GPU Acceleration of a Spacetime Solver for Hyperbolic Systems
Robert B. Haber
Award year: 2012-2013
An interdisciplinary research team at Illinois is developing an adaptive Spacetime Discontinuous Galerkin (SDG) finite element method (FEM) as a general-purpose solver for hyperbolic systems. The SDG method works with fully unstructured spacetime grids that satisfy a special causality constraint controlled by the fastest local wave speed. SDG models are asynchronous and circumvent the synchronous bottlenecks inherent to conventional time-marching schemes in high-performance computing applications. Other attractive properties of SDG methods include element-wise balance properties, reduced stabilization requirements, preservation of characteristic structure across element boundaries, and the elimination of error-inducing projection operations following adaptive remeshing. Of particular relevance to this proposal is the rich parallel structure that is intrinsic to patch-by-patch SDG solution algorithms. In previous work, we obtained near-perfect scaling for an asynchronous, parallel implementation of the non-adaptive patch-generation/solution procedure on the NCSA Abe cluster. We are currently developing an adaptive-meshing extension, in which a novel dynamic load-balancing technique matches the patch-level granularity of the meshing/solution procedure. However, we have yet to exploit available parallel structure within the patch-level FEM solution algorithm. This research will explore applications of GPU accelerators, such as those planned for Blue Waters, within the SDG patch solver. It has significant potential for near-term impact within HPC technology, because our method's nested, parallel structure is compatible with the heterogeneous architectures of today's HPC platforms. In the longer term, its asynchronous character suggests a means to circumvent the scalability limits of traditional synchronous algorithms on next-generation machines. In addition, the speed-ups this work will deliver are essential to explore cutting-edge applications of a new SDG code in 3d_time to problems in fracture and the mechanics of materials, thermal transport, and other hyperbolic systems.