| An Adaptive Uniaxial Perfectly Matched Layer Method for Time-Harmonic Scattering Problems |
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| 作者单位： | Zhiming Chen Xinming Wu LSEC，Institute of Computational Mathematics，Academy of Mathematics and System Science，Chinese Academy of Sciences，Beijing 100190，China. |
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| 基金项目： | 国家自然科学基金，国家重点基础研究发展计划(973计划) |
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| 摘 要： | The uniaxial perfectly matched layer (PML) method uses rectangular domain to define the PML problem and thus provides greater flexibility and efficiency in deal- ing with problems involving anisotropic scatterers.In this paper an adaptive uniaxial PML technique for solving the time harmonic Helmholtz scattering problem is devel- oped.The PML parameters such as the thickness of the layer and the fictitious medium property are determined through sharp a posteriori error estimates.The adaptive finite element method based on a posteriori error estimate is proposed to solve the PML equa- tion which produces automatically a coarse mesh size away from the fixed domain and thus makes the total computational costs insensitive to the thickness of the PML absorb- ing layer.Numerical experiments are included to illustrate the competitive behavior of the proposed adaptive method.In particular,it is demonstrated that the PML layer can be chosen as close to one wave-length from the scatterer and still yields good accuracy and efficiency in approximating the far fields.
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| 关 键 词： | 单轴晶体 适应性 匹配层 误差分析 |
An Adaptive Uniaxial Perfectly Matched Layer Method for Time-Harmonic Scattering Problems |
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| Authors: | Zhiming Chen Xinming Wu |
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| Institution: | LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100190, China |
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| Abstract: | The uniaxial perfectly matched layer (PML) method uses rectangular domain to define the PML problem and thus provides greater flexibility and efficiency in dealing with problems involving anisotropic scatterers. In this paper an adaptive uniaxial PML technique for solving the time harmonic Helmholtz scattering problem is developed. The PML parameters such as the thickness of the layer and the fictitious medium property are determined through sharp a posteriori error estimates. The adaptive finite element method based on a posteriori error estimate is proposed to solve the PML equation which produces automatically a coarse mesh size away from the fixed domain and thus makes the total computational costs insensitive to the thickness of the PML absorbing layer. Numerical experiments are included to illustrate the competitive behavior of the proposed adaptive method. In particular, it is demonstrated that the PML layer can be chosen as close to one wave-length from the scatterer and still yields good accuracy and efficiency in approximating the far fields. |
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| Keywords: | Adaptivity uniaxial perfectly matched layer a posteriori error analysis acoustic scat-tering problems |
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