We apply a recently developed multi-solver domain decomposition method (MS-DDM) to compute the antenna pattern of a S-band monopole antenna taking into account the couplings from the surrounding 23 other antennas, both in-band and out-of-band couplings, and the effects of the large air platform on which the S-band antenna is mounted. Since the air platform is electrically large and multi-scale in nature, the usual integral equation methods tax heavily on the computer resources and maybe even fail to converge when iterative Krylov matrix solution technique is employed. To provide a converging integral equation approach for modeling the air platform, we further apply the integral equation domain decomposition method (IE-DDM) as an effective preconditioner for the resulting combined field integral equation (CFIE) method. The fundamental strategy of the proposed MS-DDM is to decompose the entire computational domain into many sub-regions based on the local material properties and geometrical features. Moreover, the coupling between well-separated sub-regions is implemented through Stratton-Chu representation formulas. However, for the touching interfaces between neighboring sub-regions, a Robin transmission condition is introduced to mitigate the troublesome self integral terms with weak singular kernels. Numerical results of the S-band monopole antenna mounted conformally on a mockup F-16 fighter jet, together with 23 other antennas, are shown to demonstrate the flexibility and potentials of the proposed hierarchical MS-DDM and IE-DDM approach. Antenna patterns of the S-band monopole antenna in free space as well as the results including all the couplings form the other antennas and the air platform are also presented.