Solution to Electromagnetic Scattering by Bi-Isotropic Media Using Multilevel Green's Function Interpolation Method

Abstract

Abstract-In this paper, a multilevel Green's function interpolation method (MLGFIM) is developed to analyze electromagnetic scattering from an arbitrarily shaped three-dimensional objects comprised of both conductor and bi-isotropic media. The field decomposition method is adopted to split the homogeneous bi-isotropic media into two uncoupled isotropic media instead of direct calculation of complicated Green's function in bi-isotropic material. The problem is formulated using the Paggio-Miller-Chang-Harrington-WuTsai (PMCHWT) approach for multiple homogeneous isotropic media and electric field approach for conducting bodies. The resultant integral equations are discretized by the method of moment (MoM) and iteratively solved by MLGFIM. Numerical examples illustrate accuracy of this algorithm and CPU time of O(N log N ) and memory requirement of O(N ).

Multilevel Green's Function Interpolation Method Solution of Volume/Surface Integral Equation for Mixed Conducting/Bi-Isotropic Objects

“…Each subcube is recursively subdivided into smaller cubes until the finest cubes satisfy the termination criterion. For two elements in same or adjacent finest cubes, their interaction is directly calculated; while the interaction between two elements in non-adjacent cubes is approximately calculated using multilevel interpolation technique [22][23][24][25][26][27]. By observing (22)- (26), we can find that matrix elements are composed of a general integral expression:…”

“…By handling the same or adjacent finest cubes and nonadjacent cubes separately as shown above, the MLGFIM can achieve its memory saving and CPU reduction [22][23][24][25][26][27]. The near interactions are directly calculated and saved in a sparse matrix, and therefore require O (N ) memory requirement; the far interactions are approximately computed using multilevel interpolation techniques with the storage also of O (N ).…”

“…All in all, memory requirement and computational complexity of MLGFIM are O (N ) and O (N log N ), respectively. Detailed complexities analysis and interpolation techniques about the MLGFIM may refer to [22][23][24][25][26][27].…”

“…More recently, a kernel independent approach, i.e., multilevel Green's function interpolation method (MLGFIM) [22][23][24][25][26][27] has been proposed to solve complex EM problems. It inherits the tree structure of the kernel dependent MLFMA and combines interpolation ideas of PFFT.…”

Application of Chiral Layers and Metamaterials for the Reduction of Radar Cross Section

“…Basically, chirality is defined as the property of a structure of being non-superimposable onto its mirror image [1]. Recently, there is rapid development on the study of electromagnetic wave propagation in chiral media [1][2][3][4][5][6][7][8]. The possibility of realizing negative refraction by chiral nihility was first discussed by Tretyakov et al (2003) [9].…”