Research Of Finite Element Method On GPU

Recently, with the development of graphics processor (GPU) hardware architecture, GPU's programmable performance continues to strengthen which making the computing power of GPU has a major increase, and the GPU have had great success in numerical computations. With the NVIDIA CUDA parallel computing platform continue to improve, GPU parallel computing has been infiltrated into every subjects. For the special of finite element method, it y developed slowly when GPU's architecture was not yet mature. So far it is only in the initial state. By analyzing the architecture of NVIDIA GPU, and the programming model of CUDA platform, and then porting the assembling and the sparse linear equation solver which are the biggest computation parts in traditional finite element analysis programs to GPU.For the specialty of CUDA platform, we selected conjugate gradient method (CG) which is a iteration method for solving sparse linear equations in FEM and the majority of CG is in the sparse matrix-vector multiplication (SpMV). Taking into account the data reading and writing restriction, we choose CSR format to compress the global stiffness matrix, and then reorder the nodes of the model to make SpMV operation can use the precious GPU cache better. To assure the high degree of parallel computing on assembly procedure, and avoid the reading and writing conflict, we grouped the elements of the model to make the elements of each group is not adjacent to each other, so that each element matrix which calculated by one thread of GPU would not overlap any other element matrix, it prevent potential data conflicts. We replace the vector operations by CUDA BLAS library, and implement our SpMV function, so that the equation solver is also full use the resource of GPU.By calculating 4 different elements models, the results on GPU compared to CPU shows that in assembly procedure GPU can get highest speed up to 7 times, and in equation solving procedure get highest speed up to 6.4 times. The result shows that with the GPU computing resource, finite element method can get better acceleration effect.