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A Hybrid MPI PGAS Approach to Improve Strong Scalability Limits of Finite Element 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. Key bottlenecks for these methods are sparse matrix assembly, where communication latency starts to limit performance as the number of cores increases, and linear solvers, where efficient overlapping is necessary to amortize communication and synchronization cost of sparse matrix vector multiplication and dot products. 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 offered by partitioned global address space languages (PGAS), we demonstrate that the scalability of performance critical, latency sensitive sparse matrix assembly can achieve almost an order of magnitude better scalability. Linear solvers are also addressed via a signaling put algorithm for low-cost point-to-point synchronization, achieving similar performance as message passing based linear solvers. 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 Unified Parallel C (UPC). A detailed description of the implementation and the hybrid interface to FEniCS is given, and the feasibility of the approach is demonstrated via a performance study of the hybrid implementation on Cray XC40 machines.