A Fast Inverse Polynomial Reconstruction Method Based on Conformal Fourier Transformation

A fast Inverse Polynomial Reconstruction Method (IPRM) is proposed to e-ciently eliminate the Gibbs phenomenon in Fourier reconstruction of discontinuous functions. The framework of the fast IPRM is modifled 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 coe-cients. The memory cost of the fast IPRM is also signiflcantly reduced, owing to the transformation matrix being discretized in the modifled framework. The computation complexity and memory cost of the fast IPRM are O(MN log2L) 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 signiflcantly 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.

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