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A non-overlapping domain decomposition method with non-matching grids for modeling large finite antenna arrays. (English) Zbl 1059.78042
Summary: A non-overlapping domain decomposition method (DDM) is proposed herein to solve Maxwell equations in $$\mathbb R^3$$. 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 first-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 $$100\times 100$$ elements are solved on a common PC to validate the proposed non-overlapping DDM.

##### MSC:
 78M25 Numerical methods in optics (MSC2010) 78A55 Technical applications of optics and electromagnetic theory
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##### References:
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