一种降低ADI-FDTD算法数值色散的准各向同性空间差分法
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摘要
使用准各向同性的空间差分格式替代常规ADI-FDTD算法中的差分形式来改善原算法中的数值色散问题。修正后的算法依然保持了无条件稳定的优势;同时,通过合理选择加权系数,仿真过程中的数值色散误差可以显著降低。推导出了修正算法的数值色散关系,并从入射角、时间步长和网格尺寸等3个方面分析了修正算法数值色散问题的改进程度。最后,通过一个算例对比演示了改进算法的精度和计算效率。
The difference scheme of the alternating-direction-implicit finite-difference time-domain(ADI-FDTD) method is replaced by the quasi isotropic(QI) spatial difference scheme to improve its numerical dispersion characteristics. The unconditional stability advantage of QI-ADI-FDTD is analytically proven and numerically verified. The numerical dispersion of the novel method can be dramatically reduced by choosing proper weighting factor. An example is simulated to demonstrate the accuracy and efficiency of the proposed method.
The difference scheme of the alternating-direction-implicit finite-difference time-domain(ADI-FDTD) method is replaced by the quasi isotropic(QI) spatial difference scheme to improve its numerical dispersion characteristics. The unconditional stability advantage of QI-ADI-FDTD is analytically proven and numerically verified. The numerical dispersion of the novel method can be dramatically reduced by choosing proper weighting factor. An example is simulated to demonstrate the accuracy and efficiency of the proposed method.
引文
[1]A.Vaccari,A.Cala'Lesina,L.Cristoforetti,and R.Pontalti,“Parallel implementation of a 3D subgridding FDTD algorithm for large simulations,”Progress In Electromagnetics Research,Vol.120,263-292,2011.
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[13]Zheng,H.X.and K.W.Leung,“An efficient method to reduce the numerical dispersion in the ADI-FDTD,”IEEE Trans.on Microwave Theory Tech.,Vol.53,No.7,2295-2301,Jul.2005.
[14]Zhang,Y.,S.W.Lüand J.Zhang,“Reduction of numerical dispersion of 3-D higher order alternating-direction-implicit finite difference time-domain method with artificial anisotropy,”IEEE Trans.on Microwave Theory Tech.,Vol.57,No.10,2416-2428,Oct.2009.
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[16]Shibayama,J.M.Muraki,J.Yamauchi,and H.Nakano,“Efficient implicit FDTD algorithm based on locally one-dimensional scheme,”Electron.Lett.,Vol.41,No.19,1046–1047,Sep.2005.
[17]Kong,Y.D.and Q.X.Chu,“High-order split-step unconditionally-stable FDTD methods and numerical analysis,”IEEE Trans.on Antennas Propag.,Vol.59,No.9,3280–3289,Sep.2011.
[18]Kong,Y.D.and Q.X.Chu,“Reduction of numerical dispersion of the six-stages split-step unconditionally-stable FDTD method with controlling parameters,”Progress In Electromagnetics Research,Vol.122,175-196,2012.
[19]Fu,W.and E.L.Tan,“Development of split-step FDTD method with higher-order spatial accuracy,”Electron.Lett.,Vol.40,No.20,1252–1253,Sep.2004.
[20]Koh,I.S.,H.Kim,J.M.Lee,J.G.Yook and C.S.Pil,“Novel explicit 2-D FDTD scheme with isotropic dispersion and enhanced stability,”IEEE Trans.on Antennas Propag.,Vol.54,No.11,3505–3510,Nov.2006.
[2]M.Izadi,M.Z.A.Ab Kadir,and C.Gomes,“Evaluation of electromagnetic fields associated with inclined lightning channel using second order FDTD-hybrid methods,”Progress In Electromagnetics Research,Vol.117,209-236,2011.
[3]R.Xiong,B.Chen,J.-J.Han,Y.-Y.Qiu,W.Yang,and Q.Ning,“Transient resistance analysis of large grounding systems using the FDTD method,”Progress In Electromagnetics Research,Vol.132,159-175,2012.
