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Research of Finite Element Method on GPU

Author: HuYaoGuo
Tutor: YangWenBing
School: Huazhong University of Science and Technology
Course: Engineering Mechanics
Keywords: GPU CUDA Parallel computing High-performance computing Finite Element
CLC: O241.82
Type: Master's thesis
Year: 2011
Downloads: 76
Quote: 0
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Abstract


In recent years, with the continuous development of the graphics processor (GPU) hardware architecture of the GPU 's programmable performance continue to strengthen , at the same time a substantial increase in computing power , making the GPU began to appear in the field of numerical computation . With the constant improvement of the NVIDIA CUDA parallel computing platform GPU parallel computing continue to penetrate the various disciplines . Because of the particularity of the finite element method , the development is very slow GPU architecture mature before the transplant , so far only in the initial state . This article by analyzing the NVIDIA GPU architecture and programming model on CUDA platform characteristics , calculated in the conventional finite element analysis program than the larger assembly and sparse linear equations solving two parts transplanted to the GPU . Give full consideration to the CUDA platform for GPU hardware characteristics , selected conjugate gradient method (CG) iterative method of solving sparse linear equations , the method of calculation of the amount of the largest part of the sparse matrix vector multiplication ( SpMV ) . Taking into account the characteristics of the CUDA platform data read and write , first determine the total stiffness matrix of compressed storage format for the CSR , then reorder the nodes of the model , equation solver SpMV operation so valuable cache can better take advantage of the GPU . Order to ensure highly parallel computing in the assembly process , to prevent conflict in the data read and write , the model units are grouped such that each group of the unit adjacent to each other , so that a single each thread assembled calculation just in the total just in a position corresponding to not have any overlap , to prevent the potential of the data conflicts . CG method in vector operations using CUDA BLAS library instead of own SpMV operation , so that the equation solving also take full advantage of GPU resources . By calculating the 4 different types of unit model , compared with the calculation result of the CPU side , the GPU in the assembled part can be up to seven times acceleration , in the equation solving section highest reached 6.4 times the acceleration . The results show that the use of GPU resources finite element method can get better acceleration

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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