Topology-Aware Mappings for Large-Scale Eigenvalue Problems

Obtaining highly accurate predictions for properties of light atomic nuclei using the Configuration Interaction (CI) approach requires computing the lowest eigenvalues and associated eigenvectors of a large many-body nuclear Hamiltonian matrix, (H) over cap. Since (H) over cap is a large sparse matrix, a parallel iterative eigensolver designed for multi-core clusters is used. Due to the extremely large size of (H) over cap, thousands of compute nodes are required. Communication overhead may hinder the scalability of the eigensolver at such scales. In this paper, we discuss how to reduce such overhead. In particular, we quantitatively show that topology-aware mapping of computational tasks to physical processors on large-scale multi-core clusters may have a significant impact on efficiency. For typical large-scale eigenvalue calculations, we obtain up to a factor of 2.5 improvement in overall performance by using a topology-aware mapping.