An effective preconditioner for a PML system for electromagnetic scattering problem
1 LSEC, Academy of Mathematics and
Systems Science, Chinese Academy of Sciences, Beijing
2 Department of Mathematics and Computational Science, Hunan University of Science and Engineering, Hunan, 425199, P.R. China.
3 School of Mathematics and Computational Science, Xiangtan University, Hunan, 411105, P.R. China.
4 Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong.
Revised: 11 July 2014
In this work we are concerned with an efficient numerical solution of a perfectly matched layer (PML) system for a Maxwell scattering problem. The PML system is discretized by the edge finite element method, resulting in a symmetric but indefinite complex algebraic system. When the real and imaginary parts are considered independently, the complex algebraic system can be further transformed into a real generalized saddle-point system with some special structure. Based on an crucial observation to its Schur complement, we construct a symmetric and positive definite block diagonal preconditioner for the saddle-point system. Numerical experiments are presented to demonstrate the effectiveness and robustness of the new preconditioner.
Mathematics Subject Classification: 35Q60 / 65E05 / 78A45 / 78M10
Key words: Maxwell scattering problem / edge finite elements / PML equations / Schur complement-type preconditioner
This author was supported by the Major Research Plan of Natural Science Foundation of China G91130015, The Key Project of Natural Science Foundation of China G11031006 and National Basic Research Program of China G2011309702.
This author was supported by the Scientific Research Fund of the Hunan Provincial Education Department of China Grant 12A138, Specialized research Fund for the Doctoral Program of Higher Education of China Grant 20124301110003 and NSFC Projects 11201159 and 11426102.
© EDP Sciences, SMAI 2015