Design and Implementation of New Hybrid Algorithm and Solver on CPU For Large Sparse Linear Systems

It is important to have a fast, robust and scalable algorithm to solve a sparse linear system AX=B. Many multiscale modelling applications in science and engineering would like to capture more details of the system that results in more general matrices. In this work, we consider scalable direct solvers and, in particular, we examine the effectiveness of the SuperLU_DIST 3.0 for distributed memory and SuperLU_MT 2.0 for shared memory parallel machines. We use test matrices containing randomly populated sparse matrices in addition to patterned matrices. For randomly populated large sparse matrices, we find that numerical factorization, symbolic factorization, and consequently wall clock time spike up around the sparsity level of 7. We propose a new hybrid algorithm utilizing the MPI+OpenMP hybrid programming approach among other modifications to solve large sparse linear systems so that we can avoid extra communication overhead with MPI within node and we could have a better scalability than both pure MPI and OpenMP. It combines the advantages of SuperLU_DIST and SuperLU_MT and diminishes some of their limitations.