EXAHD

Higher-dimensional problems (i.e., beyond four dimensions) appear in medicine, finance, and plasma physics, posing a challenge for tomorrow's HPC. As an example application, the EXAHD project considered turbulence simulations for plasma fusion with one of the leading codes, GENE, which promises to advance science on the way to carbon-free energy production.

While higher-dimensional applications involve a huge number of degrees of freedom such that exascale computing gets necessary, mere domain decomposition approaches for their parallelization are infeasible since the communication explodes with increasing dimensionality. Thus, to ensure high scalability beyond domain decomposition, a second major level of parallelism has to be provided. To this end, we employed the sparse grid combination scheme, a model reduction approach for higher-dimensional problems. It computes the desired solution via a combination of smaller, anisotropic and independent simulations, and thus provides this extra level of parallelization. This added level of parallelization breaks the communication bottleneck in exascale computing, achieving scalability to full HPC systems.
Our two-level methodology enables novel approaches to scalability (ultra-scalable due to numerically decoupled subtasks), resilience (fault and outlier detection and even compensation without the need of recomputing), and load balancing (high-level compensation for insufficiencies on the application level).

EXAHD was funded through the DFG Priority Programme 1648 "Software for Exascale Computing" (SPPEXA) and the research associates in our group were Mario Heene and Theresa Pollinger.

More information about the EXAHD Consortium is available on the project's extensive website.

Higher-dimensional grid-based simulations were further pursued in the project "Advancing High-Dimensional Simulations".