Collision-free spatial hash functions for structural analysis of billion-vertex chemical bond networks

State-of-the-art molecular dynamics (MD) simulations generate massive datasets involving billion-vertex chemical bond networks, which makes data mining based on graph algorithms such as K-ring analysis a challenge. This paper proposes an algorithm to improve the efficiency of ring analysis of large graphs, exploiting properties of K-rings and spatial correlations of vertices in the graph. The algorithm uses dual-tree expansion (DTE) and spatial hash-function tagging (SHAFT) to optimize computation and memory access. Numerical tests show nearly perfect linear scaling of the algorithm. Also a parallel implementation of the DTE + SHAFT algorithm achieves high scalability. The algorithm has been successfully employed to analyze large MD simulations involving up to 500 million atoms.     

Scalable and portable implementation of the fast multipole method on parallel computers

A scalable and portable Fortran code is developed to calculate Coulomb interaction potentials of charged particles on parallel computers, based on the fast multipole method. The code has a unique feature to calculate microscopic stress tensors due to the Coulomb interactions, which is useful in constant-pressure simulations and local stress analyses. The code is applicable to various boundary conditions, including periodic boundary conditions in two and three dimensions, corresponding to slab and bulk systems, respectively. Numerical accuracy of the code is tested through comparison of its results with those obtained by the Ewald summation method and by direct calculations. Scalability tests show the parallel efficiency of 0.98 for 512 million charged particles on 512 IBM SP3 processors. The timing results on IBM SP3 are also compared with those on IBM SP4.     

Million atom molecular dynamics simulations of materials on parallel computers

Recent advances in computing tecnology — parallel computer architectures, portable software and development of robust O(N) algorithms — have revolutionized the field of computer simulation. Using the space-time multiresolution molecular dynamics algorithms it is possible to carry out multimillion atom simulations of materials in different ranges of density, temperature and uniaxial strain.     

Large-scale atomistic modeling of nanoelectronic structures

Large-scale molecular-dynamics simulations are performed on parallel computers to study critical issues on ultrathin dielectric films and device reliability in next-decade semiconductor devices. New interatomic-potential models based on many-body, reactive, and quantum-mechanical schemes are used to study various atomic-scale effects: growth of oxide layers; dielectric properties of high-permittivity oxides; dislocation activities at semiconductor/dielectric interfaces; effects of amorphous layers and pixellation on atomic-level stresses in lattice-mismatched nanopixels; and nanoindentation testing of thin films. Enabling technologies for 10 to 100 million-atom simulations of nanoelectronic structures are discussed, which include multiresolution algorithms for molecular dynamics, load balancing, and data management. In ten years, this scalable software infrastructure will enable trillion-atom simulations of realistic device structures with sizes well beyond μm on petaflop computers     

Multiresolution atomistic simulations of dynamic fracture in nanostructured ceramics and glasses

Multimillion atom molecular-dynamics (MD) simulations are performed to investigate dynamic fracture in glasses and nanostructured ceramics. Using multiresolution algorithms, simulations are carried out for up to 70 ps on massively parallel computers. MD results in amorphous silica (a-SiO₂) reveal the formation of nanoscale cavities ahead of the crack tip. With an increase in applied strain, these cavities grow and coalesce and their coalescence with the advancing crack causes fracture in the system. Recent AFM studies of glasses confirm this behavior. The MD value for the critical stress intensity factor of a-SiO₂ is in good agreement with experiments. Molecular dynamics simulations are also performed for nanostructured silicon nitride (n-Si₃N₄). Structural correlations in n-Si₃N₄ reveal that interfacial regions between nanoparticles are amorphous. Under an external strain, nanoscale cavities nucleate and grow in interfacial regions while the crack meanders through these regions. The fracture toughness of n-Si₃N₄ is found to be six times larger than that of crystalline -Si₃N₄. We also investigate the morphology of fracture surfaces. MD results reveal that fracture surfaces of n-Si₃N₄ are characterized by roughness exponents 0.58 below and 0.84 above a certain crossover length, which is of the order of the size of Si₃N₄ nanoparticles. Experiments on a variety of materials reveal this behavior. The final set of simulations deals with the interaction of water with a crack in strained silicon. These simulations couple MD with a quantum-mechanical (QM) method based on the density functional theory (DFT) so that chemical processes are included. For stress intensity factor K=0.4 MPa m^1/2, we find that a decomposed water molecule becomes attached to dangling bonds at the crack or forms a Si-O-Si structure. At K=0.5 MPa m^1/2, water molecules decompose to oxidize Si or break Si-Si bonds.     

A divide-and-conquer/cellular-decomposition framework for million-to-billion atom simulations of chemical reactions

To enable large-scale atomistic simulations of material processes involving chemical reactions, we have designed linear-scaling molecular dynamics (MD) algorithms based on an embedded divide-and-conquer (EDC) framework: first principles-based fast reactive force-field (F-ReaxFF) MD; and quantum-mechanical MD in the framework of the density functional theory (DFT) on adaptive multigrids. To map these O(N) algorithms onto parallel computers with deep memory hierarchies, we have developed a tunable hierarchical cellular-decomposition (THCD) framework, which achieves performance tunability through a hierarchy of parameterized cell data/computation structures and adaptive load balancing through wavelet-based computational-space decomposition. Benchmark tests on 1920 Itanium2 processors of the NASA Columbia supercomputer have achieved unprecedented scales of quantum-mechanically accurate and well validated, chemically reactive atomistic simulations—0.56 billion-atom F-ReaxFF MD and 1.4 million-atom (0.12 trillion grid points) EDC–DFT MD—in addition to 18.9 billion-atom non reactive space–time multiresolution MD. The EDC and THCD frameworks expose maximal data localities, and consequently the isogranular parallel efficiency on 1920 processors is as high as 0.953. Chemically reactive MD simulations have been applied to shock-initiated detonation of energetic materials and stress-induced bond breaking in ceramics in corrosive environments.