An effective preconditioner for a PML system for electromagnetic scattering problem
An effective preconditioner for a PML system for electromagnetic scattering problem
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DOI：
10.1051/m2an/2014058
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发表时间：
2015-05
期刊：
影响因子：
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通讯作者：
Q. Hu;Chunmei Liu;S. Shu;J. Zou
中科院分区：
文献类型：
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作者：
Q. Hu;Chunmei Liu;S. Shu;J. Zou
在这项工作中，我们关注的是麦克斯韦散射问题的完美匹配层（PML）系统的有效数值解。采用边缘有限元法对PML系统进行离散，得到一个对称但不定的复杂代数系统。当实部和虚部独立考虑时，复代数系统可进一步转化为具有特殊结构的实广义鞍点系统。基于对鞍点系统的Schur补的一个重要观察，构造了鞍点系统的对称正定块对角预条件。通过数值实验验证了该预调节器的有效性和鲁棒性。
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.