Hybridization of the Vector Finite Element Method with the Boundary Integral Method for the Solution of Finite Arrays of Cavity-Backed Slot Antennas

The vector finite element method (FEM) is hybridized with the boundary integral (BI) method to solve for the radiation characteristics of a cavity-backed slot (CBS) antenna. The hybridization of the two methods is made possible at the aperture of the antenna separating the cavity interior and the half-space exterior region above an infinite conducting ground plane. Having to solve for a finite array of CBS antennas requires an excessive amount of memory, in order to store the system matrix, and considerable CPU time for the solution of the resulting linear system of equations. Increasing the number of array elements results in a non-linear increase in the number of unknowns, thus making the solution of the linear system impossible. In this paper, we adopt array domain decomposition (ADD) and by taking advantage of the repetitive features of the array, we can reduce the memory requirements to a minimum. In addition, we introduce stationary and non-stationary iteration techniques, with or without preconditioning, to solve the system of linear equations in an efficient manner. Singular value decomposition (SVD) is also used in order to further reduce memory requirements and speed-up matrix-vector multiplications that are inherent in either type of iterative techniques. Computational statistics and comparisons between stationary and non-stationary techniques are presented and discussed.