Accelerating the finite element analysis of functionally graded materials using fixed-grid strategy on CUDA enabled GPUs

摘要

Fixed-grid discretization strategy is proposed for static structural Finite Element Analysis (FEA)of Functionally Graded Materials (FGM). The fixed-grid strategy reduces numerical integrationcost dramatically by generating a single local stiffness matrix for isotropic materials. For FGMs,domain is discretized into the layers in such a way that material properties in each layer areconstant. Therefore, for each layer, a single local stiffness matrix will be constructed. Thesematrices are directly used in the solver phase of the assembly-free FEM without constructing theglobal stiffness matrix. The fixed-grid strategy reduces the global memory transactions on theGPU by storing these elemental matrices in on-chip sharedmemory or cached constantmemory.Furthermore, the assembly-free method is adopted to leverage a fine grained parallelism on theGPU at the degree of freedom level. Numerical experiments showed the effectiveness of thediscrete layered approach for FGM using the fixed-grid strategy. For performance evaluationtwo strategies using globalmemory and shared memory are compared and found that the use ofshared memory can achieve approximately 2.4 times better performance than global memory.