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PIER PIER B PIER C PIER M PIER Letters
2009-10-16
High Frequency Scattering by an Impenetrable Sphere
By
Wei E. I. Sha,

    Dr. Wei E. I. Sha

    College of Information Science & Electronic Engineering

    Zhejiang University

    China

    Homepage

Weng Cho Chew

    Professor Weng Cho Chew

    Department of Electrical and Computer Engineering

    University of Illinois at Urbana-Champaign

    USA

    Homepage

Progress In Electromagnetics Research, Vol. 97, 291-325, 2009
doi:10.2528/PIER09100102
Abstract
The high frequency scattering of a scalar plane wave from an impenetrable sphere with a diameter of several thousand wavelengths is treated by the Sommerfeld-Watson transformation, the saddle-point technique (SPT), and the numerical steepest descent method (NSDM). Both the near and far fields for the sphere are computed within the observation angle range of 0 to 180 degree. First, with the aid of the Watson transformation, the fast-convergent residue series replacing the slow-convergent Mie series is derived. Second, a new algorithm for finding the zeros of the Hankel functions is developed. Third, a novel NSDM, which is adaptive to frequency and is hence frequency independent, is proposed to overcome the breakdown of the traditional SPT in the transition region. Numerical results show that when the observation angle is very small, the Mie series solution of the near-field will not be accurate due to error accumulation. Furthermore, using the proposed methods, the CPU times for both the near-field and far-field calculations are frequency independent with controllable error. This work can be used to benchmark future works for high-frequency scattering.
Citation
Wei E. I. Sha, and Weng Cho Chew, "High Frequency Scattering by an Impenetrable Sphere," Progress In Electromagnetics Research, Vol. 97, 291-325, 2009.
doi:10.2528/PIER09100102
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