A finite element stiffness matrix simulation method based on GPU

Abstract

The invention provides a finite element stiffness matrix simulation method based on a GPU terminal. The method comprises: a stiffness equation Ax = b is established and initialized; splitting the stiffness matrix A; correspondingly allocating a GPU video memory; copying the initialized data of the CPU end to the GPU; calling a timing function to start timing; calling an equipment end polynomial pre-optimal conjugate gradient algorithm for calculation; copying the calculation result from the GPU to the CPU end; and releasing the CPU and the GPU video memory. The method is based on an NVIDIA CUBLAS library and a CUDA language. According to the method, the advantages of a diagonal pre-optimization preprocessing method are combined, the three-diagonal rigidity matrix is split well, inverse operation on the matrix is avoided, and therefore the operation amount of a conjugate gradient algorithm is greatly reduced, and polynomial preprocessing of the rigidity matrix is achieved on a GPU.

Description

technical field [0001] The invention belongs to the field of finite element numerical simulation calculation and computer application, and relates to the accelerated solution realization of pre-optimized finite element stiffness matrix. Background technique [0002] There are more and more researches on the application of computer graphics processing unit (GPU) in general computing, especially in the field of large-scale science and computing. Because it was originally designed for graphics and image processing, GPU is inherently a computer with a large number of calculations. Unit's parallel processors, and the same computing power provided by the GPU, requires less cost and less power consumption than a CPU-based system. [0003] As a basic method of numerical simulation and simulation, the finite element method has become one of the important methods of modern engineering design and structural analysis due to its high adaptability. It is widely used in many fields such a...

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Problems solved by technology

[0006] The technical problem to be solved by the present invention is to provide a GPU-based finite element stiffness matrix simulation method based on the defects of the existing incomplete decomposition method preprocessing technology and the lack of research on the polynomial preprocessing method. The present invention is based on NVIDIA The CUBLAS library and CUDA language, combined with the advantages of the diagonal pre-optimization preprocessing method, perform a better split on the tri-diagonal stiffness matrix, avoiding the inverse operation of the matrix, thereby greatly reducing the conjugate gradient The computational load of the algorithm, thus realizing the polynomial preprocessing of the stiffness matrix on the GPU

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