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一种非条件稳定的隐式时域有限差分法 总被引:1,自引:1,他引:0
介绍一种基于交替方向隐式(ADI)技术的时域有限差分法(FDTD).该方法是非条件稳定的,时间步长不再受到Courant稳定条件的限制,而是由数值色散误差来确定.与传统的FDTD相比,ADI-FDTD增大了时间步长,从而缩短了总的计算时间,特别是当空间网格远小于波长时,优点更加突出.首次把完全匹配层(PML)边界条件应用到ADI-FDTD计算中,采用幂指数形式的时间步进算法,推导了相应的迭代公式.进行了实例计算,并与传统FDTD的结果对比,验证了ADI-FDTD的有效性与优越性. 相似文献
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Courant-Friedrich-Levy(CFL)稳定性条件会限制传统时域有限差分(FDTD)时间步长的选择,因此,采用传统FDTD对矩形缺陷接地结构(RDGS)传输系数(S21)进行计算,需要耗费大量的计算时间。为了节省计算时间,提高计算效率,采用无条件稳定的Crank-Nicolson格式FDTD(CN-FDTD)对RDGS传输系数进行计算,详细讨论了CN-FDTD时间步长与计算效率和计算精度的关系。数值结果表明:当CN-FDTD时间步长取值远大于CFL时间步长时,其计算结果与传统FDTD计算结果仍然吻合,同时计算效率能提高77.2%。比较了CN-FDTD和ADI-FDTD的计算误差,在时间步长取值相同的情况下,CN-FDTD的计算误差要远小于ADI-FDTD。 相似文献
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由于交替方向隐式时域有限差分法(Alternating-Direction Implicit Finite-Difference Time Domain,ADI-FDTD)的数值色散会随着时间步长的增加而增加,文中讨论了单轴各向异性完全匹配层(uniaxial perfectly matched layer,UPML)媒质中包络交替方向隐式时域有限差分法(Envelope ADI-FDTD),推导了二维Envelope ADI-FDTD UPML的迭代公式,并提出一种新的离散方法。与ADI-FDTD UPML相比,改进后的Envelope ADI-FDTD UPML的时间步长可以取得更大,且能有效地修正相速误差,从而减少数值色散,提高计算精度。 相似文献
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UPML媒质中无条件稳定的二维ADI-FDTD方法 总被引:2,自引:0,他引:2
对单轴各向异性PML(UPML)媒质中二维TM波的交变方向隐式时域有限差分方向(ADI-FDTD),通过计算实例表明,ADI-FDTD方法在UMPL媒质中是无条件稳定的,其时间步长不受CFL稳定性条件的限制,并且当计算区域内具有精细差分网格时,其计算效率明显优于传统的时域有限差分方向(FDTD)。 相似文献
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采用分段线性电流密度递归卷积(Piecewise Linear Current Density Recursive Convolution)方法将交替方向隐式时域有限差分方法(ADI-FDTD)推广应用于色散介质—等离子体中,得到了二维情况下等离子体中的迭代差分公式,为了验证该方法的有效性和可靠性,计算了等离子体涂敷导体圆柱的RCS和非均匀等离子体平板的反射系数,数据仿真结果表明,此算法与传统的FDTD相比,在计算结果吻合的情况下,存储量相当,计算效率更高,时间步长仅仅由计算精度来决定. 相似文献
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首次把交替方向隐式时域有限差分法(ADI-FDTD)推广到色散介质——无碰撞非磁化等离子体中,计算了非磁化等离子体与电磁波的相互怍用,使用ADI技术给出了无碰撞等离子体介质中的ADI-FDTD迭代公式.并解析地证明了等离子ADI-FDTD算法也是无条件稳定的,数值计算表明,等离子体ADI-FDTD算法与传统的FDTD的计算结果吻合,计算效率更高。 相似文献
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本文阐述了一种无时间约束条件的FDTD方法(ADI-FDTD)在三维目标电磁散射中的应用.由于散射问题的复杂性,文中分别推导了ADI-FDTD原始方程在连接边界条件、吸收边界条件和近远场外推等关键处的修正方程,并提出了ADI-FDTD方法中的时间步长上限.通过算例表明该方法与传统FDTD方法相比,时间步长可突破传统时间-空间约束条件,它的选取能远大于原有时间步长,对同一散射问题,总计算时间步可以相应大幅度减少,进而提高FDTD方法在计算散射问题中的效率.最后,数值计算显示了该方法的计算精度,并通过图表给出与传统FDTD计算时间的比较. 相似文献
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传统的时域有限差分(Finite-Difference Time-Domain, FDTD)算法受到稳定性条件的制约, 时间步长受限于空间网格的尺寸.医学应用讲究即时性, 为提高成像的速度, 文中采用无条件稳定的交替隐式时域有限差分(Alternating-Direction Implicit Finite-Difference Time-Domain, ADI-FDTD)算法替代传统的FDTD算法进行正向计算, 通过实验得出采用ADI-FDTD算法在保证精度的前提下, 计算时间可缩短为FDTD算法的四分之一, 为乳腺癌微波即时成像提供了可能. 相似文献
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Chai M. Tian Xiao Qing Huo Liu 《Electromagnetic Compatibility, IEEE Transactions on》2006,48(2):273-281
The alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is an unconditionally stable method and allows the time step to be increased beyond the Courant-Friedrich-Levy (CFL) stability condition. This method is potentially very useful for modeling electrically small but complex features often encountered in applications. As the regular FDTD method, however, the spatial discretization in the ADI-FDTD method is only first-order accurate for discontinuous media; several researchers have shown that the errors can be very high when the regular ADI-FDTD method is applied to such discontinuous media. On the other hand, the conformal FDTD method has recently emerged as an efficient FDTD method with higher order accuracy. In this work, a second-order accurate ADI-FDTD method using the conformal approximation of spatial derivatives is proposed. This new scheme, called the ADI-CFDTD method, retains the second-order accuracy in both temporal and spatial discretizations even for discontinuous media with metallic structures, and is unconditionally stable. 2D and 3D examples demonstrate the efficacy of this method and its application in EMC problems. 相似文献
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A novel 3-D FDTD method with weakly conditional stability is presented. The time step in this method is only determined by one space discretisation. Compared with the ADI-FDTD method, this method has better accuracy and higher computation efficiency. CPU time for this weakly conditionally stable FDTD method can be reduced to about 3/4 of that for the ADI-FDTD scheme 相似文献
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Chenghao Yuan Zhizhang Chen 《Microwave Theory and Techniques》2003,51(8):1929-1938
The Courant-Friedrich-Levy stability condition has prevented the conventional finite-difference time-domain (FDTD) method from being effectively applied to conductive materials because of the fine mesh required for the conducting regions. In this paper, the recently developed unconditionally stable alternating-direction-implicit (ADI) FDTD is employed because of its capability in handling a fine mesh with a relatively large time step. The results show that the unconditionally alternating-direction-implicit-finite-difference time-domain (ADI-FDTD) method can be used as an effective universal tool in modeling a medium regardless of its conductivity. In addition, the unsplit perfectly matched layer combined with the ADI-FDTD method is implemented in the cylindrical coordinates and is proven to be very effective even with the cylindrical structures that contain open conducting media. 相似文献