Hierarchical Hybrid Grids

Abstract

HHG is a Multigrid solver for Finite Elements on unstructured grids. The solver takes a coarse input grid and refines it in a structured way. The resulting regular grid structure can be exploited using extremely memory-efficient data structures. This puts simulations of impressive scale into the realms of possibility. On HLRB II at the Leibniz Computing Centre Munich, a linear system of equations with 300 billion unknowns has been solved, using 9170 cores. The parallel scalability of HHG is close to linear on up to 1000 processors and still very good over the whole range of our measurements. Nevertheless, we have to look forward and prepare for the even larger computers coming up on the road towards Petaflop performance. DECI will be an important aid in pursuing our research, because it provides access to Europe's largest computers. It also offers a variety of different architectures, which is another important point for us, because we want to find out how well our code copes with changing hardware features.