Improving the scalability of a symmetric iterative eigensolver for multi-core platforms

We describe an efficient and scalable symmetric iterative eigensolver developed for distributed memory multi-core platforms. We achieve over 80% parallel efficiency by major reductions in communication overheads for the sparse matrix-vector multiplication and basis orthogonalization tasks. We show that the scalability of the solver is significantly improved compared to an earlier version, after we carefully reorganize the computational tasks and map them to processing units in a way that exploits the network topology. We discuss the advantage of using a hybrid OpenMP/MPI programming model to implement such a solver. We also present strategies for hiding communication on a multi-core platform. We demonstrate the effectiveness of these techniques by reporting the performance improvements achieved when we apply our solver to large-scale eigenvalue problems arising in nuclear structure calculations. Because sparse matrix-vector multiplication and inner product computation constitute the main kernels in most iterative methods, our ideas are applicable in general to the solution of problems involving large-scale symmetric sparse matrices with irregular sparsity patterns. Copyright (c) 2013 John Wiley & Sons, Ltd.