Two-dimensional extrapolation technique combined adaptive frequency-sampling method with the best uniform rational approximation

Abstract

The mature two-dimensional (2-D) Stoer–Bulirsch extrapolation algorithm originated by L. Monroe was used in Ising model on the square lattice analytic results in 2002. This paper presents a novel 2-D Stoer–Bulirsch adaptive frequency-sampling method via the bivariate Chebyshev series that combines with integral equations (IE) for the fast analysis of electromagnetic scattering involving dielectric objects in both the frequency and angular domains simultaneously. In addition to its efficiency, Beale’s MATHEMATICA program is substituted by the bivariate Chebyshev series and the Chebyshev nodes performed by rational function are chosen as the initial samples for the Stoer–Bulirsch algorithm employing an adaptive frequency sampling. The innovative recursive rules are proceeding along the concept of the minimal rectangular region in both the frequency and angular domains simultaneously. Compared to the traditional 2-D fast sweep techniques based on the best uniform rational approximation, no more information is needed except the initial value. Besides the original advantages, the hybrid approach also makes the least number of sampling points required to satisfy the precision criteria in the meantime. By the 2-D extensive application of Stoer–Bulirsch adaptive frequency-sampling method, the accurate and fast radar cross-section results turn into precision adjusted, complexity simplified, and reliable in high stability. To reduce the high computational costs of the conventional PMCHWT approach, the Fourier transform (FFT) is introduced into the scheme. Numerical results demonstrate our proposed 2-D sampling strategy that performs well for two canonical dielectric scatterers.

Keywords:

• extrapolation technique
• adaptive frequency-sampling method
• best uniform rational approximation

Acknowledgement

This article is support by program for the financial support from national natural science fund of P. R. China (No. 61201018), the fundamental research funds for the center universities (K5051202010, K5051302024) and Specialized Research Fund for the Doctoral Program of Higher Education (20120203120011).