Open AccessEfficient Filon‐type solution of highly oscillatory physical optics integrals by demodulating complementary error function
Author(s) -
MokhtariKoushyar Farzad,
Shishegar Amir Ahmad
Publication year - 2016
Publication title -
iet microwaves, antennas and propagation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.555
H-Index - 69
eISSN - 1751-8733
pISSN - 1751-8725
DOI - 10.1049/iet-map.2015.0385
Subject(s) - mathematics , transformation (genetics) , mathematical analysis , function (biology) , exponential function , basis function , affine transformation , quadratic equation , type (biology) , numerical integration , error function , algorithm , geometry , ecology , biochemistry , chemistry , evolutionary biology , biology , gene
In this study, an efficient frequency‐independent and error‐controllable Filon‐type solution of highly oscillatory physical optics (PO) integrals on the quadratic surfaces is presented. In this method first, PO surface integral is decomposed into some analytically solvable integrals and one highly oscillatory integral (HOI) which must be solved numerically. Then, by demodulating complementary error function, the integrand of this HOI is decomposed into an oscillatory part and a slowly varying part (demodulated part). The demodulated part can be easily approximated by various types of basis functions, especially in high frequencies. Therefore, after approximating the demodulated part using the polynomials and exponential functions, the whole integrand is solved in closed form. Additionally, a new affine transformation is presented which approximately halves the total integration time. Finally, the accuracy and time efficiency of the proposed method and the transformation are studied and compared with numerical steepest descend path and brute force integration methods.