Reduced-Rank Approximations to the Far-Field Transform in the Gridded Fast Multipole Method.
Reduced-Rank Approximations to the Far-Field Transform in the Gridded Fast Multipole Method.
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DOI：
10.1016/j.jcp.2011.02.016
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发表时间：
2011-05-10
影响因子：
4.1
通讯作者：
Waag, Robert C.
中科院分区：
文献类型：
--
作者：
Hesford, Andrew J.;Waag, Robert C.
关键词：
快速多极方法（FMM）已显示出对元素定位在常规网格上时，对最优质元素组的大小的计算依赖性降低，并且使用FFT卷积来表示相邻的相互作用。但是，当最优质组较大时，用于FMM相互作用的平面波扩展和相邻相互作用的压力分布之间的转换仍然是FMM计算成本的重要原因。转换算子是向前和逆傅立叶变换，波浪空间局限于单位球体，使用降低的级别分解是平滑且近似的，从而进一步降低了FMM对最优质组大小的计算依赖性。选择自适应交叉近似（ACA）以表示FMM所需的前进和伴随远场变换算子。但是，发现ACA的实际误差大于使用传统估计的预测，并且ACA的性能通常比由截断的单数值分解（SVD）造成的近似值差。为了克服这些问题，同时避免了全尺度SVD的成本，ACA的精度要求更高，并使用减少的，截短的SVD进行重新压缩。结果表明，与全尺寸截短的SVD相当降低了近似误差，而不会降低与ACA矩阵组件相关的渐近计算效率。
The fast multipole method (FMM) has been shown to have a reduced computational dependence on the size of finest-level groups of elements when the elements are positioned on a regular grid and FFT convolution is used to represent neighboring interactions. However, transformations between plane-wave expansions used for FMM interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of FMM computations when finest-level groups are large. The transformation operators, which are forward and inverse Fourier transforms with the wave space confined to the unit sphere, are smooth and well approximated using reduced-rank decompositions that further reduce the computational dependence of the FMM on finest-level group size. The adaptive cross approximation (ACA) is selected to represent the forward and adjoint far-field transformation operators required by the FMM. However, the actual error of the ACA is found to be greater than that predicted using traditional estimates, and the ACA generally performs worse than the approximation resulting from a truncated singular-value decomposition (SVD). To overcome these issues while avoiding the cost of a full-scale SVD, the ACA is employed with more stringent accuracy demands and recompressed using a reduced, truncated SVD. The results show a greatly reduced approximation error that performs comparably to the full-scale truncated SVD without degrading the asymptotic computational efficiency associated with ACA matrix assembly.
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影响因子：
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作者：
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通讯作者：
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影响因子：
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DOI：
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发表时间：
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期刊：
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影响因子：
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DOI：
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发表时间：
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影响因子：
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作者：
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