Analysis Of Time Domain Integral Equations For Electromagnetic Scattering Properties Of Rotating Symmetry

Body of revolution (BOR) has been a hot topic in the area of computational electromagnetic for a long time. Due to its special geometry, the equivalent surface electric/magnetic current densities and field of BOR can be expressed in a Fourier series. In the implementation of the method of moments (MOM) for BOR, one need just discrete the structure along a longitudinal by taking advantage of the rotational property of the object. Thus, the computational cost could be reduced largely.A marching-on-in-degree (MOD) procedure based time domain integral equation method has been proposed for solving bodies of revolution problems in this article. At first, the definition of the coordinate system of BOR is introduced. Triangular functions along the generatrix of BOR and weighted Laguerre polynomials are used as spatial and temporal basis functions respectively to expand the unknown equivalent surface electric/magnetic current densities. Radar cross section calculation method is also shown in the first part. A MOD procedure based time domain integral equation method has been proposed to analyze the scattering property of the bodies of revolution, including perfectly electric conducting objects, dielectric objects and coated objects. Time domain electric field integral equation (TD-EFIE) is used to analyze open structure conducting BOR. objects, time domain combined field integral equation (TD-CFIE) is used to analyze closed structure conducting BOR objects. Time domain Poggio-Miller-Chang-Harrington-Wu (PMCHW) equation and time domain electric and magnetic current combined field integral equation (JMCFIE) is implemented to analyze homogeneous BOR’s problems. Coated BOR conductor is then simulated with TD-CFIE in conductor-region and time domain PMCHW equation or time domain JMCFIE in dielectric region. In addition, since the impedance matrices of each Fourier mode are dense matrices in the MOD solver of time domain integral equation (TDIE), the MOD solver of TDIE calls for very high computational cost and memory requirement for large-scale scattering problems. The adaptive cross approximate (ACA) algorithm is utilized to speed up the transient electromagnetic scattering analysis of BOR. Moreover, the hybrid MPI and OpenMP parallel programming technique is adopted to further accelerate the solving process on a shared-memory computer system.