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

Abstract

Abstract 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. Highlights CUDA Warp based strategies for FE matrix generation and assembly. Performed using coloring method and on linear hexahedral element meshing in 3D. Obtained speedup of 5.17×− 8.2× over single thread per element strategy on GPU. Strategies showed better arithmetic throughput and bandwidth through code profiling.