The Implementation of Multilevel Green's Function Interpolation Method for Full-Wave Electromagnetic Problems

We extend the multilevel Green's function interpolation method (MLGFIM) developed for quasi-electrostatic problems to full-wave simulations. The difficulty in applying the interpolation approach lies in the additional rapidly changing phase term associated with the full-wave Green's functions. To enhance the efficiency and accuracy of the full-wave Green's function interpolation, a scattered point set consisting of two staggered Tartan grids in conjunction with radial basis function interpolation is employed. To further reduce the computational complexity, the QR factorization technique is applied to compress the low rank Green's function matrices. For electromagnetic scattering from PEC spheres up to a diameter of eight wavelengths, the proposed method compares well with Mie's scattering in accuracy and shows the O(NlogN) efficiency. As the method is "kernel independent", its extension to structures in layered medium is straightforward. In the numerical simulations of finite microstrip patch arrays up to 11 by 11 elements, the proposed method demonstrates very favorable dependencies of CPU time and memory storage requirement versus the number of unknowns