An algebraic multigrid method for solving very large electromagnetic systems

Although most finite element programs have quite effective iterative solvers such as an incomplete Cholesky (IC) or symmetric successive overrelaxation (SSOR) preconditioned conjugate gradient (CG) method, the solution time may still become unacceptably long for very large systems. Convergence and thus total solution time can be shortened by using better preconditioners such as geometric multigrid methods. Algebraic multigrid methods have the supplementary advantage that no geometric information is needed and can thus be used as black box equation solvers. In the case of a finite element solution of a non-linear magnetostatic problem, the algebraic multigrid method reduces the overall computation time by a factor of 6 compared to a SSOR-CG solver.