三维时谐电磁散射问题优化PML方法的收敛性
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摘要
给出解三维时谐电磁散射问题的一种优化完美匹配层(PML)方法.该方法基于频域复坐标拉伸,通过在吸收函数中引入一个小参数ε_0,使得散射问题优化PML方法的计算不依赖PML的厚度.并证明了只要参数ε_0充分小,优化的PML解指数收敛于原三维时谐电磁散射问题的解.
The author gave an optimal perfectly matched layer(PML)method for solving the 3 Dtime harmonic electromagnetic scattering problems.The method was based on the complex coordinate stretching in the frequency domain.The calculation of the optimal PML problem for the scattering problem was not dependent on the thickness of the PML layer by introducing a small parameter ε_0 in the absorbing function.The author proved that the numerical solution converged exponentially to the original 3 Dtime harmonic electromagnetic scattering problems if the parameter ε_0 was sufficiently small.
The author gave an optimal perfectly matched layer(PML)method for solving the 3 Dtime harmonic electromagnetic scattering problems.The method was based on the complex coordinate stretching in the frequency domain.The calculation of the optimal PML problem for the scattering problem was not dependent on the thickness of the PML layer by introducing a small parameter ε_0 in the absorbing function.The author proved that the numerical solution converged exponentially to the original 3 Dtime harmonic electromagnetic scattering problems if the parameter ε_0 was sufficiently small.
引文
[1]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.)
[2]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.)
[3]CHEN Zhiming,WU Xinming.Long-Time Stability and Convergence of the Uniaxial Perfectly Matched Layer Method for Time-Domain Acoustic Scattering Problems[J].SIAM J Numer Anal,2012,50(5):2632-2655.
[4]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.)
[5]杨孝英.双层介质散射问题单轴优化PML方法的收敛性[J].吉林大学学报(理学版),2016,54(5):983-988.(YANG Xiaoying.Convergence of Single Axis Optimal Perfectly Matched Layer Method for Scattering Problems in Two-Layered Media[J].Journal of Jilin Univeristy(Science Edition),2016,54(5):983-988.)
[6]杨孝英.散射问题优化PML方法的收敛性[J].吉林大学学报(理学版),2016,54(4):709-714.(YANG Xiaoying.Convergence of Optimal Perfectly Matched Layer Method for Scattering Problems[J].Journal of Jilin University(Science Edition),2016,54(4):709-714.)
[7]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.
[8]Colton D,Kress R.Inverse Acoustic and Electromagnetic Scattering Theory[M].New York:Springer,1998.
[2]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.)
[3]CHEN Zhiming,WU Xinming.Long-Time Stability and Convergence of the Uniaxial Perfectly Matched Layer Method for Time-Domain Acoustic Scattering Problems[J].SIAM J Numer Anal,2012,50(5):2632-2655.
[4]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.)
[5]杨孝英.双层介质散射问题单轴优化PML方法的收敛性[J].吉林大学学报(理学版),2016,54(5):983-988.(YANG Xiaoying.Convergence of Single Axis Optimal Perfectly Matched Layer Method for Scattering Problems in Two-Layered Media[J].Journal of Jilin Univeristy(Science Edition),2016,54(5):983-988.)
[6]杨孝英.散射问题优化PML方法的收敛性[J].吉林大学学报(理学版),2016,54(4):709-714.(YANG Xiaoying.Convergence of Optimal Perfectly Matched Layer Method for Scattering Problems[J].Journal of Jilin University(Science Edition),2016,54(4):709-714.)
[7]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.
[8]Colton D,Kress R.Inverse Acoustic and Electromagnetic Scattering Theory[M].New York:Springer,1998.