2HOT: An Improved Parallel Hashed Oct-Tree N-Body Algorithm for Cosmological Simulation

We report on improvements made over the past two decades to our adaptive treecode N-body method (HOT). A mathematical and computational approach to the cosmological N-body problem is described, with performance and scalability measured up to 256k ($2^{18}$) processors. We present error analysis and scientific application results from a series of more than ten 69 billion ($4096^3$) particle cosmological simulations, accounting for $4 \times 10^{20}$ floating point operations. These results include the first simulations using the new constraints on the standard model of cosmology from the Planck satellite. Our simulations set a new standard for accuracy and scientific throughput, while meeting or exceeding the computational efficiency of the latest generation of hybrid TreePM N-body methods.Comment: 12 pages, 8 figures, 77 references; To appear in Proceedings of SC '1

Scalable parallel molecular dynamics algorithms for organic systems

A scalable parallel algorithm, Macro-Molecular Dynamics (MMD), has been developed for large-scale molecular dynamics simulations of organic macromolecules, based on space-time multi-resolution techniques and dynamic management of distributed lists. The algorithm also includes the calculation of long range forces using Fast Multipole Method (FMM). FMM is based on the octree data structure, in which each parent cell is divided into 8 child cells and this division continues until the cell size is equal to the non-bonded interaction cutoff length. Due to constant number of operations performed at each stage of the octree, the FMM algorithm scales as O(N). Design and analysis of MMD and FMM algorithms are presented. Scalability tests are performed on three tera-flop machines: 1024-processor Intel Xeon-based Linux cluster, SuperMike at LSU, 1184-processor IBM SP4 Marcellus and the 512-processor Compaq AlphaServer Emerald at the U.S. Army Engineer Research and Development Center (ERDC) MSRC. The tests show that the Linux cluster outperforms the SP4 for the MMD application. The tests also show significant effects of memory- and cache-sharing on the performance

A new algorithm for electrostatic interactions in Monte Carlo simulations of charged particles

To minimise systematic errors in Monte Carlo simulations of charged particles, long range electrostatic interactions have to be calculated accurately and efficiently. Standard approaches, such as Ewald summation or the naive application of the classical Fast Multipole Method, result in a cost per Metropolis-Hastings step which grows in proportion to some positive power of the number of particles $N$ in the system. This prohibitively large cost prevents accurate simulations of systems with a sizeable number of particles. Currently, large systems are often simulated by truncating the Coulomb potential which introduces uncontrollable systematic errors. In this paper we present a new multilevel method which reduces the computational complexity to $\mathcal{O}(\log(N))$ per Metropolis-Hastings step, while maintaining errors which are comparable to direct Ewald summation. We show that compared to related previous work, our approach reduces the overall cost by better balancing time spent in the proposal- and acceptance- stages of each Metropolis-Hastings step. By simulating large systems with up to $N=10^5$ particles we demonstrate that our implementation is competitive with state-of-the-art MC packages and allows the simulation of very large systems of charged particles with accurate electrostatics.Comment: 19 pages, 9 figures, 1 tabl

Polarizable Density Embedding for Large Biomolecular Systems

This document is the Accepted Manuscript version of a Published Work that appeared in final form in Journal of Chemical Theory and Computation, Copyright © 2020 American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://doi.org/10.1021/acs.jctc.0c00763.We present an efficient and robust fragment-based quantum–classical embedding model capable of accurately capturing effects from complex environments such as proteins and nucleic acids. This is realized by combining the molecular fractionation with conjugate caps (MFCC) procedure with the polarizable density embedding (PDE) model at the level of Fock matrix construction. The PDE contributions to the Fock matrix of the core region are constructed using the local molecular basis of the individual fragments rather than the supermolecular basis of the entire system. Thereby, we avoid complications associated with the application of the MFCC procedure on environment quantities such as electronic densities and molecular-orbital energies. Moreover, the computational cost associated with solving self-consistent field (SCF) equations of the core region remains unchanged from that of purely classical polarized embedding models. We analyze the performance of the resulting model in terms of the reproduction of the electrostatic potential of an insulin monomer protein and further in the context of solving problems related to electron spill-out. Finally, we showcase the model for the calculation of one- and two-photon properties of the Nile red molecule in a protein environment. Based on our analyses, we find that the combination of the MFCC approach with the PDE model is an efficient, yet accurate approach for calculating molecular properties of molecules embedded in structured biomolecular environments

The MOLDY short-range molecular dynamics package

We describe a parallelised version of the MOLDY molecular dynamics program. This Fortran code is aimed at systems which may be described by short-range potentials and specifically those which may be addressed with the embedded atom method. This includes a wide range of transition metals and alloys. MOLDY provides a range of options in terms of the molecular dynamics ensemble used and the boundary conditions which may be applied. A number of standard potentials are provided, and the modular structure of the code allows new potentials to be added easily. The code is parallelised using OpenMP and can therefore be run on shared memory systems, including modern multicore processors. Particular attention is paid to the updates required in the main force loop, where synchronisation is often required in OpenMP implementations of molecular dynamics. We examine the performance of the parallel code in detail and give some examples of applications to realistic problems, including the dynamic compression of copper and carbon migration in an iron-carbon alloy

