Aiichiro Nakano

Hybrid finite-element/molecular-dynamics/electronic-density-functional approach to materials simulations on parallel computers

A hybrid simulation approach is developed to study chemical reactions coupled with long-range mechanical phenomena in materials. The finite-element method for continuum mechanics is coupled with the molecular dynamics method for an atomic system that embeds a cluster of atoms described quantum-mechanically with the electronic density-functional method based on real-space multigrids. The hybrid simulation approach is implemented on parallel computers using both task and spatial decompositions. Additive hybridization and unified finite-element/molecular-dynamics schemes allow scalable parallel implementation and rapid code development, respectively. A hybrid simulation of oxidation of Si(111) surface demonstrates seamless coupling of the continuum region with the classical and the quantum atomic regions.

Interaction potential for silicon carbide: A molecular dynamics study of elastic constants and vibrational density of states for crystalline and amorphous silicon carbide

An effective interatomic interaction potential for SiC is proposed. The potential consists of two-body and three-body covalent interactions. The two-body potential includes steric repulsions due to atomic sizes, Coulomb interactions resulting from charge transfer between atoms, charge-induced dipole-interactions due to the electronic polarizability of ions, and induced dipole-dipole (van der Waals) interactions. The covalent characters of the Si–C–Si and C–Si–C bonds are described by the three-body potential. The proposed three-body interaction potential is a modification of the Stillinger-Weber form proposed to describe Si. Using the molecular dynamics method, the interaction potential is used to study structural, elastic, and dynamical properties of crystalline (3C), amorphous, and liquid states of SiC for several densities and temperatures. The structural energy for cubic (3C) structure has the lowest energy, followed by the wurtzite (2H) and rock-salt (RS) structures. The pressure for the structural t...

Multiscale simulation of nanosystems

The authors describe simulation approaches that seamlessly combine continuum mechanics with atomistic simulations and quantum mechanics. They also discuss computational and visualization issues associated with these simulations on massively parallel computers. Scientists are combining continuum mechanics and atomistic simulations through integrated multidisciplinary efforts so that a single simulation couples diverse length scales. However, the complexity of these hybrid schemes poses an unprecedented challenge, and developments in scalable parallel algorithms as well as interactive and immersive visualization are crucial for their success. This article describes such multiscale simulation approaches and associated computational issues using recent work as an example.

Linear-scaling density-functional-theory calculations of electronic structure based on real-space grids: Design, analysis, and scalability test of parallel algorithms

We have implemented parallel algorithms for density-functional-theory (DFT) based electronic-structure calculations. These include a plane-wave based algorithm, a real-space-grid algorithm based on a high-order finite difference method, and a linear-scaling real-space algorithm using localized orbitals. Parallelization schemes are described for these algorithms, and the computational complexity and the communications involved in the resulting parallel algorithms are analyzed. Scalability tests of these algorithms on massively parallel computers show that the linear-scaling DFT algorithm is highly scalable. For a 110,592-atom gallium arsenide system on 1024 IBM SP3 processors, the parallel efficiency is as high as 93%.

Interaction potentials for alumina and molecular dynamics simulations of amorphous and liquid alumina

Structural and dynamical properties of crystalline alumina α-Al2O3 and amorphous and molten alumina are investigated with molecular dynamics simulation based on an effective interatomic potentials consisting of two- and three-body terms. Structural correlations are examined through pair distribution functions, coordination numbers, static structure factors, bond angle distributions, and shortest-path ring analyses. The calculated results for neutron and x-ray static structure factors are in good agreement with experimental results. Dynamical correlations, such as velocity autocorrelation function, vibrational density of states, current-current correlation function, and frequency-dependent conductivity, are also discussed.

Multiresolution molecular dynamics algorithm for realistic materials modeling on parallel computers

Abstract For realistic modeling of materials, a molecular-dynamics (MD) algorithm is developed based on multiresolutions in both space and time. Materials of interest are characterized by the long-range Coulomb, steric and charge-dipole interactions as well as three-body covalent potentials. The long-range Coulomb interaction is computed with the fast multipole method. For bulk systems with periodic boundary conditions, infinite summation over repeated image charges is carried out with the reduced cell multipole method. Short- and medium-range non-Coulombic interactions are computed with the multiple time-step approach. A separable tensor decomposition scheme is used to compute three-body potentials. For a 4.2 million-particle SiO 2 system, one MD step takes only 4.8 seconds on the 512-node Intel Touchstone Delta machine and 10.3 seconds on 64 nodes of an IBM SP1 system. The constant-grain parallel efficiency of the program is η ′ = 0.92 and the communication overhead is 8% on the Delta machine. On the SP1 system, η ′ = 0.91 and communication overhead is 7%.

Parallel multilevel preconditioned conjugate-gradient approach to variable-charge molecular dynamics

Abstract Physical realism of molecular dynamics (MD) simulations is greatly enhanced by incorporating variable atomic charges which adapt to the local environment dynamically. In the electrostatic plus (ES+) model, atomic charges are determined to equalize electronegativity. However, this model involves costly minimization of the electrostatic energy at each MD step. A preconditioned conjugate-gradient method is developed for this minimization problem by splitting the Coulomb-interaction matrix into short- and long-range components; the computationally less intensive short-range matrix is used as a preconditioner. This preconditioning scheme is found to speed up the convergence significantly. Numerical tests involving up to 26.5 million atoms are performed on a parallel computer, and the preconditioner is shown to improve the parallel efficiency by increasing data locality. The computational cost is further amortized due to the algorithmic similarity to the multiple-time-scale MD.

Brittle dynamic fracture of crystalline cubic silicon carbide "3C-SiC… via molecular dynamics simulation

Brittle fracture dynamics for three low-index crack surfaces, i.e., (110), (111), and (100), in crystalline cubic silicon carbide (3C-SiC) is studied using molecular dynamics simulation. The results exhibit significant orientation dependence: (110) fracture propagates in a cleavage manner; (111) fracture involves slip in the {111¯} planes; and crack branching is observed in (001) fracture. Calculated critical energy release rates, which characterize fracture toughness, are compared with available experimental and ab initio calculation data.

Nanoindentation of silicon nitride: A multimillion-atom molecular dynamics study

Nanoindentation of crystalline and amorphous silicon nitride films is studied using 10-million-atom molecular dynamics simulations. A rigid pyramid-shaped indenter tip is used. Load–displacement curves are computed and are used to derive hardness and elastic moduli of the simulated crystalline and amorphous films. Computer images of local pressure distributions and configuration snapshots show that plastic deformation in the film extends to regions far from the actual indent.

A space–time-ensemble parallel nudged elastic band algorithm for molecular kinetics simulation

Abstract A scalable parallel algorithm has been designed to study long-time dynamics of many-atom systems based on the nudged elastic band method, which performs mutually constrained molecular dynamics simulations for a sequence of atomic configurations (or states) to obtain a minimum energy path between initial and final local minimum-energy states. A directionally heated nudged elastic band method is introduced to search for thermally activated events without the knowledge of final states, which is then applied to an ensemble of bands in a path ensemble method for long-time simulation in the framework of the transition state theory. The resulting molecular kinetics (MK) simulation method is parallelized with a space–time-ensemble parallel nudged elastic band (STEP-NEB) algorithm, which employs spatial decomposition within each state, while temporal parallelism across the states within each band and band-ensemble parallelism are implemented using a hierarchy of communicator constructs in the Message Passing Interface library. The STEP-NEB algorithm exhibits good scalability with respect to spatial, temporal and ensemble decompositions on massively parallel computers. The MK simulation method is used to study low strain-rate deformation of amorphous silica.