## 1. Introduction

[2] Different electromagnetic scattering problems have been studied in recent years. They include, but are not limited to, radar cross section (RCS) computations, antenna analysis, remote sensing, biomedicine, electromagnetic interference (EMI), and electromagnetic compatibility (EMC). In this paper, the scattering and transmission properties of finite planar frequency selective surfaces (FSS) are analyzed, along with the scattering of the complex object in free space. Simulating these problems is very time demanding, and good numerical methods are required to compute their solutions quickly and efficiently. The method of moments (MoM) [*Mahachoklertwattana et al.*, 2008; *Ye and Jin*, 2008; *Rao et al.*, 1982; *Kim et al.*, 2004; *Michalski and Zheng*, 1990a, 1990b; *Michalski and Hsu*, 1994] is one of the most widely used techniques for solving electromagnetic problems. For a large electromagnetic problem, the number of unknowns, *N*, will be large and it would be difficult to solve the matrix equation. This is because the memory requirement and computational complexity are proportional to *O*(*N*^{2}) and *O*(*N*^{3}), respectively. This difficulty can be circumvented by using the Krylov iterative method, which can reduce the operation count to *O*(*N*^{2}).

[3] A number of fast methods have been developed to accelerate solving iterative solutions of the MoM-based electromagnetic integral equations. Most of them are based on the multilevel subdomain decomposition technique and require a computational order of*N*log*N*. One of the most popular techniques is MLFMA [*Coifman et al.*, 1993; *Chew et al.*, 2001; *Pan et al.*, 2001; *Malas and Gurel*, 2009], which has been widely used to solve very large electromagnetic problems due to its excellent computational efficiency. For the MLFMA, however, a priori knowledge of the Green's function is needed. As a result, it cannot be easily applied to analyze the layered media problems.

[4] The MDA is another popular technique for analyzing scattering/radiation problems. It makes use of the well known fact that the approximate rank of the sub-matrices is low when the sub-scatterers are sufficiently separated. In this case, the sub-matrices can be compressed [*Michielssen and Boag*, 1996; *Heldring et al.*, 2007; *Rius et al.*, 1999; *Parron et al.*, 2006, 2002, 2000, 2003; *Rius et al.*, 2006; *Bebendorf*, 2000; *Zhao et al.*, 2005; *Ozdemir and Lee*, 2004; *Hu et al.*, 2012]. The computational complexity and memory requirement of the MLMDA is *N*log^{2}*N* given by *Michielssen and Boag* [1996]. Compared to the MLFMA, the MDA is purely algebraic and therefore does not depend on the priori knowledge of the Green's function. In general, the MDA requires considerable computation time and memory. To improve the efficiency, the MDA-SVD was studied by*Rius et al.* [2008] which efficiently recompresses the matrices of MDA using the SVD technique.

[5] The aim of this paper is to present a modified MDA for solving electromagnetic problems. It utilizes SVD techniques [*Golub and Van Loan*, 1989] to recompress the matrices of MDA. Simulation results show that the modified MDA is computationally more efficient than the MLMDA and traditional MDA-SVD.

[6] This paper is organized as follows. Section 2 describes the modified MDA in detail. Section 3 provides numerical examples to show the accuracy and efficiency of the modified MDA. Section 4 provides the conclusions of the study.