Parallel Monte Carlo simulations by asynchronous domain decomposition

A simple general method for performing Metropolis Monte Carlo condensed matter simulations on parallel processors is examined. The method is based on the cyclic generation of temporary discrete domains within the system, which are separated by distances greater than the inter-particle interaction range. Particle configurations within each domain are then sampled independently by an assigned processor, whilst particles outside these domains are held fixed. Results for a simulated Lennard-Jones fluid confirm that the method rigorously satisfies the detailed balance condition, and that the efficiency of configurational sampling scales almost linearly with the number of processors. Furthermore, the number of iterations performed on a given processor can be essentially arbitrary, with very low levels of inter-process communication. Provided the CPU time per step is not state-dependent, the method can then be used to perform large calculations as unsupervised background tasks on heterogeneous networks.     

Cluster Monte Carlo and numerical mean field analysis for the water liquid-liquid phase transition

Using Wolff's cluster Monte Carlo simulations and numerical minimization within a mean field approach, we study the low temperature phase diagram of water, adopting a cell model that reproduces the known properties of water in its fluid phases. Both methods allow us to study the thermodynamic behavior of water at temperatures, where other numerical approaches - both Monte Carlo and molecular dynamics - are seriously hampered by the large increase of the correlation times. The cluster algorithm also allows us to emphasize that the liquid-liquid phase transition corresponds to the percolation transition of tetrahedrally ordered water molecules.     

Accurate and efficient methods for modeling colloidal mixtures in an explicit solvent using molecular dynamics

Most simulations of colloidal suspensions treat the solvent implicitly or as a continuum. However as particle size decreases to the nanometer scale, this approximation fails and one needs to treat the solvent explicitly. Due to the large number of smaller solvent particles, such simulations are computationally challenging. Additionally, as the ratio of nanoparticle size to solvent size increases, commonly-used molecular dynamics algorithms for neighbor finding and parallel communication become inefficient. Here we present modified algorithms that enable fast single processor performance and reasonable parallel scalability for mixtures with a wide range of particle size ratios. The methods developed are applicable for any system with widely varying force distance cutoffs, independent of particle sizes and independent of the interaction potential. As a demonstration of the new algorithm's effectiveness, we present results for the pair correlation function and diffusion constant for mixtures where colloidal particles interact via integrated potentials. In these systems, with nanoparticles 20 times larger than the surrounding solvent particles, our parallel molecular dynamics code runs more than 100 times faster using the new algorithms.     

Parallel Monte Carlo Driver (PMCD)—a software package for Monte Carlo simulations in parallel

Thanks to the dramatic decrease of computer costs and the no less dramatic increase in those same computer's capabilities and also thanks to the availability of specific free software and libraries that allow the set up of small parallel computation installations the scientific community is now in a position where parallel computation is within easy reach even to moderately budgeted research groups. The software package PMCD (Parallel Monte Carlo Driver) was developed to drive the Monte Carlo simulation of a wide range of user supplied models in parallel computation environments. The typical Monte Carlo simulation involves using a software implementation of a function to repeatedly generate function values. Typically these software implementations were developed for sequential runs. Our driver was developed to enable the run in parallel of the Monte Carlo simulation, with minimum changes to the original code that implements the function of interest to the researcher. In this communication we present the main goals and characteristics of our software, together with a simple study its expected performance. Monte Carlo simulations are informally classified as “embarrassingly parallel”, meaning that the gains in parallelizing a Monte Carlo run should be close to ideal, i.e. with speed ups close to linear. In this paper our simple study shows that without compromising the easiness of use and implementation, one can get performances very close to the ideal.     

MDVRY: a polarizable classical molecular dynamics package for biomolecules

The MDVRY classical molecular dynamics package is presented for the study of biomolecules in the gas and liquid phase. Electrostatic polarization has been implemented in the formalism of point induced dipoles following the model of Thole. Two schemes have been implemented for the calculation of induced dipoles, i.e. resolution of the self-consistent equations and a ‘Car-Parrinello’ dynamical approach. In this latter, the induced dipoles are calculated at each time step of the dynamics through the dynamics of additional degrees of freedom associated with the dipoles. This method saves computer time and allows to study polarized solvated proteins at a very low CPU cost. The program is written in C-language and runs on LINUX machines. A detailed manual of the code is given. The main features of the package are illustrated taking on examples of proteins in the gas phase or immersed in liquid water.

