Algebraic multigrid preconditioning for 3-D magnetic finite-element analyses using nodal elements and edge elements

Most computation costs in magnetic finite-element analyses are consumed solving large-scale linear systems of equations; therefore, the development of fast linear solvers would be effective to reduce the computation time. This research is aimed to develop an efficient algebraic multigrid (AMG) preconditioner for three-dimensional (3-D) magnetic finite-element analyses utilizing nodal and edge elements. A new AMG preconditioner for eddy-current analyses is proposed, which separately treats nodal elements and edge elements in the construction of the coarse grids. Numerical results demonstrated the performances of AMG solvers in magnetostatic analyses and eddy-current analyses. The proposed AMG preconditioner achieves a better convergence than a conventional one in eddy-current analyses.