Geodesic
An effective preconditioner for a PML system for electromagnetic scattering problem
Hu, Qiya1 ; Liu, Chunmei2  ; Shu, Shi2 ; Zou, Jun3
1 LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P.R. China.
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.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 3, pp. 839-854

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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.

Reçu le :
DOI : 10.1051/m2an/2014058
Classification : 35Q60, 65E05, 78A45, 78M10
Keywords: Maxwell scattering problem, edge finite elements, PML equations, Schur complement-type preconditioner

Hu, Qiya 1 ; Liu, Chunmei 2 ; Shu, Shi 2 ; Zou, Jun 3

1 LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P.R. China.
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. 
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     author = {Hu, Qiya and Liu, Chunmei and Shu, Shi and Zou, Jun},
     title = {An effective preconditioner for a {PML} system for electromagnetic scattering problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {839--854},
     publisher = {EDP-Sciences},
     volume = {49},
     number = {3},
     year = {2015},
     doi = {10.1051/m2an/2014058},
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     zbl = {1318.35115},
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Hu, Qiya; Liu, Chunmei; Shu, Shi; Zou, Jun. An effective preconditioner for a PML system for electromagnetic scattering problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 3, pp. 839-854. doi: 10.1051/m2an/2014058

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