An Automatic Mesh Refinement Method Based on Phase Extracted Basis Functions for Electromagnetic Scattering Analysis of Electrically Extra-Large Objects

Electromagnetic (EM) scattering problems are commonly solved by numerical methods such as the finite element method (FEM) and the method of moments (MoM). In a numerical simulation, the solution domain needs to be discretized into small mesh elements. The quality of the mesh is critical for the solution accuracy. While a denser mesh with smaller elements can result in a better numerical accuracy, it also leads to higher computational and storage costs, making it expensive to solve scattering problems from electrically large objects. To reduce such costs, higher order basis functions (HOBFs) [1] have been developed and applied in EM analysis. By expanding the amplitude of the induced surface currents with the HOBFs, larger mesh elements can be used, which reduce effectively the total number of unknowns required in solving an EM problem. For objects with smooth and convex surfaces, it has been shown in [2] that describing the phase variation of the induced surface currents can reduce the total number of unknowns even more effectively. By incorporating a traveling wave phase factor into the traditionally used low-order curvilinear Rao-Wilton-Glisson (RWG) basis functions, the resulting phase extracted basis functions (PEBFs) can be defined on mesh elements as large as half a wavelength. The combination of the PEBFs and HOBFs can reduce the number of unknowns by two orders of magnitude, which improved the simulation efficiency significantly while maintaining a good numerical accuracy [3].