A non-overlapping domain decomposition method with non-matching grids for modeling large finite antenna arrays

A non-overlapping domain decomposition method (DDM) is proposed herein to solve Maxwell equations in R3. In this work, the Maxwell equations are discretized using a vector finite element method with hierarchical H(curl) vector basis functions. There are two major ingredients in the proposed non-overlapping DDM: (a) A proper 1st order transmission condition to enforce field continuity across domain boundaries and (b) A cement technique to allow non-matching grids for neighboring domains. Moreover, a detail Fourier analysis of the transmission condition for a canonical half-space example is presented. The analysis provides significant insights into the convergence behavior of the proposed non-overlapping DDM for solving electromagnetic radiation problems, such as the large finite antenna arrays. Particularly for the antenna arrays, the proposed non-overlapping DDM is extremely efficient since the formulation can easily incorporate geometrical repetitions. Exponentially tapered notch (Vivaldi) antenna arrays with size up to 100 × 100 elements are solved on a common PC to validate the proposed non-overlapping DDM.