Reduction of FDTD Stair-Casing Error regarding to Metamaterials by Using High-Order Polynomial Transformation Functions

A high-order polynomial fitting method is proposed to accelerate the computation of double-Gaussian fitting in the retrieval of the Brillouin frequency shifts (BFS) in optical fibers showing two local Brillouin peaks. The method is experimentally validated in a distributed Brillouin sensor under different signal-to noise ratios and realistic spectral scenarios. Results verify that a sixth-order polynomial fitting can provide a reliable initial estimation of the dual local BFS values, which can be subsequently used as initial parameters of a nonlinear double-Gaussian fitting. The method demonstrates a 4.9-fold reduction in the number of iterations required by double-Gaussian fitting and a 3.4-fold improvement in processing time.

A moving fitting method for edge detection is proposed in this work. Polynomial function is used for the curve fitting of the column of pixels near the edge. Proposed method is compared with polynomial fitting method without sub-segment. The comparison shows that even with low order polynomial, the effects of moving fitting are significantly better than that with high order polynomial fitting without sub-segment.

Yoshida-Uemori model (Y-U model) can be used with any types of yield functions. The calculated stress strain response will be, however, different depending on the chosen yield function if the yield function and the effective strain definition are inappropriate. Thus several modifications to Y-U model were proposed in the 10th International Conference on Technology of Plasticity. It was ascertained that in the modified Y-U model, the same set of material parameters can be used with von Mises, Hill’s 1948, and Hill’s 1990 yield function. In this study, Yld2000-2d and Yoshida’s 6th-order polynomial type 3D yield function were examined and it was clarified that the same set of Y-U parameters can be used with these yield functions.