Research On GPU Acceleration Of Element-Free Galerkin Method For Parallel Computing

Element-free Galerkin(EFG)method,which can effectively deal with the difficulties faced by the conventional FEM due to the absence of element,is very prevalent on large displacements and discontinuous problems.Nevertheless,the computational cost for the solution of the problem is much higher than the conventional FEM,which have limited the application of EFG in large-scale engineering computation problems.With the launching of CUDA,GPU acceleration parallel computing which is developed in recent years has been widely applied in the field of scientific and engineering computing.In this paper,GPU acceleration is used for the purpose reducing the computing time of EFG.The main research contents are summarized as follows:Firstly,the task allocation style of the sparse matrix vector multiplication in parallel computing based on CUDA is discussed,and a GPU-accelerated method which used to solve a linear algebraic system of symmetric and positive equations is investigated.The codes of conjugate gradient method based on GPU are written,and computational performance of it solving the coefficient matrix of different scale is compared.The example results obtained show that the scale of coefficient matrix larger.the speed-up ratio higher.Secondly,the assembling and sparse storage of stiffness matrix is researched,based on the idea of interacting node pairs and the CSR format.The local search method for searching node and integral points is proposed.The essential boundary condition is imposed by penalty function method,and the unified format of stiffness matrix and penalty stiffness matrix was derived.An improved algorithm of EFG method by means of the triangular integral mesh for integral calculation is proposed,and the correlative C programs are written.The numerical example results obtained show that the improved algorithm can save memory effectively on the premise that the calculating accuracy is met.and improve the search efficiency of node and integral point,and be well adapted to complex geometry models.Thirdly,according to the improved EFG algorithm,the parallel algorithm of EFG is proposed through GPU to accelerate the calculation of shape function and its derivative and solving of equations.The parallel codes were programmed on CUDA,and algorithm testing was finished on the device of NVIDIA GeForce GTX 660 by numerical examples.The factors of affecting speedup ratio were discussed.The example results show that the proposed algorithm can achieve a good speedup on the premise that the calculating accuracy is met,and to solve linear equations and calculate the stiffness matrix are the major factors in the speedup.The computing time of EFG is reduced significantly by GPU acceleration,the research of this paper is provided a novel algorithm for EFG method being used in large-scale application.The results obtained have an important theory significant to EFG method applied to engineering problem.