Fast evaluation of time domain fields in sub-wavelength source/observer distributions using accelerated Cartesian expansions (ACE)
Fast evaluation of time domain fields in sub-wavelength source/observer distributions using accelerated Cartesian expansions (ACE)
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DOI：
10.1016/j.jcp.2007.08.017
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发表时间：
2007-12
期刊：
影响因子：
--
通讯作者：
M. Vikram;B. Shanker
中科院分区：
文献类型：
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作者：
M. Vikram;B. Shanker
电大尺寸物体瞬态散射的时域积分方程求解器从平面波时域（PWTD）算法等加速技术中受益匪浅;这些技术降低了渐近CPU和内存成本。然而，PWTD故障时，用于分析的结构，具有亚波长的功能或功能的长度尺度是数量级小于入射脉冲中的最小波长。这些发生在电磁学的范围从天线拓扑结构，馈电结构等，在这种制度下，它是几何约束，决定了计算的复杂性，而不是感兴趣的波长。在这项工作中，我们提出了一种有效的分析方法，这样的亚波长源/观察者分布在时域中。我们寻求利用的方法是最近开发的基于笛卡尔展开的算法，用于加速形式Rν的势的计算。在本文中，我们提出了一种有效的方法来计算这些多项式的两种不同的情况下，域的大小跨越光在（i）一个时间步长和（ii）多个时间步长的距离。这些算法都是在均匀分布和非均匀分布的框架内进行的。结果表明，该算法的效率和收敛性。
Time domain integral equation solvers for transient scattering from electrically large objects have benefitted significantly from acceleration techniques like the plane wave time domain (PWTD) algorithm; these techniques reduce the asymptotic CPU and memory cost. However, PWTD breaks down when used in the analysis of structures that have subwavelength features or features whose length scales are orders of magnitude smaller than the smallest wavelength in the incident pulse. Instances of these occurring in electromagnetics range from antenna topologies, to feed structures, etc. In this regime, it is the geometric constraints that dictate the computational complexity, as opposed to the wavelength of interest. In this work, we present an approach for efficient analysis of such sub-wavelength source/observer distributions in time domain. The methodology that we seek to exploit is the recently developed algorithm based on Cartesian expansions for accelerating the computation of potentials of the form Rν. In this paper, we present an efficient methodology for computing these polynomials for two different scenarios; where the size of the domain spans the distance travelled by light in (i) one time step and (ii) multiple time steps. These algorithms are cast within the framework of both uniform and non-uniform distributions. Results that demonstrate the efficiency and convergence of the proposed algorithm are presented.