Parallel Solution of Small and Medium Sized Linear Equations Based on GPU

Complex systems usually contain a large number of small and medium-sized nonlinear simulation model units, which needs to be approximated in a linearized form, and the most time-consuming step is the solving of these linear equations. Existing batched algorithms suffer from the global memory access latency bottleneck, and the performance is poor. This paper designs and implements a GPU based highly parallelized batched LU decomposition algorithm as well as the corresponding parallel back-substitution algorithm to solve linear systems simultaneously. The experiment result shows very promising efficiency, it achieves more than 17.15 speedup ratio compared with CUBLAS provided by NVIDIA.