Fuyuki Shimojo

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.

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%.

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.

The semiconductor-metal transition in fluid selenium : an ab initio molecular-dynamics simulation

The semiconductor-metal transition in fluid selenium is investigated by means of an ab initio molecular-dynamics simulation using the generalized-gradient-corrected density functional theory. It is found that the chain-like structure persists even in the metallic state, although the chain structure is substantially disrupted. The average chain length decreases with increasing temperature, in agreement with the experimentally observed tendency. The detailed investigation of the time change of the chain structure shows that the interaction between the Se chains is crucially important for bond breaking, and that bond breaking and rearrangement of the Se chains occur more frequently at higher temperatures. It is important to note that when the Se-Se bonds break, the anti-bonding states above the Fermi level are stabilized while the bonding or non-bonding states below the become unstable, and, therefore, the gap at disappears at high temperatures.

Hybrid quantum mechanical/molecular dynamics simulation on parallel computers: density functional theory on real-space multigrids

A hybrid quantum mechanical/molecular dynamics simulation scheme is developed, in which a quantum mechanical system described by the density functional theory on real-space multigrids is embedded in a classical system of atoms interacting via an empirical interatomic potential. Handshake atoms coupling the quantum and the classical systems are treated by a novel scaled position method. The scheme is implemented on parallel computers using both task and spatial decompositions. An application to oxidation of Si (100) surface demonstrates seamless coupling of the quantum and the classical systems.

Variable-charge interatomic potentials for molecular-dynamics simulations of TiO2

An interatomic potential model has been developed for molecular-dynamics simulations of TiO2 (rutile) based on the formalism of Streitz and Mintmire [J. Adhes. Sci. Technol. 8, 853 (1994)], in which atomic charges vary dynamically according to the generalized electronegativity equalization principle. The present model potential reproduces the vibrational density of states, the pressure-dependent static dielectric constants, the melting temperature, and the surface relaxation of the rutile crystal, as well as the cohesive energy, the lattice constants, and the elastic moduli. We find the physical properties of rutile are significantly affected by dynamic charge transfer between Ti and O atoms. The potential allows us to perform atomistic simulations on nanostructured TiO2 with various kinds of interfaces (surfaces, grain boundaries, dislocations, etc.).

Embedded divide-and-conquer algorithm on hierarchical real-space grids: parallel molecular dynamics simulation based on linear-scaling density functional theory

A linear-scaling algorithm has been developed to perform large-scale molecular-dynamics (MD) simulations, in which interatomic forces are computed quantum mechanically in the framework of the density functional theory. A divide-and-conquer algorithm is used to compute the electronic structure, where non-additive contribution to the kinetic energy is included with an embedded cluster scheme. Electronic wave functions are represented on a real-space grid, which is augmented with coarse multigrids to accelerate the convergence of iterative solutions and adaptive fine grids around atoms to accurately calculate ionic pseudopotentials. Spatial decomposition is employed to implement the hierarchical-grid algorithm on massively parallel computers. A converged solution to the electronic-structure problem is obtained for a 32,768-atom amorphous CdSe system on 512 IBM POWER4 processors. The total energy is well conserved during MD simulations of liquid Rb, showing the applicability of this algorithm to first principles MD simulations. The parallel efficiency is 0.985 on 128 Intel Xeon processors for a 65,536-atom CdSe system.

De Novo Ultrascale Atomistic Simulations On High-End Parallel Supercomputers

We present a de novo hierarchical simulation framework for first-principles based predictive simulations of materials and their validation on high-end parallel supercomputers and geographically distributed clusters. In this framework, high-end chemically reactive and non-reactive molecular dynamics (MD) simulations explore a wide solution space to discover microscopic mechanisms that govern macroscopic material properties, into which highly accurate quantum mechanical (QM) simulations are embedded to validate the discovered mechanisms and quantify the uncertainty of the solution. The framework includes an embedded divide-and-conquer (EDC) algorithmic framework for the design of linear-scaling simulation algorithms with minimal bandwidth complexity and tight error control. The EDC framework also enables adaptive hierarchical simulation with automated model transitioning assisted by graph-based event tracking. A tunable hierarchical cellular decomposition parallelization framework then maps the O(N) EDC algorithms onto petaflops computers, while achieving performance tunability through a hierarchy of parameterized cell data/ computation structures, as well as its implementation using hybrid grid remote procedure call + message passing + threads programming. High-end computing platforms such as IBM BlueGene/L, SGI Altix 3000 and the NSF TeraGrid provide an excellent test grounds for the framework. On these platforms, we have achieved unprecedented scales of quantum-mechanically accurate and well validated, chemically reactive atomistic simulations—1.06 billion-atom fast reactive force-field MD and 11.8 million-atom (1.04 trillion grid points) quantum-mechanical MD in the framework of the EDC density functional theory on adaptive multigrids— in addition to 134 billion-atom non-reactive space—time multiresolution MD, with the parallel efficiency as high as 0.998 on 65,536 dual-processor BlueGene/L nodes. We have also achieved an automated execution of hierarchical QM/MD simulation on a grid consisting of 6 supercomputer centers in the US and Japan (in total of 150,000 processor hours), in which the number of processors change dynamically on demand and resources are allocated and migrated dynamically in response to faults. Furthermore, performance portability has been demonstrated on a wide range of platforms such as BlueGene/L, Altix 3000, and AMD Opteron-based Linux clusters.

Density functional study of 1,3,5-trinitro-1,3,5-triazine molecular crystal with van der Waals interactions

Volume dependence of the total energy and vibrational properties of crystalline l,3,5-trinitro-l,3,5-triazine (RDX) are calculated using the density functional theory (DFT). For this molecular crystal, properties calculated with a generalized gradient approximation to the exchange-correlation energy differ drastically from experimental values. This discrepancy arises from the inadequacy in treating weak van der Waals (vdW) interactions between molecules in the crystal, and an empirical vdW correction to DFT (DFT-D approach by Grimme) is shown to account for the dispersion effects accurately for the RDX crystal, while incurring little computational overhead. The nonempirical van der Waals density-functional (vdW-DF) method also provides an accurate description of the vdW corrections but with orders-of-magnitude more computation. We find that the vibrational properties of RDX are affected in a nontrivial manner by the vdW correction due to its dual role--reduction of the equilibrium volume and additional atomic forces.