Fast 3-D edge element analysis by the geometric multigrid method using an accelerated symmetric Gauss-Seidel smoother

A fast magnetostatic field analysis by the three-dimensional (3-D) geometric multigrid method with edge hexahedra is presented. The multigrid method uses a symmetric Gauss-Seidel smoother with conjugate gradient acceleration. The convergence and the speed of the V- and W-cycle multigrid method using this smoother are compared with the multigrid using Gauss-Seidel. Comparison is also made with the finite-element method (FEM) using ICCG. The multigrid with the accelerated symmetric Gauss-Seidel shows a stable convergence rate that does not deteriorate for bad quality meshes. It is much faster than the conventional multigrid with Gauss-Seidel and the FEM using ICCG.