An adaptive inverse iteration for Maxwell eigenvalue problem based on edge elements

Authors:
Junqing Chen;Yifeng Xu;Jun Zou
Affiliations:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China;Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
Venue:
Journal of Computational Physics
Year:
2010

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Abstract

We propose and analyze an adaptive inverse iterative method for solving the Maxwell eigenvalue problem with discontinuous physical parameters in three dimensions. The adaptive method updates the eigenvalue and eigenfunction based on an a posteriori error estimate of the edge element discretization. At each iteration, the involved saddle-point Maxwell system is transformed into an equivalent system consisting of a singular Maxwell equation and two Poisson equations, for both of which preconditioned iterative solvers are available with optimal convergence rate in terms of the total degrees of freedom. Numerical results are presented, which confirms the quasi-optimal convergence of the adaptive edge element method in terms of the numerical accuracy and the total degrees of freedom.