Ased-Aim Analysis of Scattering by Large-Scale Finite Periodic Arrays

Abstract

Abstract-In this paper, the Adaptive Integral Method (AIM) has been extended to characterizing electromagnetic scattering by large scale finite periodic arrays with each cell comprising of either dielectric or metallic objects, by utilizing accurate sub-entire-domain (ASED) basis function. The solution process can be carried out in two steps. In the first step, a small problem is solved in order to construct ASED basis functions to be implemented for the second step. When dielectric materials are involved in the cell which results in a large number of unknowns for the small problem, the AIM can be used to accelerate the solution process and reduce the memory requirement. In the second step, the entire problem is solved using the ASED basis function constructed in the first step. The AIM can be enhanced with the ASED basis function implemented to solve the entire problem more efficiently. When calculating the near interaction impedance matrix, computation time can be significantly reduced by using the near impedance matrix in the first step. The complexity analysis shows that the computational time is O(N 0 log N 0 ) + O(M log M ) and memory requirement is O(N 0 ) + O(M ), where N 0 denotes the number of cells and M stands for the number of elements in one cell. The results calculated respectively by the ASED-AIM and the existing AIM are then compared and an excellent agreement has been observed, which demonstrates the accuracy of the proposed method. In the meantime, memory and computational time requirements have been considerably reduced using the ASED-AIM as compared to the existing AIM. Finally, an example with over 10 million unknowns is given to demonstrate the efficiency of the proposed method.

Analysis of finite frequency selective surfaces backed by dielectric substrate using sub-entire-domain basis function method

“…chiral, bianisotropic) and multilayered dielectric substrates are used, further study should be carried out. The standard SED basis function method can be accelerated by CG-FFT (Lu et al, 2005), FMM (Lu et al, 2007), AIM (Hu et al, 2009;Freni et al, 2011), and the extended SED basis function method (Du et al, 2007(Du et al, , 2008a, etc. to further reduce the memory requirements.…”

“…Therefore, instead of solving an original MoM matrix equation, only two smaller problems are under consideration: the generation of SED basis functions involving only nine cells of the FSS, and the solution of a reduced matrix with a size of the total number of cells in the FSS. Numerous modifications and applications are available (Lu et al, 2005(Lu et al, , 2007Du et al, 2007Du et al, , 2008aZhao et al, 2008;Hu et al, 2009;Wang et al, 2009Wang et al, , 2014, e.g. the SED basis function can be accelerated by the conjugate-gradient fast Fourier transform (CG-FFT) (Lu et al, 2005), the fast multipole method (FMM) (Lu et al, 2007), and the adaptive integral method (AIM) (Hu et al, 2009;Freni et al, 2011) to greatly reduce computational complexity and the memory requirement.…”

“…The SED basis function method is mostly used to analyze the electromagnetic scattering (radar cross section (RCS)) of periodic PEC structures in free space, and exhaustive references are available (Lu et al, 2005(Lu et al, , 2007Du et al, 2007Du et al, , 2008aHu et al, 2009). Wang et al (2009Wang et al ( , 2014 extend the method from free space to planar finite periodic microstrip patch array with a substrate.…”

Interpolation Scheme Based on Adaptive Integral Method for Solving Electrically Large Radiation Problem by Surface/Surface Configuration

“…It usually requires O(N 2 ) memory to store the impedance matrix and O(N 2 ) operations to perform the matrix-vector product via an iterative solver, where N is the number of unknowns. The memory requirements and CPU time for solving the matrix equation are dramatically reduced by using some fast algorithms in the MoM such as Precorrected-FFT method (P-FFT) [7,8], Adaptive Integral Method (AIM) [9][10][11][12][13][14] and Multilevel Fast Multipole Algoithm (MLFMA) [15,16].…”

“…To facilitate the analysis of electrically large antennas, the AIM has been used to reduce the memory requirements and accelerate the matrix-vector multiplications in the iterative solver. Different from the existing AIM codes [9][10][11][12][13][14], the Gauss interpolation scheme is used in our implementation of AIM. Numerical results for a cube mounted on a monopole and two monopoles placed on a helicopter are presented in Section 4.…”