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

โœ Scribed by C.M. Linton; I. Thompson

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
365 KB
Volume
228
Category
Article
ISSN
0021-9991

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โœฆ Synopsis

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 twodimensional. 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 onedimensional 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.

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