Quantum-based molecular dynamics (QMD) is a highly accurate and transferable method for material science simulations. However, the time scales and system sizes accessible to QMD are typically limited to picoseconds and a few hundred atoms. These constraints arise due to expensive self-consistent ground-state electronic structure calculations that can often scale cubically with the number of atoms. Linearly scaling methods depend on computing the density matrix P from the Hamiltonian matrix H by exploiting the sparsity in both matrices. The second-order spectral projection (SP2) algorithm is an O(N ) algorithm that computes P with a sequence of 40 − 50 matrix-matrix multiplications. In this paper, we present task-based implementations of a recently developed data-parallel graph-based approach to the SP2 algorithm, G-SP2. We represent the density matrix P as an undirected graph and use graph partitioning techniques to divide the computation into smaller independent tasks. The partitions thus obtained are generally not of equal size and give rise to undesirable load imbalances in standard MPI -based implementations. This load-balancing challenge can be mitigated by dynamically scheduling parallel computations at runtime using task-based programming models. We develop task-based implementations of the data-parallel G-SP2 algorithm using both Intel's Concurrent Collections (CnC ) as well as the Charm++ programming model and evaluate these implementations for future use. Scaling and performance results of our implementations are investigated for representative segments of QMD simulations for solvated protein systems containing more than 10, 000 atoms.
In field emission plasmas, electrons that initiate plasma formation come from the surface of a metallic electrode, or wall, with emission controlled by the electron-work function of the wall, and can be computed via the Fowler-Nordheim formula. Impinging ions modify the rate at which electrons leave the surface, and are accounted via the coefficient of secondary electron emission. However, in the case of dielectric surfaces, the microscopic mechanism by which electrons are emitted is not as well understood. While simulations of dielectric barrier discharge plasmas assume an initial density of electrons in a time-dependent simulation, whether the presence of electrons is a necessary ambient condition or whether it is a result of emission from a surface is not clear. This is particularly relevant in the context of micro and nanoscale plasma generators when surface-related effects become more important. Here we consider electron emission from dielectric surfaces in the context of dielectric barrier discharges. The configuration of interest consists of two parallel-plate metallic electrodes, each covered by a dielectric layer. Assuming that the initial electrons for plasma formation arise from the surface, we compute the rate of charge transfer from surfaces, which is a necessary, but not sufficient, condition for plasma formation. The novelty of this work is the application of the theory of nonadiabatic transitions (dynamical level-crossing) to the problem of electron emission from dielectric surfaces in dielectric barrier discharges. The microscopic model of electron transfer described here has potential applications in the design of micro and nano-scale plasma generators.
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