We discuss the use of multigrid techniques for several novel electromagnetic systems. One of these is the frequency-domain Maxwell problem, which presents a significant challenge due to the indefiniteness of the operator. We present methods for addressing this challenge, including a complex frequency shift and careful tuning of the relaxation on each level, and discuss their benefits and limitations. Another challenge discussed for this problem is the null-space of the curl operator.
We also discuss the use of smoothed-aggregation AMG to magnetostatic systems involving highly anisotropic, nonlinear materials. Finally, we describe the use of SA-AMG together with hybrid relaxation in an implementation of the implicit moment particle-in-cell method.
Work supported by U.S. Department of Energy Office of Science/High-Energy Physics grants DE-SC0008920 (SciDAC), DE-SC0009532, and DE-SC0011258 (SBIR).