Deflated Conjugate Gradient Method for Magnetostatic Analysis

The deflated conjugate gradient (CG) method which can improve the convergence of CG is discussed. The distorted finite element mesh produces the system matrix with a large condition number, which results in poor convergence of CG method. The deflation technique replaces small eigenvalues with zeros in the system matrix. Therefore the deflated CG method is a useful solver for such ill-conditioned finite element analyses. However, the computational cost to obtain the eigenvectors is significantly high. To solve this problem, quasi eigenvectors which can be obtained with low cost are used in this paper. Moreover, the robustness of deflated CG method against distorted finite mesh with flat elements which bring ill-condition is presented.