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High-dimensional problems pose a challenge for tomorrow’s supercomputing. Problems that require the joint discretization of more dimensions than space and time are among the most compute-hungry ones and thus standard candidates for exascale computing and even beyond. This project tackles such problems by a hierarchical extrapolation approach, the sparse grid combination technique. The method not only enables their treatment in the first place. The hierarchical approach also provides novel ways to deal with central problems in high-performance computing such as scalability and resilience: Global communication can be avoided and reduced to a small subset, and faults can be compensated for without the need for recomputations or checkpoint-restart. As an exemplary prototype for high-dimensional problems, turbulence simulations in plasma physics are studied

EXAHD: An Exa-scalable Two-Level Sparse Grid Approach for Higher-Dimensional Problems in Plasma Physics and Beyond