Advancing High-Dimensional Simulations

As an extension to the EXAHD project, we are improving upon the approximation, conservation, and stability properties of the sparse grid combination technique by using biorthogonal (wavelet) basis functions in place of the commonly used hierarchical hat functions:

The numerical instabilities that were previously observed for initial-value Vlasov-Poisson simulations are resolved by the biorthogonal approach, and the approximation quality is improved.

This is illustrated by the results obtained with the SeLaLib code:

Another aspect of the project is adding another level of parallelism by distributing the simulation to multiple HPC systems.

By a clever assignment of the subtasks to the HPC systems, we can achieve very low data volumes, which are exchanged through a file-based communication scheme.

We successfully connected pairs of the German national Tier-0/Tier-1 supercumputers to perform six-dimensional grid-based simulations jointly.

These features are implemented and published through the DisCoTec code under an open-source license (LGPL).