In this article, the multilevel UV algorithm is utilized to reduce both the memory requirement and CPU time in the time‐domain combined field integral equation (TD‐CFIE) method to analyze transient electromagnetic scattering from conducting structures.The UV method is kernel‐independent, and is based on the rank‐deficiency feature of the impedance submatrix which represents far interaction. To obtain an unconditionally stable solution, finite orders of weighted Laguerre polynomials are used as temporal basis functions and the unknown expansion coefficients of the time variable are solved recursively order by order, as the so‐called matching‐on‐in‐order (MOO) procedure. RWG basis function is used as the spatial basis function for its flexibility in modeling arbitrary geometries. The spatial and temporal testing procedures are separate, and both of them are carried on with the Galerkin's method. Numerical results are given to verify the proposed method. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:158–163, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25646

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A fast algorithm is proposed to calculate the difference field RCS (d-RCS) of the electromagnetic scattering from an object above rough surface. The electric field integral equation (EFIE) of the difference induced field on the rough surface and the induced field on the target are derived, and is solved by an iterative solver. The characteristic basis functions (CBFs) are used to calculate the induced field on the rough surface, which is part of the right-hand side of the system. Since the coupling matrices between the object and rough surface and the non-self interaction matrices of the rough surface are rank deficient, it is accelerated by the adaptive cross approximation (ACA) algorithm. Through numerical experiments, it is concluded that the proposed method is efficient in analyzing the electromagnetic scattering from an object above rough surface.

In this paper, the time domain integral equation is solved by marching-on-in-degree method with near-orthogonal higher order hierarchical Legendre basis as spatial basis functions and causal weighted Laguerre polynomials as temporal basis functions. In the traditional marching-on-in-degree solver of time domain integral equation, RWG basis functions are used as spatial basis functions. The memory requirement and time consuming is very large, which becomes a bottleneck of marching-on-in-degree method. In order to solve this problem, the object is meshed with second-order nine-node curved quadrilateral elements and near-orthogonal higher order hierarchical Legendre basis functions are adopted as spatial basis functions. Numerical results show that this method can greatly reduce the unknowns of the problem, by which it can save memory and CPU time.