An Improved Full-Wave Multilevel Green’s Function Interpolation Method With RBF-QR Technique for Fast Field Evaluation

Abstract

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.

Keywords

• Fast integral equation solver
• Green’s function interpolation
• radial basis functions
• ill-condition