A parallel wavelet-enhanced PWTD algorithm for analyzing transient scattering from electrically very large PEC targets
A parallel wavelet-enhanced PWTD algorithm for analyzing transient scattering from electrically very large PEC targets
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用于分析电超大 PEC 目标瞬态散射的并行小波增强 PWTD 算法
DOI：
10.1109/usnc-ursi.2014.6955559
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
E. Michielssen
中科院分区：
文献类型：
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作者：
Yang Liu;A. Yucel;H. Bağcı;E. Michielssen
仅提供摘要表格。经典的基于时间推进(MOT)的表面积分方程(SIE)解算器的计算复杂度和存储需求分别为O(Nt NS2)和O(NS2)，其中Nt和NS表示电流密度的时间和空间自由度的数目。多电平平面波时间域(PWTD)算法，即多电平快速多极子方法的时间域对应算法，将这些成本降低到O(Nt Nslog2 NS)和O(Ns1.5)(Ergin等人，IEEE Trans.天线杂志，41，39-52,1999)。以前，PWTD加速的MOT-SIE求解器被用来分析按一百万个空间未知数离散化的理想导电(PEC)和均匀介质对象的瞬时散射(Shanker等，IEEE Transans)。天线问题，51,628-641,2003)。最近，一个高效的并行求解器已经被开发出来，它采用了先进的分层和可证明可扩展的空间、角度和时间负载划分策略来分析涉及一千万个空间未知数的瞬时散射问题(Liu et.Al.，《乌尔西文摘》，2013年)。在这项工作中，通过使用沿时间维度的局部余弦小波压缩来进一步提高上述求解器的效率(Coifman et.等，L科学研究院，巴黎，第一辑，第312页，第259-261页，1991年)。局部余弦小波基(LCB)由局域化的、准带限的和正交化的类余弦函数组成，非常适合在多分辨率框架中表示许多(自然产生/工程的)高频平面波脉冲。因此，它们允许通过仅存储幅度超过规定阈值的小波系数来减少PWTD解算器中的内存。此外，通过使用直接在小波域中表示的平移矩阵来耦合输入和输出平面波的小波系数，可以降低PWTD平移运算的计算成本。由于LCB的窄带性质，这些矩阵往往非常稀疏，因此可以快速高效地计算；一旦计算，由于平移操作符的平移不变性，它们可以重复使用。到目前为止，我们已经通过利用LCB在内存和计算成本方面实现了一个数量级的减少。我们注意到，该方案使PWTD内核的并行化复杂化，并且需要对计算和通信任务进行明智的重新安排。所提出的求解器将被用来解决非常大的瞬变散射问题，远远超出了我们以前工作中报道的那些问题。
Summary form only given. The computational complexity and memory requirements of classically formulated marching-on-in-time (MOT)-based surface integral equation (SIE) solvers scale as O(Nt Ns2) and O(Ns2), respectively; here Nt and Ns denote the number of temporal and spatial degrees of freedom of the current density. The multilevel plane wave time domain (PWTD) algorithm, viz., the time domain counterpart of the multilevel fast multipole method, reduces these costs to O(Nt Nslog2 Ns) and O(Ns1.5) (Ergin et al., IEEE Trans. Antennas Mag., 41, 39-52, 1999). Previously, PWTD-accelerated MOT-SIE solvers have been used to analyze transient scattering from perfect electrically conducting (PEC) and homogeneous dielectric objects discretized in terms of a million spatial unknowns (Shanker et al., IEEE Trans. Antennas Propag., 51, 628-641, 2003). More recently, an efficient parallelized solver that employs an advanced hierarchical and provably scalable spatial, angular, and temporal load partitioning strategy has been developed to analyze transient scattering problems that involve ten million spatial unknowns (Liu et. al., in URSI Digest, 2013). In this work, the efficiency of the abovementioned solver is further enhanced by employing local cosine wavelet compression along the temporal dimension (Coifman et. al., Comptes Rendus de l'Academie des Sciences, Paris, Serie I, 312, 259-261, 1991). Local cosine wavelet bases (LCBs) consist of localized, quasibandlimited, and orthonormal cosine-like functions that are well-suited to represent many (naturally occurring/engineering) high frequency plane wave pulses in a multiresolution framework. As a result, they permit a memory reduction in PWTD solvers by only storing wavelet coefficients with magnitudes that exceed a prescribed threshold. Furthermore, the computational cost of the PWTD translation operation can be reduced by coupling the wavelet coefficients of incoming and outgoing plane waves using translation matrices expressed directly in the wavelet domain. These matrices tend to be very sparse due to the narrowband nature of the LCBs and hence can be calculated efficiently on-the-fly; once calculated they can be re-used due to the translational invariance of the translation operator. To date we have achieved one order of magnitude reductions in memory and computational cost by leveraging LCBs. We note that this scheme complicates the parallelization of the PWTD kernel and requires judicious rearrangement of the computation and communication tasks. The proposed solver will be used to solve very large transient scattering problems well beyond those reported in our previous work.