李义丰;李国峰;王云;

• 1:南京工业大学电子与信息工程学院
• 2:廊坊师范学院物理与电子信息学院
• 3:廊坊师范学院数学与信息科学学院

摘要：

将基于复坐标变换和复频移扩展坐标变量的卷积完全匹配层Convolution Perfectly Machted Layer(CPML)引入到两维声波方程的有限元(FEM)计算中,该匹配层作为一种吸收边界条件Absorbing Boundary Condition(ABC)应用在有限元计算的边界截断上。文中分别给出了频域和时域的CPML方程的表达形式,并在有限元计算软件COMSOL中完成数值计算。相对于经典的PML,CPML最大的优势在于它不需要把场分裂开,这使其具有更好的稳定性和更高的吸收性能,且更易于实现。数值计算结果表明,CPML边界层有着比PML更好的吸收效果,其更有效的吸收了进入其中的声场能量。

关键词：

Abstract: A method is presented to extend the Convolution Perfectly Matched Layer(CPML),which bases on the complex coordinates transformation and complex frequency shifted stretched-coordinate metrics,to the 2D acoustic equation calculated with the method of Finite Element Method(FEM).This non-physical layer is used at the computational edge of a FEM as an Absorbing Boundary Condition(ABC) to truncate unbounded media.In this paper,the CPML equations have been presented in frequency domain and in time domain,respectively,and the calculations have been realized in the FEM software of COMSOL.The main advantage of CPML over the classical PML layer is that it is based on the unsplit components of the wave field leading to a more stable,highly effective absorption and a more facility to realize.The results of numerical simulation demonstrate that CPML has better absorbability than PML and it absorbs the outgoing energy more effectively.

Keywords:

基金项目:

通讯作者:

Email:

参考文献：

• 1 Berenger J P.A perfectly matched layer for the absorption of electromagnetic waves.J.Comput.Phys.,1994;114: 195-200
• 2 Gedney S D.Perfeclty matched layer absorbing boundary conditions,in Computational Electrodynamics:The Finite-Difference Time-Domain Method.edited by A. Taflove and S.C.Hagness.Norwood:Artech House.2005: 273-328
• 3 Liu Q H,Tao J.The perfectly matched layer for acoustic waves in absorptive media.J.Acoust.Soc.Am.,1997; 102(4):2072-2082
• 4 Chew W C,Liu Q H.Perfectly matched layers for elasto-dynamics :A new absorbing boundary condition.J.Comp. Acoust.,1996;4(4):341-359
• 5 Hasting F D,Schneider J B,Broschat S L.Application of the perfectly matched layer(pml) absorbing boundary condition to elastic wave propagation.J.Acoust.Soc.Am., 1996;100(5):3061-3069
• 6 Roden J A,Gedney S D.Convolution PML(CPML):An efficient FDTD implementation of the CFS-PML for arbitrary media.Microwave Opt.Technol.Lett.,2000;27: 334-339
• 7 Teixeira F L,Chew W C.General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media.IEEE Microwave and Guided Wave Letters.,1998;8:223-225
• 8 Becache E,Petropoulos P G,Gedney S D.On the longtime behavior of unsplit perfectly matched layers.IEEE Trans.Antennas Propagat,2004;52(5):1335-1342
• 9 Appel(o|¨) D,Kreiss G.Application of the perfectly matched layer to the nonlinear wave equation.Wave Motion,2007; 44:531-548
• 10 Bou Matar O,Preobrazhensky V,Pernod P.Two-dimensional axisymetric numerical simulation of supercritical phase conjugation of ultrasound in active solid media. J.Acoust.Soc.Am.,2005;118(5):2880-2890
• 11 Drossaert F H,Giannopoulos A.Complex frequency shifted convolution PML for FDTD modeling of elastic waves. Wave Motion,2007;44(7-8):593-604
• 12 Komatitsch D,Martin R.An unsplit convolutional Perfectly Matched Layer improved at grazing incidence for the seismic wave equation.Geophysics,2007;72(5):SM155- SM167
• 13 Becache E,Petropoulos P G,Gedney S D.On the longtime behavior of unsplit perfectly matched layers.IEEE Trans.Antennas Propagat.,2004;52(5):1335-1342
• 14 Chew W C,Jin J M,Michelssen E.Complex coordinate system as a generalized absorbing boundary condition.Microwave Opt.Technol.Lett.,1997;15:363-369
• 15 Kuzuoglu M,Mittra R.Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers.IEEE Microwave Guided Wave Lett.,1996;6:447-449
• 16 LI Y F,Bou Matar O.Convolutional Perfectly Matched Layer for elastic second-order wave equation.J.Acoust. Soc.Am.,2010;127(3):1318-1327
• 17 LI Y F,Bou Matar O,Preobrazhensky V,Pernod P. Convolution-Perfectly Matched Layer(C-PML) absorbing boundary condition for wave propagation in piezoelectric solid.In the Proceedings of 2008 IEEE Ultrasonic Symp., 2008:1568-1571
• 18袁伟良,梁昌洪.理想匹配层的综合优化.通信学报,2000; 21(3):47-51
• 19 Katsibas T K,Antonopoulos C S.A general form of perfectly matched layers for three-dimensional problems of acoustic scattering in lossless and lossy fluid media.IEEE Trans.Ultrason.,Ferroelect.,Freq.Contr.,2004;51(8): 976-972
• 20 Berenger J p.Numerical reflection from FDTD-PMLs:A comparison of the split PML with the unsplit and CFS PMLs.IEEE Antennas Propagat.,2002;50(3):258-265