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We present a novel, quadrature-based finite element integration method for low-order elements on GPUs, using a pattern we call textit{thread transposition} to avoid reductions while vectorizing aggressively. On the NVIDIA GTX580, which has a nominal single precision peak flop rate of 1.5 TF/s and a memory bandwidth of 192 GB/s, we achieve close to 300 GF/s for element integration on first-order discretization of the Laplacian operator with variable coefficients in two dimensions, and over 400 GF/s in three dimensions. From our performance model we find that this corresponds to 90% of our measured achievable bandwidth peak of 310 GF/s. Further experimental results also match the predicted performance when used with double precision (120 GF/s in two dimensions, 150 GF/s in three dimensions). Results obtained for the linear elasticity equations (220 GF/s and 70 GF/s in two dimensions, 180 GF/s and 60 GF/s in three dimensions) also demonstrate the applicability of our method to vector-valued partial differential equations.
We present an algorithm for the optimization of a class of finite element integration loop nests. This algorithm, which exploits fundamental mathematical properties of finite element operators, is proven to achieve a locally optimal operation count.
In this work we formally derive and prove the correctness of the algorithms and data structures in a parallel, distributed-memory, generic finite element framework that supports h-adaptivity on computational domains represented as forest-of-trees. Th
The numerical solution of partial differential equations using the finite element method is one of the key applications of high performance computing. Local assembly is its characteristic operation. This entails the execution of a problem-specific ke
This paper is devoted to the development of highly efficient kernels performing vector operations relevant in linear system solvers. In particular, we focus on the low arithmetic intensity operations (i.e., streaming operations) performed within the
This work is a user guide to the FEMPAR scientific software library. FEMPAR is an open-source object-oriented framework for the simulation of partial differential equations (PDEs) using finite element methods on distributed-memory platforms. It provi