Efficient and scalable distributed-memory hierarchization algorithms for the sparse grid combination technique

Finding solutions to higher dimensional problems, such as the simulation of plasma turbulence in a fusion device as described by the five-dimensional gyrokinetic equations, is a grand challenge facing current and future high performance computing (HPC). The sparse grid combination technique is a promising approach to the solution of these problems on large scale distributed memory systems. The combination technique numerically decomposes a single large problem into multiple moderately sized partial problems that can be computed in parallel, independently and asynchronously of each other. The ability to efficiently combine the individual partial solutions to a common sparse grid solution is a key consideration to the overall performance of large scale computations with the combination technique. This requires a transfer of each partial solution from the nodal basis representation into the hierarchical basis representation by hierarchization. In this work we will present a new, efficient and scalable algorithm for the hierarchization of partial solutions that are distributed over multiple process groups of an HPC system.