title: TWO-GRID METHODS FOR MAXWELL EIGENVALUE PROBLEMS.
abstract: 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.
authors.affiliation: School of Mathematical and Computational Sciences, Xiangtan University, Xiangtan 411105, China.
authors.forename: J
authors.initials: J
authors.lastname: Zhou
authors.affiliation: Department of Mathematics, Pennsylvania State University, University Park, PA 16802.
authors.forename: X
authors.initials: X
authors.lastname: Hu
authors.affiliation: School of Mathematics Science, South China Normal University, Guangzhou 510631, China.
authors.forename: L
authors.initials: L
authors.lastname: Zhong
authors.affiliation: School of Mathematical and Computational Sciences, Xiangtan University, Xiangtan 411105, China.
authors.forename: S
authors.initials: S
authors.lastname: Shu
authors.affiliation: Department of Mathematics, University of California at Irvine, Irvine, CA 92697.
authors.forename: L
authors.initials: L
authors.lastname: Chen
keywords: Maxwell eigenvalue problem; edge element; two-grid method