Analysis and optimization of sparse LU factorization of power matrix based on GLU

With the continuous improvement of power grid stability and reliability requirements, improving the efficiency and accuracy of power system simulation has become an important research topic. The sparse LU factorization is one of the key modules of the sparse direct solver, which usually plays a dominant role in the solving time of the sparse linear algebra equation of power system. In order to improve the efficiency of sparse LU factorization, we propose: 1) an adaptive mode partition strategy based on GLU, and select the mode to be used according to the characteristics of the matrix to be decomposed, which improves the computational efficiency of LU factorization; 2) a dynamic Nstream value taking method for the stream pattern, which determines the number of streams to be used based on the dimensions of the sub-matrix, 3) a pipeline model for the continuous layer with the size of 1 in GLU, which improves the parallelism of sparse LU factorization and helps to improve the computing efficiency. The results show that the proposed improvement can achieve better results, and the speed of LU factorization is increased by more than 30% on rajat12 and circuit_2.