Geometric Multigrid With Plane Smoothing for Thin Elements in 3-D Magnetic Fields Calculation

The geometric multigrid (MG) method using the point-wise iterative method as the smoother converges slowly for 3-D magnetic fields calculation when there are thin edge elements in the finite element mesh. This paper proposes an edge based plane smoother so that the convergence of the MG method can be significantly improved. Numerical examples show that the MG method with the proposed smoother retains its good efficiency even for problems discretized by edge elements with extremely high aspect ratios.