Analysis of Radiation from X-band Slotted-waveguide Antenna Arrays Using the Parallel DDA-FE-BI-MLFMA

The hybrid flnite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) approach is adopted for fast and accurate computation of radiation from large slotted-waveguide antenna arrays. A simplifled model is presented by using a thin current probe as the excitation and a layer of perfectly matched layer (PML) as the termination for slotted- waveguide antenna. Since each slotted-waveguide antenna can be generally considered as a single sub-domain, the domain decomposition algorithm (DDA) is applied in the FE-BI-MLFMA to re- duce computation resource and achieve high e-ciency. This DDA-FE-BI-MLMFA is parallelized to further strength its capability. To validate the presented approach for computing radiation from slotted-waveguide antenna arrays, a series of numerical experiments are performed. Good agreement between our calculated results and results from commercial software CST validates accuracy of the presented approach. To show capability of the proposed DDA-FE-BI-MLFMA, a large X-band slotted-waveguide antenna array containing eighteen waveguides is designed and its radiation characteristics are studied. 1. INTRODUCTION The slotted-waveguide antenna arrays are widely used in real-life communication and radar system applications, because of their small size, light weight, compact structure, high e-ciency, and low side lobe characteristics. The computation of radiation from slotted-waveguide antenna arrays is of growing interest due to its importance in practical applications. Various methods have been devel- oped to compute the radiation from slotted-waveguide antennas, such as the variational approach in terms of equivalent network, the method of moments (MoM), the flnite-difierence time-domain (FDTD) method, the flnite element method (FEM) and the hybrid flnite element-boundary integral (FE-BI) method (1{10). However, due to large number of slots and the mutual coupling between the slots through the waveguides and the exterior space, previous researches mainly focus on analysis of radiation by a single slot in a waveguide, 1-D slotted-waveguide arrays or small 2-D slotted-waveguide arrays in a planar surface. In real application, fast and accurate analysis of radiation from large slotted- waveguide antenna arrays containing tens of slotted-waveguides and comprising thousands slot elements cut in the wall of the waveguides still faces great challenges. In this paper, an e-cient approach is presented for fast and accurate analysis of radiation from large slotted-waveguide antenna arrays by using the FE-BI-MLFMA (11{13). To simplify the cal- culation, for each single slotted-waveguide, a short and inflnitesimally thin current probe is used as the front-end excitation. A perfectly matched layer (PML) is used to terminate end of the waveg- uide port and absorb the re∞ected wave from the antenna to make each slotted-waveguide antenna work in the travelling wave mode. Since each slotted-waveguide antenna can be considered as a single sub-domain, the domain decomposition algorithm (DDA) is applied to reduce computation resource and achieve high e-ciency. To improve the convergence, the sparse approximate inverse (SAI) technique is applied to construct an e-cient preconditioner (14,15). To further improve the capability, it is parallelized on a memory distributed computer system (13,14). The comparison between DDA-FE-BI-MLFMA computed results and the commercial software CST results for the radiation patterns of a slotted-waveguide array validates the accuracy of the presented approach. To show capability of the presented approach, a large X-band slotted-waveguide antenna array containing eighteen waveguides with Taylor amplitude and inverse phase excitation distribution is designed and its radiation characteristics are computed and analyzed.