A Non-overlapping and Non-conformal Domain Decomposition Method with Second Order Transmission Condition for Modelling Large Finite Antenna Arrays Zhen Peng 1 , Jin-Fa Lee 2 ElectroScience Lab, The Ohio State University 1320 Kinnear Road, OH 43212, USA 1 peng.98@osu.edu 2 lee.1863@osu.edu Abstract—A non-overlapping and non-conformal domain decomposition method (DDM) is presented for modelling large finite antenna arrays. There are two major ingredients in the proposed DDM: (a) A new second-order transmission condition is introduced, which improves convergence of the iterative process. In contrast to previous high order interface conditions, the new condition uses two second-order transverse derivatives to address the slow convergence issue of both TE and TM evanescent modes. Numerical experiments demonstrate that the convergence of the proposed algorithm is quite insensitive to the size of array. (b) The proposed non-conformal DDM not only permits the use of completely independent discretization for each of the sub-domains, but also allows adjacent sub-domains to be geometrically non-conformal. The benefits of the non-conformal nature of the proposed DDM will be fully enjoyed by a large- scale problem of practical interest, which is a 50 by 50 ultra wide band (UWB) array in the presence of a slot frequency selective surface (FSS). Numerical results verify the effectiveness of the proposed method. I. INTRODUCTION Large finite antenna arrays are commonly used in modern wireless communication systems and radars to transmit and receive signals through spaces. The accurate and efficient modelling of large finite antenna arrays is of great importance in antenna design and electromagnetic compatibility analysis. However, the full wave electromagnetic analysis of large finite antenna arrays is also posing a great hurdle. These challenges include large problem size because of the large number of antenna elements, complex geometrical features and material properties. Worse, these arrays usually work in presence of frequency selective surfaces and polarizers, which make the numerical simulation more challenge. We can fully appreciate the associated technical difficulties by considering a 50 by 50 ultra wide band (UWB) array in the presence of a slot frequency selective surface (FSS) (Fig. 1). We first notice that this problem includes numerous fine geometrical features and multilayer dielectric structure. Finite element method (FEM) may be the natural choice because it provides accurate results while accounting for complex geometrical features and spatially varying material properties. Secondly, we see that the electrical size of this problem is very large. By using FEM, the total computational domain is discretized into 250 millions DOFs at 15 GHz. The greatest challenge in this application then becomes the solution of the resulting large, sparse, complex, non-Hermitian, and indefinite matrix equation. A robust and accurate iterative solution approach poses an immense challenge. Fig. 1. Ultra wide band antenna array with frequency selective surface Here, we introduce a new non-overlapping and non- conformal DDM for the FEM solution of the large complicate antenna arrays. It differs from previous non-overlapping and non-conformal DDMs in two significant respects. First, we introduce a new second-order transmission condition (SOTC), which involves two second-order transverse derivatives, to facilitate fast convergence in the non-conformal DDM algorithm. The second difference is that the presented non- conformal DDM not only permits the use of completely independent discretization for each of the sub-domains (non- matching grids), but also allows adjacent sub-domains to be geometrically non-conformal. This gives us great flexibility to partition the original global domain into sub-domains. 2010 URSI International Symposium on Electromagnetic Theory 978-1-4244-5153-1/10/$26.00 ©2010 IEEE 160