Published

Two-Grid Methods for Maxwell Eigenvalue Problems

J. Zhou, X. Hu, L. Zhong, S. Shu, and L. Chen

SIAM Journal on Numerical Analysis, 52(4), 2027--2047, 2014.

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ABSTRACT:

 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., 70:17--25,
2001), and further developed by Hu and Cheng
(Math. Comp. 80:1287--1301, 2011) 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 significantly on
total computational cost.  This paper shows that the error estimates
of the two-grid methods maintain an asymptotically optimal accuracy,
and the numerical experiments presented confirm the theoretical
results.