Parallel multigrid on hierarchical hybrid grids: a performance study on current high performance computing clusters

摘要

This article studies the performance and scalability of a geometric multigrid solver implemented within thernhierarchical hybrid grids (HHG) software package on current high performance computing clusters up tornnearly 300, 000 cores. HHG is based on unstructured tetrahedral finite elements that are regularly refinedrnto obtain a block-structured computational grid. One challenge is the parallel mesh generation from anrnunstructured input grid that roughly approximates a human head within a 3D magnetic resonance imagingrndata set. This grid is then regularly refined to create the HHG grid hierarchy. As test platforms, a BlueGene/Prncluster located at Jülich supercomputing center and an Intel Xeon 5650 cluster located at the local computingrncenter in Erlangen are chosen. To estimate the quality of our implementation and to predict runtime for thernmultigrid solver, a detailed performance and communication model is developed and used to evaluate thernmeasured single node performance, as well as weak and strong scaling experiments on both clusters. Thus,rnfor a given problem size, one can predict the number of compute nodes that minimize the overall runtime ofrnthe multigrid solver. Overall, HHG scales up to the full machines, where the biggest linear system solved onrnJugene had more than one trillion unknowns.