Method of moments analysis for antenna arrays with optimum memory and time consumption

Abstract

For some applications, single element antennas are unable to meet the gain or radiation pattern requirements. Combining several antenna elements in an array is a possible solution. In order to get accurate analysis of the antenna arrays, full wave analysis techniques such as the method of moments (MoM), the flnite difierence time domain (FDTD), etc are required. Unfortunately, these methods are heavy computational methods that consume long time and large computational resources. Even with the appearance of the high performance parallel processing resources, the computational time and memory usage still large due to the nature of the problem. So, in this paper, the MoM is chosen to analyze large problems such as antenna arrays taking into consideration the reduction of its needed computational resources and time consuming. The MoM is a well-established and an accurate full wave analysis method. The MoM is applied to solve the electric fleld integral equation (EFIE) on conducting objects with the use of RWG basis function that is used with triangular segmentation of the scatterer surface. The proposed procedure is to decompose the computational domain into subdomains taking interaction between domains iteratevly until steady state is noticed. The proposed procedure minimizes the time and memory consumption greatly. 1. INTRODUCTION The MoM for discretizing integral equations in electromagnetics is an extremely powerful and ver- satile general numerical methodology for electromagnetic fleld simulation in antenna and scattering applications (1). However, traditional MoM analysis is inherently limited to electrically small and moderately large electromagnetic structures, because its computation costs (in terms of memory and CPU time) increase rapidly with an increase in electrical size of the problem. Since that time computer technology has grown at a staggering pace, and computational electromagnetics and the moment method have followed closely behind (2). The domain decomposition method (DDM) (3{ 11) is one of the most successful approaches to the Method of Moments (MoM) analysis of large scattering and antenna problems. The idea behind the DDM is to decompose the whole computa- tional domain into small sub-domains with some prescribed partition boundary conditions. Such a procedure divides large electromagnetic problems to small sub-domain problems, transform com- plex boundary conditions to simple ones, and presents an efiective means to break through the bottleneck of memory storage. At the same time, a highly parallelizable computation structure is achieved. The key point of the DDM is the enforcement of boundary conditions on subdomain in- terfaces. There are usually two DDM approaches: one is the approach of (4{8) based on the Schwarz alternating method, which ensures coupling between the adjacent elements by the transmission con- dition (TC) (9) and proceeds with iterative solution until convergence is achieved by changing data interfaces between subdomains. Another one is the direct method using Steklov technique (12{14), which imposes the continuity of the flelds on the partition interfaces and generates a global cou- pling matrix. The solution of this matrix produces the unknown tangential flelds on the partition interfaces. In this paper, the problem of antenna array is treated since the array elements is already separated and does not need boundary conditions between domains. The separation between array elements are exploited by dividing the array into separate elements each analayzed separately. The mutual coupling between elements are taken into consideration by taking the scattered fleld from the adjacent elements as incident wave on the current analyzed element. By repeating the analysis several times until steady state is observed, the coupling between elements is considered to be taken into consideration accurately. So, the problem of time and memory consumption will be solved for large extent.