Efficient methods for the computation of Pollaczek integrals in the magnetic field

Article type: Research Article

Authors: Xiang, Shuhuang^{a; *} | Ma, Junjie^a

Affiliations: [a] Department of Information and Scientific Computing, Central South University, Changsha, Hunan, China

Correspondence: [*] Corresponding author: Shuhuang Xiang, Department of Information and Scientific Computing, Central South University, Changsha, Hunan 410083, China. E-mail: xiangsh@mail.csu.edu.cn

Abstract: Calculation of the Pollaczek integral is very important in evaluating the magnetic field in air generated by an underground conductor. This paper provides an efficient algorithm to calculate these integrals by splitting the semi-infinite range into two parts, where the integral tail is evaluated by complex integration methods, and the integral on the finite segment is calculated by the Clenshaw-Curtis quadrature. The computational cost remains the same regardless the frequency, and the higher the oscillation the better the accuracy of the calculation. The efficiency and accuracy are tested by numerical examples.

Keywords: Pollaczek integral, mutual impedance, complex integration, Clenshaw-Curtis quadrature

DOI: 10.3233/JAE-121607

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 41, no. 3, pp. 227-236, 2013