New algebraic multigrid preconditioning for iterative solvers in electromagnetic finite edge-element analyses

The algebraic multigrid (AMG) method is an algebraic multilevel solver for linear systems of equations, which stem from the discretization of partial differential equations. This paper develops an efficient AMG solver for singular linear systems of equations arising from electromagnetic finite element (FE) analyses using edge elements. The presented solver can solve singular equations using a technique similar to the shifted incomplete Cholesky conjugate gradient method. Shifted global coefficient matrices are utilized to construct the AMG preconditioner. The numerical results show that the proposed AMG conjugate gradient (AMGCG) solver can converge with a wide range of "shift".