Zhou J, Hu X, Zhong L, Shu S, Chen L
School of Mathematical and Computational Sciences, Xiangtan University, Xiangtan 411105, China.
Department of Mathematics, Pennsylvania State University, University Park, PA 16802.
SIAM J Numer Anal. 2014;52(4):2027-2047. doi: 10.1137/130919921.
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 [, 70 (2001), pp. 17-25] and further developed by Hu and Cheng [, 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.
提出了两种新的两重网格算法来求解麦克斯韦本征值问题。新方法基于徐和周[《计算数学》，70 (2001)，第17 - 25页]最近提出并由胡和程[《计算数学》，80 (2011)，第1287 - 1301页]进一步发展的用于椭圆型本征值问题的两重网格方法。新的两重网格格式将精细网格上的麦克斯韦本征值问题的求解简化为同一精细网格上的一个线性不定麦克斯韦方程和一个在粗得多的网格上的原本征值问题。因此，新格式节省了总的计算成本。误差估计表明两重网格方法保持渐近最优精度，并且所给出的数值实验证实了理论结果。
