Dynamic Parallelization Strategies for Multifrontal Sparse Cholesky Factorization

This paper discusses parallelization of the computationally intensive numerical factorization phase of sparse Cholesky factorization on shared memory systems. We propose and compare two parallel algorithms based on the multifrontal method. Both algorithms are implemented in a task-based fashion employing dynamic load balance. The first algorithm associates OpenMP tasks with the nodes of an elimination tree and relies on the OpenMP scheduler. The second algorithm employs a concurrent priority queue to implement balancing. Experimental results on symmetric positive definite matrices from the University of Florida Sparse Matrix Collection show that our implementation is comparable to MUMPS and Intel MKL PARDISO in terms of performance and scaling efficiency on shared memory systems.