EXAHD - An Exa-Scalable Two-Level Sparse Grid Approach for Higher-Dimensional Problems in Plasma Physics and Beyond
Mathematics
Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
Final Report Abstract
Plasma fusion is one of the promising candidates for an emission-free energy source and is heavily investigated with high-resolution numerical simulations. Unfortunately, these simulations suffer from the curse of dimensionality due to the five-plus-one-dimensional nature of the equations. Hence, we propose a sparse grid approach based on the sparse grid combination technique which splits the simulation grid into multiple smaller grids of varying resolution. This enables us to increase the maximum resolution as well as the parallel efficiency of the current solvers. At the same time we introduce fault tolerance within the algorithmic design and increase the resilience of the application code. We base our implementation on a manager-worker approach which computes multiple solver runs in parallel by distributing tasks to different process groups. Our results demonstrate good convergence for linear fusion runs and show high parallel efficiency up to 180k cores. In addition, our framework achieves accurate results with low overhead in faulty environments. Moreover, for nonlinear fusion runs, we show the effectiveness of the combination technique and discuss existing shortcomings that are still under investigation.
