散射问题优化PML方法的收敛性
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摘要
给出一种带小参数ε_0的优化完美匹配层(PML)方法,求解时谐散射问题.结果表明,该方法使得散射问题优化PML方法的计算不依赖于PML的厚度δ,且优化的PML解指数收敛于原问题的解.
The author proposed an optimal perfectly matched layer(PML) method with small parameter ε_0 for solving time-harmonic scattering problem.The results show that the proposed method makes the calculation of the scattering problem of optimal PML method do not depend on the thicknessδof the PML,and the exponential convergence of the optimal PML is the solution of the original problem.
The author proposed an optimal perfectly matched layer(PML) method with small parameter ε_0 for solving time-harmonic scattering problem.The results show that the proposed method makes the calculation of the scattering problem of optimal PML method do not depend on the thicknessδof the PML,and the exponential convergence of the optimal PML is the solution of the original problem.
引文
[1]Bérenger J P.Perfectly Matched Layer(PML)for Computational Electromagnetics[M].Arcueil:Morgan and Claypool Publishers,2007.
[2]Bermúdez A,Hervella-Nieto L,Prieto A,et al.An Optimal Perfectly Matched Layer with Unbounded Absorbing Function for Time-Harmonic Acoustic Scattering Problems[J].J Comput Phys,2007,223(2):469-488.
[3]CHEN Zhiming,LIANG Chao,XIANG Xueshuang.An Anisotropic Perfectly Matched Layer Method for Helmholtz Scattering Problems with Discontinuous Wave Number[J].Inverse Problems and Imaging,2013,7(3):663-678.
[4]CHEN Zhiming,CUI Tao,ZHANG Linbo.An Adaptive Anisotropic Perfectly Matched Layer Method for 3-D Time Harmonic Electromagnetic Scattering Problems[J].Numer Math,2013,125(4):639-677.
[5]张德悦,马富明,方明.求解洞穴散射问题的带有吸收边界层的有限元方法[J].计算物理,2008,25(3):301-308.(ZHANG Deyue,MA Fuming,FANG Ming.Finite Element Method with Perfectly Matched Absorbing Layers for Wave Scattering from a Cavity[J].Chinese Journal of Computational Physics,2008,25(3):301-308.)
[6]杨孝英,马富明,杜新伟.计算开洞穴电磁散射问题的一种优化PML方法[J].吉林大学学报(理学版),2009,47(2):185-190.(YANG Xiaoying,MA Fuming,DU Xinwei.An Optimal PML Method for Electromagnetic Scattering from Cavities[J].Journal of Jilin University(Science Edition),2009,47(2):185-190.)
[7]杨孝英,王旖旎.解声波散射问题的一种优化PML方法[J].吉林大学学报(理学版),2013,51(1):89-91.(YANG Xiaoying,WANG Yini.An Optimal Perfectly Matched Layer Technique for Uniaxial Scattering Problems[J].Journal of Jilin University(Science Edition),2013,51(1):89-91.)
[8]CHEN Zhiming,LIU Xuezhe.An Adaptive Perfectly Matched Layer Technique for Time-Harmonic Scattering Problems[J].SIAM J Numer Anal,2005,43(2):645-671.
[9]Colton D,Kress R.Integral Equation Methods in Scattering Theory[M].New York:John Wiley,1983.
[10]Babuka I,Aziz A K.Survey Lectures on Mathematical Foundations of the Finite Element Method[R].New York:Academic Press,1972.
[11]CHEN Zhiming,WU Haijun.An Adaptive Finite Element Method with Perfectly Matched Absorbing Layers for the Wave Scattering by Periodic Structures[J].SIAM J Numer Anal,2003,41(3):799-826.
[2]Bermúdez A,Hervella-Nieto L,Prieto A,et al.An Optimal Perfectly Matched Layer with Unbounded Absorbing Function for Time-Harmonic Acoustic Scattering Problems[J].J Comput Phys,2007,223(2):469-488.
[3]CHEN Zhiming,LIANG Chao,XIANG Xueshuang.An Anisotropic Perfectly Matched Layer Method for Helmholtz Scattering Problems with Discontinuous Wave Number[J].Inverse Problems and Imaging,2013,7(3):663-678.
[4]CHEN Zhiming,CUI Tao,ZHANG Linbo.An Adaptive Anisotropic Perfectly Matched Layer Method for 3-D Time Harmonic Electromagnetic Scattering Problems[J].Numer Math,2013,125(4):639-677.
[5]张德悦,马富明,方明.求解洞穴散射问题的带有吸收边界层的有限元方法[J].计算物理,2008,25(3):301-308.(ZHANG Deyue,MA Fuming,FANG Ming.Finite Element Method with Perfectly Matched Absorbing Layers for Wave Scattering from a Cavity[J].Chinese Journal of Computational Physics,2008,25(3):301-308.)
[6]杨孝英,马富明,杜新伟.计算开洞穴电磁散射问题的一种优化PML方法[J].吉林大学学报(理学版),2009,47(2):185-190.(YANG Xiaoying,MA Fuming,DU Xinwei.An Optimal PML Method for Electromagnetic Scattering from Cavities[J].Journal of Jilin University(Science Edition),2009,47(2):185-190.)
[7]杨孝英,王旖旎.解声波散射问题的一种优化PML方法[J].吉林大学学报(理学版),2013,51(1):89-91.(YANG Xiaoying,WANG Yini.An Optimal Perfectly Matched Layer Technique for Uniaxial Scattering Problems[J].Journal of Jilin University(Science Edition),2013,51(1):89-91.)
[8]CHEN Zhiming,LIU Xuezhe.An Adaptive Perfectly Matched Layer Technique for Time-Harmonic Scattering Problems[J].SIAM J Numer Anal,2005,43(2):645-671.
[9]Colton D,Kress R.Integral Equation Methods in Scattering Theory[M].New York:John Wiley,1983.
[10]Babuka I,Aziz A K.Survey Lectures on Mathematical Foundations of the Finite Element Method[R].New York:Academic Press,1972.
[11]CHEN Zhiming,WU Haijun.An Adaptive Finite Element Method with Perfectly Matched Absorbing Layers for the Wave Scattering by Periodic Structures[J].SIAM J Numer Anal,2003,41(3):799-826.