An O(N) Algorithm for Stokes and Laplace Interactions of Particles

A method for computing Laplace and Stokes interactions among N spherical particles arbitrarily placed in a unit cell of a periodic array is described. The method is based on an algorithm by Greengard and Rokhlin [J. Comput. Phys. 73, 325 (1987)] for rapidly summing the Laplace interactions among particles by organizing the particles into a number of different groups of varying sizes. The far-field induced by each group of particles is expressed by a multipole expansion technique into an equivalent field with its singularities at the center of the group. The resulting computational effort increases only linearly with N. The method is applied to a number of problems in suspension mechanics with the goal of assessing the efficiency and the potential usefulness of the method in studying dynamics of large systems. It is shown that reasonably accurate results for the interaction forces are obtained in most cases even with relatively low-order multipole expansions

Molecular-dynamics simulations of self-assembled monolayers (SAM) on parallel computers

The purpose of this dissertation is to investigate the properties of self-assembled monolayers, particularly alkanethiols and Poly (ethylene glycol) terminated alkanethiols. These simulations are based on realistic interatomic potentials and require scalable and portable multiresolution algorithms implemented on parallel computers. Large-scale molecular dynamics simulations of self-assembled alkanethiol monolayer systems have been carried out using an all-atom model involving a million atoms to investigate their structural properties as a function of temperature, lattice spacing and molecular chain-length. Results show that the alkanethiol chains tilt from the surface normal by a collective angle of 25o along next-nearest neighbor direction at 300K. At 350K the system transforms to a disordered phase characterized by small tilt angle, flexible tilt direction, and random distribution of backbone planes. With increasing lattice spacing, a, the tilt angle increases rapidly from a nearly zero value at a = 4.7Å to as high as 34 o at a = 5.3Å at 300K. We also studied the effect of end groups on the tilt structure of SAM films. We characterized the system with respect to temperature, the alkane chain length, lattice spacing, and the length of the end group. We found that the gauche defects were predominant only in the tails, and the gauche defects increased with the temperature and number of EG units. Effect of electric field on the structure of poly (ethylene glycol) (PEG) terminated alkanethiol self assembled monolayer (SAM) on gold has been studied using parallel molecular dynamics method. An applied electric field triggers a conformational transition from all-trans to a mostly gauche conformation. The polarity of the electric field has a significant effect on the surface structure of PEG leading to a profound effect on the hydrophilicity of the surface. The electric field applied anti-parallel to the surface normal causes a reversible transition to an ordered state in which the oxygen atoms are exposed. On the other hand, an electric field applied in a direction parallel to the surface normal introduces considerable disorder in the system and the oxygen atoms are buried inside

Parallel molecular dynamics simulations of dynamics of oxidation and reactive wetting in metal/ceramic systems

Oxidation of a flat aluminum (111) surface and the reactive wetting of the aluminum (Al) droplet on a flat alumina (α-Al2O3) surface are investigated by using parallel molecular-dynamics simulations with dynamic charge transfer among atoms on a microscopic length scale. The interatomic potential, based on the formalism of Streitz and Mintmire, allows atoms to vary their charges dynamically between anions and cations, when atoms move and their local environment is altered. We investigate the oxidation thickness as a function of time and the oxygen density which is 10-40 times that of the normal state (1 atm and 300 K). Stable amorphous oxide scales form around 51 Å at 4.42 ns, 2.862 ns, and 2.524 ns, respectively, and molecular oxygen density 10-40 times the normal state. We also study structural correlations in the resulting final oxide scale. The structure of final oxide scales depend on depth, where density of aluminum (Al) and oxygen (O) atoms change. Reactive wetting of aluminum nanodroplet on alumina surface is also studied using parallel MD. We study heat transfer, diffusion within droplet, and the structure of the inter-metallic phases in the liquid-solid interface. Oxygen (O) atoms diffuse into the spherical aluminum (Al) droplet and form an interface between the flat solid substrate and the Al droplet. This diffusion of oxygen atoms may be the main source of adhesion between the Al drop and the flat α-Al2O3 substrate. The temperature in the flat α-Al2O3 bulk substrate rises from 0K to 200 K at the end of the simulation, 8.5 ps, but the temperature becomes much higher at the reactive interface. We have examined which oxygen atoms from the substrate participate in the wetting and the formation of a solder joint at the Al/α-Al2O3 interface

Coulomb Interactions via Local Dynamics: A Molecular--Dynamics Algorithm

We derive and describe in detail a recently proposed method for obtaining Coulomb interactions as the potential of mean force between charges which are dynamically coupled to a local electromagnetic field. We focus on the Molecular Dynamics version of the method and show that it is intimately related to the Car--Parrinello approach, while being equivalent to solving Maxwell's equations with freely adjustable speed of light. Unphysical self--energies arise as a result of the lattice interpolation of charges, and are corrected by a subtraction scheme based on the exact lattice Green's function. The method can be straightforwardly parallelized using standard domain decomposition. Some preliminary benchmark results are presented.Comment: 8 figure