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Accelerating the finite element analysis of functionally graded materials using fixed‐grid strategy on CUDA‐enabled GPUs
Author(s) -
Pikle Nileshchandra K.,
Sathe Shailesh R.,
Vyavahare Arvind Y.
Publication year - 2019
Publication title -
concurrency and computation: practice and experience
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.309
H-Index - 67
eISSN - 1532-0634
pISSN - 1532-0626
DOI - 10.1002/cpe.5207
Subject(s) - discretization , stiffness matrix , finite element method , grid , computer science , cuda , parallel computing , computational science , leverage (statistics) , solver , direct stiffness method , shared memory , isotropy , structural engineering , mathematics , geometry , engineering , mathematical analysis , physics , quantum mechanics , machine learning , programming language
Summary Fixed‐grid discretization strategy is proposed for static structural Finite Element Analysis (FEA) of Functionally Graded Materials (FGM). The fixed‐grid strategy reduces numerical integration cost 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 are constant. Therefore, for each layer, a single local stiffness matrix will be constructed. These matrices are directly used in the solver phase of the assembly‐free FEM without constructing the global stiffness matrix. The fixed‐grid strategy reduces the global memory transactions on the GPU by storing these elemental matrices in on‐chip shared memory or cached constant memory. Furthermore, the assembly‐free method is adopted to leverage a fine grained parallelism on the GPU at the degree of freedom level. Numerical experiments showed the effectiveness of the discrete layered approach for FGM using the fixed‐grid strategy. For performance evaluation two strategies using global memory and shared memory are compared and found that the use of shared memory can achieve approximately 2.4 times better performance than global memory.