Distributing Higher-Dimensional Simulations Across Compute Systems: A Widely Distributed Combination Technique

The numerical solution of high-dimensional PDE problems is essential for many research questions, such as understanding relativistic astrophysics, quantum physics, or hot fusion plasmas. At the same time, it is haunted by the curse of dimensionality, rendering finely resolved simulations infeasible even on modern architectures. The Sparse Grid Combination Technique helps to break the curse of dimensionality for high-dimensional PDE problems to some extent. But even then, simulations are restricted by the size of HPC systems. A new implementation based on the open-source code DisCoTec allows to distribute existing solvers even across compute systems: The widely distributed combination technique enables simulations at scales that would otherwise be intractable.This paper introduces the extended algorithm and showcases a proof of concept for the remote communication set-up. The scaling properties for the single-system and two-system cases are presented, and the numerical correctness of the implementation is validated.The widely distributed combination technique is useful in cases where the memory and/or compute resources are not sufficient for a particular problem to fit on one single available system, but multiple systems are able to accommodate it.