GPU-based multifrontal optimizing method in sparse Cholesky factorization

In many scientific computing applications, sparse Cholesky factorization is used to solve large sparse linear equations in distributed environment. GPU computing is a new way to solve the problem. However, sparse Cholesky factorization on GPU is hardly to achieve excellent performance due to the structure irregularity of matrix and the low GPU resource utilization. A hybrid CPU-GPU implementation of sparse Cholesky factorization is proposed based on multifrontal method. A large sparse coefficient matrix is decomposed into a series of small dense matrices (frontal matrices) in the method, and then multiple GEMM (General Matrix-matrix Multiplication) operations are computed. GEMMs are the main operations in sparse Cholesky factorization, but they are hardly to perform better in parallel on GPU. In order to improve the performance, the scheme of multiple task queues is adopted when performing multiple GEMMs parallelized with multifrontal method; all GEMM tasks are scheduled dynamically on GPU and CPU based on computation scales for load balance and computing-time reduction. Experimental results show that the approach can outperform the implementations of BLAS and cuBLAS, achieving up to 3.15× and 1.98× speedup, respectively.