Scalable Hierarchical Schur Linear System Solver with Multilevel Parallelism on CUDA Enabled Clusters

Sparse linear system solver is one of the core of scientific computing. As the scale of problem increases, to solve sparse linear systems efficiently is necessary. In recent computer architecture, the frequency of computation core is bounded by physical limitations, thus current design of computatation unit as CPU and GPU use multiple cores to improve the performance. Hierarchical Schur method expolits the block structure of multilevel nested dissection reordered sparse linear system and decompose the direct matrix factorization scheme into concurrent subproblems. In each subproblems we properly applied different techniques for lower level parallelism. Moreover by analyzing the computation cost of each subproblems, it is able to distribute the computation load to different resources to improve overall scalability.