## 1. Introduction

[2] Recently, the EM scattering analysis of two-dimensional (2-D) objects has been playing an increasingly important role in electromagnetic field theory and practicable applications, especially in the radar cross-section (RCS) analysis [*Arvas and Sarkar*, 1989; *Massoudi et al.*, 1988; *Andreasen*, 1964] and the wave propagation prediction in urban microcells of mobile communication networks [*Xia et al.*, 1994; *Kotterman et al.*, 1994; *Schuster and Luebbers*, 1997]. With the increase of frequency used in these applications a fast and rigorous method for solving the EM scattering by electrically large or even extremely large objects is needed.

[3] Many numerical methods have been proposed for solving such problems. As one of the most popular techniques, the method of moments (MOM) is widely used for the solution of integral equations defined on the surface of object [*Arvas and Sarkar*, 1989; *Massoudi et al.*, 1988]. The finite difference (FD) method is another important method used for solving complex scattering problems of irregular, nonuniform objects [*Mur*, 1981]. Compared with MOM, the FD method results in a sparse coefficient matrix (with dimensions of *N*_{f}= *L* × *N*_{c}, where *L* is the number of grids in the normal direction and *N*_{c} is the number of grids along the cylinder circumference), whose consumption of computer memory and CPU time are *O*(*N*) and *O*(*N*_{f}^{2}), respectively. However, the absorbing boundary condition (ABC) has to be applied to truncate the unbounded spatial domain. For most ABCs the distance between the cylinder surface and the truncated boundary must be large enough to reduce the spurious reflection on the truncated boundary. This demands a large *L*, which will lead to a huge coefficient matrix. Then, for large problems, this method will also exhaust computer resources.

[4] To promote the computational efficiency of the FD method, many works were focused on the improvement of ABCs, such as the development of the measured equation of invariance (MEI) and perfectly matched layer (PML) techniques. As a mesh termination boundary condition in the FD method, the MEI greatly reduced the dimensions of the FD matrix because the truncated boundary can be placed very close to the surface of the cylinder [*Mei et al.*, 1994; *Hong et al.*, 1994]. The fast-MEI further enhanced the computational efficiency of MEI [*Zai and Hong*, 1998]. By renumbering the nodes of the conformal meshes around the cylinder, a band matrix with very narrow bandwidth is then deduced in fast-MEI, whose computing cost and memory needs are both proportional to *N*_{f}. To convert the original sparse matrix into a narrow band matrix, however, it has to sacrifice nearly double the memory and is also not very efficient for some complex problems, such as the scattering analysis of concave cylinders. The PML method will encounter the same problem that the MEI method did.

[5] The domain decomposition method (DDM) is a promising method for solving large problems [*Despr'es*, 1992; *Strupfel*, 1996]. Unlike traditional methods, the DDM does not deal with the whole problem directly, but decomposes it into some independent small problems. For different subdomains, the most efficient method can be chosen independently for solving the EM equations on the subdomain. The DDM then greatly decreases the scale of the original problem. Moreover, it is well suited for numerical implementation on parallel computers and can considerably reduce both memory requirements and CPU time.

[6] In this paper, we present a novel fast algorithm based on the combination of the FD method and the DDM for electromagnetic scattering analysis of electrically large or extralarge conducting cylinders. The original FD method is introduced in section 2, and the implementation of the DDM under the FD equations is discussed in section 3. By decomposing the original domain into *m* subdomains along the cylinder circumference the new method obtains a series of band coefficient matrices with bandwidth (2*N* + 1)(*N*is the number of mesh layers). This can both save memory and accelerate the solving process compared with fast-MEI. It can also be easily expanded to analyze some complex structures, for example, a cylinder with slots, by taking the slots as separated subdomains and treating them independently. Therefore the computing time and memory requirements of the new method are only proportional to *N*_{D}and *N*_{D}/*M*, respectively, and *N*_{D} is the dimension of the coefficient matrix. These advantages make it possible to apply the new method to extremely large cylinders with complex cross sections. Some typical examples, including a circular cylinder, a rectangular cylinder, and a slotted cylinder with perimeter from 10λ_{0} to 100,000λ_{0} are computed and illustrated in section 4. All numerical results demonstrated the estimate of computational effort and memory requirements and agree very well with the data obtained by using MOM and MEI method.