Array decomposition method for the accurate analysis of finite arrays

Presented in this paper is a fast method to accurately model finite arrays of arbitrary three-dimensional elements. The proposed technique, referred to as the array decomposition method (ADM), exploits the repeating features of finite arrays and the free-space Green´s function to assemble a nonsymmetric block-Toeplitz matrix system. The Toeplitz property is used to significantly reduce storage requirements and allows the fast Fourier transform (FFT) to be applied in accelerating the matrix-vector product operations of the iterative solution process. Each element of the array is modeled using the finite element-boundary integral (FE-BI) technique for rigorous analysis. Consequently, we demonstrate that the complete LU decomposition of the matrix system from a single array element can be used as a highly effective block-diagonal preconditioner on the larger array matrix system. This rigorous method is compared to the standard FE-BI technique for several tapered-slot antenna (TSA) arrays and is demonstrated to generate the same accuracy with a fraction of the storage and solution time.