[4]D.L.Markovich,K.S.Ladutenko,and P.A.Belov,“Performance of FDTD method CPU implementations for simulation of electromagnetic processes,”Progress In Electromagnetics Research,Vol.139,655-670,2013.
[5]Ashutosh and P.K.Jain,“FDTD analysis of the dispersion characteristics of the metal PBG structures,”Progress In Electromagnetics Research B,Vol.39,71-88,2012.
[6]X.-M.Guo,Q.-X.Guo,W.Zhao,and W.Yu,“Parallel FDTD simulation using NUMA acceleration technique,”Progress In Electromagnetics Research Letters,Vol.28,1-8,2012.
[7]邵振海洪伟.一种新的吸收边界条件及三维微波结构的FDTD分析[J].微波学报,2000,16(4):361-365Shao Zhenhai,Hong Wei.Analysis of 3D MICs by Using FDTD with New Absorbing Boundary Condition
[8]Zheng,F.H.,Z.Z.Chen,and J.Z.Zhang,“Toward the development of a three-dimensional unconditionally stable finite-difference time-domain method,”IEEE Trans.on Microwave Theory Tech.,Vol.48,No.9,1550-1558,Sep.2000.
[9]Wang,M.H.,Z.Wang,and J.Chen,“A parameter optimized ADI-FDTD method,”IEEE Antennas Wireless Propag.Lett.,Vol.2,No.1,118-121,2003.
[10]Fu,W.M.and E.L.Tan,“A parameter optimized ADI-FDTD method based on the(2,4)stencil,”IEEE Trans.on Antennas Propag.,Vol.54,No.6,1836-1842,Jun.2006.
[11]Ahmed,I.and Z.Chen,“Dispersion-error optimized ADI FDTD,”Proc.IEEE MTT-S Int.Microw.Symp.Dig.,173-176,Jun.2006.
[12]Juntunen,J.S.and T.D.Tsiboukis,“Reduction of numerical dispersion in FDTD method through artificial anisotropy,”IEEE Trans.on Microwave Theory Tech.,Vol.48,No.4,582-588,Apr.2000.
[13]Zheng,H.X.and K.W.Leung,“An efficient method to reduce the numerical dispersion in the ADI-FDTD,”IEEE Trans.on Microwave Theory Tech.,Vol.53,No.7,2295-2301,Jul.2005.
[14]Zhang,Y.,S.W.Lüand J.Zhang,“Reduction of numerical dispersion of 3-D higher order alternating-direction-implicit finite difference time-domain method with artificial anisotropy,”IEEE Trans.on Microwave Theory Tech.,Vol.57,No.10,2416-2428,Oct.2009.
[15]Lee,J.and B.Fornberg,“A split step approach for the3-D Maxwell’s equations,”J.Comput.Appl.Math.,No.158,485–505,Mar.2003.
[16]Shibayama,J.M.Muraki,J.Yamauchi,and H.Nakano,“Efficient implicit FDTD algorithm based on locally one-dimensional scheme,”Electron.Lett.,Vol.41,No.19,1046–1047,Sep.2005.
[17]Kong,Y.D.and Q.X.Chu,“High-order split-step unconditionally-stable FDTD methods and numerical analysis,”IEEE Trans.on Antennas Propag.,Vol.59,No.9,3280–3289,Sep.2011.
[18]Kong,Y.D.and Q.X.Chu,“Reduction of numerical dispersion of the six-stages split-step unconditionally-stable FDTD method with controlling parameters,”Progress In Electromagnetics Research,Vol.122,175-196,2012.
[19]Fu,W.and E.L.Tan,“Development of split-step FDTD method with higher-order spatial accuracy,”Electron.Lett.,Vol.40,No.20,1252–1253,Sep.2004.
[20]Koh,I.S.,H.Kim,J.M.Lee,J.G.Yook and C.S.Pil,“Novel explicit 2-D FDTD scheme with isotropic dispersion and enhanced stability,”IEEE Trans.on Antennas Propag.,Vol.54,No.11,3505–3510,Nov.2006.