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Improving Strong Scalability Limits of Finite Element Based Solvers


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Current finite element codes scale reasonably well as long as each core has sufficient amount of local work that can balance communication costs. However, achieving efficient performance at exascale will require unreasonable large problem sizes, in particular for low-order methods, where the small amount of work per element already is a limiting factor on current post petascale machines. One of the key bottlenecks for these methods is sparse matrix assembly, where communication latency starts to limit performance as the number of cores increases. We present our work on improving strong scalability limits of message passing based general low-order finite element based solvers. Using lightweight one-sided communication, we demonstrate that the scalability of performance critical, latency sensitive kernels can achieve almost an order of magnitude better scalability. We introduce a new hybrid MPI/PGAS implementation of the open source general finite element framework FEniCS, replacing the linear algebra backend with a new library written in UPC. A detailed description of the implementation and the hybrid interface to FEniCS is given, and we present a detailed performance study of the hybrid implementation on Cray XC40 machines.