MLFMM-based, fast multiple-reflection physical optics for large-scale electromagnetic scattering analysis

Abstract

The asymptotic, physical optics (PO) approximation is applicable to electromagnetic scattering analysis of electrically large, conducting objects, which is important for various applications, such as radar cross-section (RCS) calculations. It relates the incident magnetic field to the induced surface current at points on a scatterer's surface with line-of-sight visibility to the source. Here, the focus is on mesh-based PO, using a triangle element mesh with standard Rao–Wilton–Glisson basis functions to represent the surface current density. The multiple-reflection PO (MRPO) method involves applying the PO approximation to the field radiated by the present current solution towards the scatterer itself, to account for successive internal reflections. The visibility status between every pair of basis functions is required, taking into account all geometry. In a conventional implementation, internal reflected field calculation and internal shadowing determination runtimes both scale as O(N2); N denotes the number of mesh elements. In this paper an accelerated version of the mesh-based MRPO method is presented: fast MRPO (FMRPO). The multi-level, fast multipole method (MLFMM) is used to accelerate internal reflected field calculation. The key aspect to achieving acceleration for general geometries, is to incorporate internal shadowing into the MLFMM interaction tree. This requires an alteration to the inter-group interaction criterion of the MLFMM, as well as efficient evaluation of inter-group shadowing status flags, to preserve the beneficial cost-scaling property of the MLFMM. Algorithmic parameters are introduced, which control the accuracy of internal shadowing determination. The FMRPO runtime scales as O(NlogN), in the high-frequency limit. Numerical results are presented, demonstrating accuracy and efficiency for general scattering objects.