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International audience; Transmit-arrays (TAs) are a popular cost-effective solution for high-gain antennas at millimeter waves (mmW). The design of these antennas relies on the fine tuning of the sub-wavelength unit-cells that compose the aperture. The intricacy of the unit-cells increases as new features are implemented, such as dual-band operation and wide-angle beam steering, making this antenna even more computationally challenging. In this work, a high gain (25 dBi @ 20 GHz and 28 dBi @ 30 GHz) multi-scale Ka dual-band TA for beam-steering applications is analyzed using a massively parallel implementation on multicores clusters of the Finite Element Tearing and Interconnecting method, with a two Lagrange Multiplier (FETI-2LM) technique. The main contribution of this work is the implementation of 3D non-periodic grids with sub-domains of different scales, that is suitable for proper modelling of different regions of the antenna (horn feed, lens cells, air region). An automatic batch file procedure is proposed for the TA meshing, allowing the limited set of constitutive unit-cells of the TA to be meshed separately. Additionally, we are using a block-Krylov strategy to efficiently capture the TA beam-steering capability, without restarting from scratch the interface problem for each feed position. Since other Finite Element Method (FEM) results were not accessible due the size of the problem, the FETI-2LM numerical results provided in this work are compared with other MultiLevel Fast Multipole Method (MLFMM) [1] and Transmission Line Modeling Method (TLM) [2] of CST Microwave Studio solvers, as well as with the measured results of the corresponding Ka dual-band prototype. The computational infrastructure has been used only a fraction of its capacity. Therefore, a much higher gain design (40 dBi) can be assessed, opening a new realm of applicability of TAs in the space segment usually occupied by reflector-based solutions.