A novel approach for fast evaluation of 1-D and 2-D infinite summations

摘要

In many engineering applications, relatively difficult infinite summations with quite complex terms need to be computed numerically. These applications may include the calculation of free-space or planar-media periodic Green's functions in electromagnetics (EM), the determination of the electrostatic energy of ionic crystals in chemistry and the nucleic acid simulations in molecular dynamics. The difficulty of such computations usually arises from the fast oscillatory and slowly convergent nature of the summations. For instance, the EM analysis of cylindrical geometries may require the computation of slow convergent infinite summations of cylindrical Hankel and Bessel type functions; in numerical simulations of periodic structures, e.g. in the analysis of antenna arrays and photonic band gap materials, the periodic Green's functions need to be calculated for each impedance matrix elements in the method of moments, requiring the evaluation of many infinite summations of complex functions to fill in the entire matrix.