An Improved Full-Wave Multilevel Green’s Function Interpolation Method With RBF-QR Technique for Fast Field Evaluation
An Improved Full-Wave Multilevel Green’s Function Interpolation Method With RBF-QR Technique for Fast Field Evaluation
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DOI：
10.1109/access.2017.2710160
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发表时间：
2017-05
期刊：
影响因子：
3.9
通讯作者：
Peng Zhao;C. Chan;Gaofeng Wang
中科院分区：
文献类型：
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作者：
Peng Zhao;C. Chan;Gaofeng Wang
提出了一种基于RBF-QR技术的改进全波多能级格林函数插值法（MLGFIM），用于电磁场的快速评估。径向基函数插值方法的难点在于随着插值点的增加，求解矩阵方程的奇异性越来越大。在以前的RBF实现中使用了使基函数相对不那么平滑的折衷方法来解决这个问题。本文将一种新的插值方案RBF-QR技术应用于格林函数的插值，在不妥协的情况下解决了病态问题。利用qr分解技术生成了较好的条件基函数，并解决了基函数对形状参数值的敏感性问题。此外，采用一种新的混合插补模式对网格模式进行优化，如减少所需插补点数和边界插补误差。将所提出的RBF-QR技术与混合插值模式相结合，大大提高了MLGFIM的效率。该算法适用于涉及贴片阵列、光子带隙结构、超表面结构、双负超材料等物体的问题分析。最后给出了5个算例，验证了该算法的正确性和有效性。
An improved full-wave multilevel Green’s function interpolation method (MLGFIM) with RBF-QR technique is proposed for the fast evaluation of electromagnetic field. The difficulty in applying the interpolation approach with radial basis functions (RBFs) lies in solving the increasingly singular matrix equation with the increase of the number of interpolation points. The compromise of making the basis functions relatively less smooth was used in the previous RBF implementations to address this problem. In this paper, a new interpolation scheme, the RBF-QR technique is applied to the interpolation of Green’s function to resolve the ill-conditioning issue without such a compromise. A better conditioned basis function is generated by the QR-factorization technique, and it also solves the sensitivity of the basis function to the value of shape parameter. Moreover, a new hybrid interpolation pattern is adopted to optimize the grid pattern, e.g., reduce the number of interpolation points required and the boundary interpolation errors. The employment of the proposed RBF-QR technique in conjunction with hybrid interpolation pattern makes the efficiency of the MLGFIM greatly improved. The proposed algorithm is used for the analysis of problems involving objects, such as patch arrays, photonic bandgap structures, metasurface structures, double negative metamaterial and so on. Five numerical examples are given to validate this new algorithm, and show the accuracy and efficiency of the improved MLGFIM.