Spherical Bessel transform via exponential sum approximation of spherical Bessel function

JOURNAL OF COMPUTATIONAL PHYSICS

卷:355

Article

Ikeno, Hidekazu^1,2 

[1] Osaka Prefecture Univ, Org Res Promot, Res Ctr 21 Century, NanoSq Res Inst,Naka Ku, 1-2 Gakuen Cho, Sakai, Osaka 5998570, Japan

[2] JST PRESTO, 4-1-8 Hon Cho, Kawaguchi, Saitama 3320012, Japan

关键词: Hankel transform;    Spherical Bessel transform;    Bessel function;    Oscillatory integrals;    Balanced truncation method;   

DOI  :  10.1016/j.jcp.2017.11.016

来源: Elsevier

【 摘 要 】

A new algorithm for numerical evaluation of spherical Bessel transform is proposed in this paper. In this method, the spherical Bessel function is approximately represented as an exponential sum with complex parameters. This is obtained by expressing an integral representation of spherical Bessel function in complex plane, and discretizing contour integrals along steepest descent paths and a contour path parallel to real axis using numerical quadrature rule with the double-exponential transformation. The number of terms in the expression is reduced using the modified balanced truncation method. The residual part of integrand is also expanded by exponential functions using Prony-like method. The spherical Bessel transform can be evaluated analytically on arbitrary points in half-open interval. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free