A Combination of Multilevel Green’s Function Interpolation Method with Multilevel Fast Multipole Algorithm for Efficient Simulation of Scattering of Dielectric and Conductive Objects

In this paper, a combination of multilevel Green’s function interpolation method (MLGFIM) with multilevel fast multipole algorithm (MLFMA) for solving the electromagnetic radiation and scattering problems from dielectric and conductive objects is proposed. The combination of MLGFIM and MLFMA was initially proposed by Ming Chen et al. [1] and it exclusively employs electric field integral equation (EFIE), which limits its application to PEC (Perfect Electric Conductor) scenarios only. This paper expands the scope by integrating Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) equations in integral formulation with MLFMA-MLGFIM to solve homogeneous dielectric and metallic problems. In conventional MLFMA, the length of the minimum box needs to exceed a specific threshold, usually $0.2 \lambda$, leading to an excessive number of unknowns within lowest boxes, particularly when problem involves refined elements. This, in turn, increases the memory demands for storing the nearfield impedance matrix of the MLFMA. The MLGFIM is utilized here to compute near-field part of the MLFMA, effectively reducing the number of unknowns per box, irrespective of its size. Additionally, QR factorization is implemented to compress the Green’s function with low rank for accelerating the far-field matrix calculation process in MLGFIM, thereby expediting the matrix-vector multiplications (MVM) for the MLFMA-MLGFIM. The numerical examples provided in this paper illustrate the precision and computational effectiveness of the method. In the numerical simulations of a fine structured metal dielectric composite, the proposed method exhibits a notable near-field memory storage reduction by the factor of 15.5 without compromising the accuracy and maintaining the same calculation time for each MVM.