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arXiv 0704.0033physics.opticsphysics.comp-ph
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离散偶极子近似的收敛性。I.理论分析

Convergence of the discrete dipole approximation. I. Theoretical analysis

Maxim A. Yurkin, Valeri P. Maltsev, Alfons G. Hoekstra

备注：
23 pages, 5 figures; added several corrections according to the published erratum except for Eq.(6) (it was correct in the original paper) and with additional correction in Eq.(96) [$\bar{\mathbf{G}}(...)\mathbf{P}_i^s -\bar{\mathbf{G}}^s(...)\mathbf{P}_i^p$ instead of $(\bar{\mathbf{G}}(...) - \bar{\mathbf{G}}^s(...))\mathbf{P}_i^s$]
发表信息：
J.Opt.Soc.Am.A 23, 2578-2591 (2006); Erratum: J.Opt.Soc.Am.A 32, 2407-2408 (2015)
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摘要：

我们进行了严格的理论收敛性分析的离散偶极子近似（DDA）。我们证明，在任何测量量的误差是有界的偶极子d的大小的线性和二次项的总和，当后者是在DDA的适用范围。此外，线性项是显着小于立方比非立方形状的散射体。因此，对于小d，立方体形状的颗粒的误差比非立方体形状的小得多。线性项的相对重要性随着尺寸的增加而减小，因此对于足够大的散射体，DDA的收敛性在d的公共范围内是二次的。进行了广泛的数值模拟，为一个广泛的d。最后，我们讨论了一些新的发展，在DDA和他们的后果收敛。

英文摘要：

We performed a rigorous theoretical convergence analysis of the discrete dipole approximation (DDA). We prove that errors in any measured quantity are bounded by a sum of a linear and quadratic term in the size of a dipole d, when the latter is in the range of DDA applicability. Moreover, the linear term is significantly smaller for cubically than for non-cubically shaped scatterers. Therefore, for small d errors for cubically shaped particles are much smaller than for non-cubically shaped. The relative importance of the linear term decreases with increasing size, hence convergence of DDA for large enough scatterers is quadratic in the common range of d. Extensive numerical simulations were carried out for a wide range of d. Finally we discuss a number of new developments in DDA and their consequences for convergence.

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