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Finite element method has been successfully implemented on the graphics processing units to achieve a significant reduction in simulation time. In this paper, new strategies for the finite element matrix generation including numerical integration and assembly are proposed by using a warp per element for a given mesh. These strategies are developed using the well-known coloring method. The proposed strategies use a specialized algorithm to realize fine-grain parallelism and efficient use of on-chip memory resources. The warp shuffle feature of Compute Unified Device Architecture (CUDA) is used to accelerate numerical integration. The evaluation of elemental stiffness matrix is further optimized by adopting a partial parallel implementation of numerical integration. Performance evaluations of the proposed strategies are done for three-dimensional elasticity problem using the 8-noded hexahedral elements with three degrees of freedom per node. We obtain a speedup of up to 8.2 × over the coloring based assembly by element strategy (using a single thread per element) on NVIDIA Tesla K40 GPU. Also, the proposed strategies achieve better arithmetic throughput and bandwidth.

GPU-warp based finite element matrices generation and assembly using coloring method