Modern high-tech steels offer many possibilities for improvements in engineering applications, while virtual labs can help to taylor the materials to be best suited for an underlying application. A realistic modeling of the inherent phenomena acting on the microstructural level are inevitable for reliable computations. In the case of dual-phase steel, the interaction of the two phases in the microstructure together with the polycrystalline structure of each phase contribute to the complex macroscopic material response. Homogenization approaches are necessary to account for the effects on both scales, such as the FE2- method. Due to the enormous size of the simulations, the computational power of modern supercomputers is necessary. State-of-the-art computer architectures provide up to ten million parallel processing units and to exploit them efficiently, it is mandatory that the mayor part of the underlying computations of a numerical method can be performed in parallel. This is possible in the FE2-method as well as in domain decomposition methods as FETI-DP (Finite Element Tearing and Interconnecting – Dual-Primal). The combination of both methods, named FE2TI, managed to run efficiently on some of the largest supercomputers.