an optimal acceleration factor in the shifted incomplete Cholesky conjugate gradient (ICCG) method. Although a useful method focused on the maximum diagonal entry in the incomplete Cholesky (IC) preconditioner was already proposed, it cannot always provide the optimal acceleration factor. In this paper, we propose new automatic determination methods based on the minimization of the norms of the remainder matrix, the residual, and the functional in the shifted ICCG method and discuss its effectiveness in the 3-D electromagnetic field analyses using the edge-based finite element method. It is concluded that the proposed methods based on the minimization of the norm of the residual or the functional can determine an appropriate acceleration factor within the acceptable computational cost and improve the convergence property of the shifted ICCG method.