Optimized sparse Cholesky factorization on hybrid multicore architectures

Abstract

We present techniques for supernodal sparse Cholesky factorization on a hybrid multicore platform consisting of a multicore CPU and GPU. The techniques are the subtree algorithm, pipelining and multithreading. The subtree algorithm [15] minimizes PCIe transmissions by storing an entire branch of the elimination tree in the GPU memory (the elimination tree is a tree data structure describing the workflow of the factorization), and also reduces the total kernel launch time by launching BLAS kernels in batches. The pipelining technique overlaps the execution of GPU kernels and PCIe data transfers. The multithreading technique [17] creates multiple threads for both the CPU and the GPU, to utilize concurrency of the elimination tree. Our experimental results on a platform consisting of an Intel multicore processor along with an Nvidia GPU indicate a significant improvement in performance and energy over CHOLMOD (SuiteSparse 4.5.3), a sparse algorithm, after these techniques are applied.