Convergence of Multigrid Method for Edge-based FEM

Abstract—This paper discusses robustness of the multigrid (MG) method against distortion of finite elements. The conver-gence of MG method becomes considerably worse as the finite elements become flat. It is shown that the smoother used in the MG method cannot effectively eliminate the high-frequency component of the residue for flat elements, and this gives rise to deterioration in the convergence. Moreover, the multigrid method with conjugate gradient (CG) smoother is shown to be more robust against mesh distortion than that with Gauss–Seidel smoother. Index Terms—Convergence, eigenvalue, multigrid (MG). I