Two-Grid Methods for Maxwell Eigenvalue Problems. - Zhou, J.; Hu, Xiaozhe.; Zhong, L.; Shu, S.; Chen, L. (Tufts University. Tisch Library., 2019)
Two new two-grid algorithms are proposed for solving the Maxwell eigenvalue problem. The new methods are based on the two-grid methodology recently proposed by Xu and Zhou [Math. Comp., 70 (2001), pp. 17--25] and further developed by Hu and Cheng [Math. Comp., 80 (2011), pp. 1287--1301] for elliptic eigenvalue problems. The new two-grid schemes reduce the solution of the Maxwell eigenvalue problem on a fine grid to one linear indefinite Maxwell equation on the same fine grid and an original eigenvalue problem on a much coarser grid. The new schemes, therefore, save total computational cost. The error estimates reveals that the two-grid methods maintain asymptotically optimal accuracy, and the numerical experiments presented confirm the theoretical results.