Revisiting aggregation-based multigrid for edge elements

Abstract

We consider a modification of the Reitzinger-Schoberl algebraic multigrid method for the iterative solution of the curl-curl boundary value problem discretized with edge elements. The Reitzinger-Schoberl method is attractive for its low memory requirements and moderate cost per iteration, but the number of iterations typically tends to increase with the problem size. Here we propose several modifications to the method that aim at curing the size-dependent convergence behavior without significantly affecting the attractive features of the original method. The comparison with an auxiliary space preconditioner, a state-of-the-art solver for the considered problems, further indicates that both methods typically require a comparable amount of work to solve a given discretized problem but that the proposed approach requires less memory.