Comparison of Interpolating Functions and Interpolating Points in Full-Wave Multilevel Green´s Function Interpolation Method

The difficulty for the solution of full-wave electromagnetic problems using multilevel Green´s function interpolation method (MLGFIM) lies in applying interpolating approaches to efficiently and accurately approximate Green´s function with rapidly changing phase term. We compare various interpolating schemes when radial basis function (RBF) is employed for the interpolation of scattered data of Green´s function. We show that the infinitely smooth Gaussian (GA) RBF has the best interpolation accuracy. In order to improve the interpolation efficiency, a new kind of staggered Tartan grid is proposed. A good calculation method for the shape parameter in GA RBF is given to solve its sensitivity to the group size and the number of interpolation points. Based on the analysis of variation of the number of interpolation points with electric length of the group, adaptive choice of the types of interpolation functions and interpolation points are employed. Numerical examples show that the computational efficiency of this new interpolation scheme is much improved over the previously reported ones.