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PIER PIER B PIER C PIER M PIER Letters
2011-11-16
A Fast Inverse Polynomial Reconstruction Method Based on Conformal Fourier Transformation
By
Zhe Liu,

    Dr. Zhe Liu

    School of Electronic Engineering

    University of Electronic Science and Technology of China

    China

    Homepage

Qing Huo Liu,

    Prof. Qing Huo Liu

    Department of Electrical and Computer Engineering

    Duke University

    USA

    Homepage

Chun-Hui Zhu,

    Dr. Chun-Hui Zhu

    Department of Control Science and Engineering

    Harbin Institute of Technology

    China

    Homepage

Jianyu Yang

    Dr. Jianyu Yang

    School of Electronic Engineering

    University of Electronic Science and Technology of China

    China

    Homepage

Progress In Electromagnetics Research, Vol. 122, 119-136, 2012
doi:10.2528/PIER11092008
Abstract
A fast Inverse Polynomial Reconstruction Method (IPRM) is proposed to efficiently eliminate the Gibbs phenomenon in Fourier reconstruction of discontinuous functions. The framework of the fast IPRM is modified by reconstructing the function in discretized elements, then the Conformal Fourier Transform (CFT) and the Chirp Z-Transform (CZT) algorithms are applied to accelerate the evaluation of reconstruction coefficients. The memory cost of the fast IPRM is also significantly reduced, owing to the transformation matrix being discretized in the modified framework. The computation complexity and memory cost of the fast IPRM are O(MN log 2L) and O(MN), respectively, where L is the number of the discretized elements, M is the degree of polynomials for the reconstruction of each element, and N is the number of the Fourier series. Numerical results demonstrate that the fast IPRM method not only inherits the robustness of the Generalized IPRM (G-IPRM) method, but also significantly reduces the computation time and the memory cost. Therefore, the fast IPRM method is useful for the pseudospectral time domain methods and for the volume integral equation of the discontinuous material distributions.
Citation
Zhe Liu, Qing Huo Liu, Chun-Hui Zhu, and Jianyu Yang, "A Fast Inverse Polynomial Reconstruction Method Based on Conformal Fourier Transformation," Progress In Electromagnetics Research, Vol. 122, 119-136, 2012.
doi:10.2528/PIER11092008
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