One- and two-dimensional lattice sums for the three-dimensional Helmholtz equation

Linton CM; Thompson I

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One- and two-dimensional lattice sums for the three-dimensional Helmholtz equation

机译：三维Helmholtz方程的一维和二维晶格和

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摘要

The accurate and efficient computation of lattice sums for the three-dimensional Helmholtz equation is considered for the cases where the underlying lattice is one- or two-dimensional. We demonstrate, using careful numerical computations, that the reduction method, in which the sums for a two-dimensional lattice are expressed as a sum of one-dimensional lattice sums leads to an order-of-magnitude improvement in performance over the well-known Ewald method. In the process we clarify and improve on a number of results originally formulated by Twersky in the 1970s. (C) 2008 Elsevier Inc. All rights reserved.

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《Journal of Computational Physics》 |2009年第6期|共15页
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Linton CM; Thompson I;
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正文语种 eng
中图分类应用物理学;
关键词
Lattice sum; Helmholtz equation; Ewald summation; Lattice reduction; Clausen function; Schlomilch series; PERIODIC GREENS-FUNCTION; ELECTROMAGNETIC-WAVES; MULTIPLE-SCATTERING; SCHLOMILCH SERIES; PLANAR ARRAY; DIFFRACTION; CONVERGENCE; COMPUTATION; OBSTACLES; GRATINGS;

机译：格和;Helmholtz方程;Ewald总和;格约简;Clausen函数;Schlomilch级数;周期格林函数;电磁波;多重散射;SchloMilch系列;平面阵列;衍射;收敛;计算;障碍;梯度;

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机译：三维Helmholtz方程的一维和二维晶格和
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7. One- and two-dimensional lattice sums for the three-dimensional Helmholtz equation [O] . C M Linton, I Thompson 2013

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One- and two-dimensional lattice sums for the three-dimensional Helmholtz equation

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