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We present simulations of the nucleation and equiaxed dendritic growth of the primary HCP α-Mg phase followed by the nucleation of the β-phase in interdendritic regions. A zoomed-in region of a melt channel under eutectic conditions is investigated and compared to experiments. The presented simulations allow to predict final properties of an alloy based on process parameters. The obtained results give insight into the solidification processes governing the microstructure formation of Mg-Al alloys allowing their targeted design for different applications.

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The multiphase field method is a commonly used tool to simulate the evolution of microstructure during materials processing. Even when using a concept called active parameter tracking, which substantially reduces the computational complexity, the resource demands of the multiphase field method remain significant in both time and memory. A hybrid-parallelization is presented, that combines MPI and OpenMP and allows considerably larger system sizes. Due to the utilization of active parameter tracking the computational load can be heterogeneously distributed in the system, which makes load-balancing necessary in order to obtain an efficient parallelization. In this thesis two different load-balancing schemes are presented. The first uses graphpartitioning and an adaptive sub-domain decomposition. The second is based on the multiphase field method itself. Results are presented for performance benchmarks as well as for a variety of applications, including grain growth in polycrystalline materials with hundreds of thousands of different phase fields and Mg-Al alloy solidification as well as a coupling with the Lattice-Boltzmann method. One of the load-balancing schemes is also applied to a cell-based particle method. In addition a way of utilizing the multiphase field method is shown that allows the construction of microstructures and the corresponding Laguerre generator points with a given grain size distribution. 4Declaration/Erklärung I, Marvin Tegeler, born on July, 31st, 1985 in Gelsenkirchen, hereby declare that this dissertation is my own work.