Comparison of geometric and algebraic multigrid methods in edge-based finite-element analysis

This paper discusses the comparison between the geometric multigrid (GMG) method and the algebraic multigrid (AMG) method in edge-based finite-element (FE) analysis. The GMG method requires the hierarchical meshes. On the other hand, the AMG method requires the only a single mesh information. The system matrices of the coarse grids are generated using algebraic operation in AMG. The numerical results show that both multigrid methods are faster than the conventional solvers in large-scale analysis. Although multigrid methods require the setup procedures, the calculation time of these procedures is comparatively short and increase linearly with the number of unknowns.