Program summary

Program title: MDVRYCatalogue identifier: AEBY_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBY_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 39 156No. of bytes in distributed program, including test data, etc.: 277 197Distribution format: tar.bz2Programming language: CComputer: Linux machines with FFTW Fourier Transform package installedOperating system: Linux machines, SUSE & RedHat distributionsClassification: 3, 16.13, 23External routines: FFTW (http://www.fftw.org/)Nature of problem: Molecular Dynamics Software package.Solution method: Velocity Verlet algorithm. The implemented force field is composed of intra-molecular interactions and inter-molecular interactions (electrostatics, polarization, van der Waals). Polarization is accounted through induced point dipoles at each atomic site. Supplementary degrees of freedom are associated to the induced dipoles so that a modified Hamiltonian of the dynamics is written. This allows to calculate the induced dipoles with a very fast ‘Car-Parrinello’ type of dynamics.Running time: The test run provided takes approximately 6 minutes to run.     

Coding coarse grained polymer model for LAMMPS and its application to polymer crystallization

We present a patch code for LAMMPS to implement a coarse grained (CG) model of poly(vinyl alcohol) (PVA). LAMMPS is a powerful molecular dynamics (MD) simulator developed at Sandia National Laboratories. Our patch code implements tabulated angular potential and Lennard-Jones-9-6 (LJ96) style interaction for PVA. Benefited from the excellent parallel efficiency of LAMMPS, our patch code is suitable for large-scale simulations.This CG-PVA code is used to study polymer crystallization, which is a long-standing unsolved problem in polymer physics. By using parallel computing, cooling and heating processes for long chains are simulated. The results show that chain-folded structures resembling the lamellae of polymer crystals are formed during the cooling process. The evolution of the static structure factor during the crystallization transition indicates that long-range density order appears before local crystalline packing. This is consistent with some experimental observations by small/wide angle X-ray scattering (SAXS/WAXS). During the heating process, it is found that the crystalline regions are still growing until they are fully melted, which can be confirmed by the evolution both of the static structure factor and average stem length formed by the chains. This two-stage behavior indicates that melting of polymer crystals is far from thermodynamic equilibrium. Our results concur with various experiments. It is the first time that such growth/reorganization behavior is clearly observed by MD simulations.Our code can be easily used to model other type of polymers by providing a file containing the tabulated angle potential data and a set of appropriate parameters.

Program summary

Program title: lammps-cgpvaCatalogue identifier: AEDE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDE_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GNU's GPLNo. of lines in distributed program, including test data, etc.: 940 798No. of bytes in distributed program, including test data, etc.: 12 536 245Distribution format: tar.gzProgramming language: C++/MPIComputer: Tested on Intel-x86 and AMD64 architectures. Should run on any architecture providing a C++ compilerOperating system: Tested under Linux. Any other OS with C++ compiler and MPI library should sufficeHas the code been vectorized or parallelized?: YesRAM: Depends on system size and how many CPUs are usedClassification: 7.7External routines: LAMMPS (http://lammps.sandia.gov/), FFTW (http://www.fftw.org/)Nature of problem: Implementing special tabular angle potentials and Lennard-Jones-9-6 style interactions of a coarse grained polymer model for LAMMPS code.Solution method: Cubic spline interpolation of input tabulated angle potential data.Restrictions: The code is based on a former version of LAMMPS.Unusual features.: Any special angular potential can be used if it can be tabulated.Running time: Seconds to weeks, depending on system size, speed of CPU and how many CPUs are used. The test run provided with the package takes about 5 minutes on 4 AMD's opteron (2.6 GHz) CPUs.References:

[1]

D. Reith, H. Meyer, F. Müller-Plathe, Macromolecules 34 (2001) 2335-2345.

[2]

H. Meyer, F. Müller-Plathe, J. Chem. Phys. 115 (2001) 7807.

[3]

H. Meyer, F. Müller-Plathe, Macromolecules 35 (2002) 1241-1252.

     

An optimized algorithm for ionized impurity scattering in Monte Carlo simulations

We present a new optimized model of Brookes-Herring ionized impurity scattering for use in Monte Carlo simulations of semiconductors. When implemented, it greatly decreases the execution time needed for simulations (typically by a factor of the order of 100), and also properly incorporates the great proportion of small angle scatterings that are neglected in the standard algorithm. It achieves this performance by using an anisotropic choice of scattering angle which accurately mimics the true angular distribution of ionized impurity scattering.     

REVLD: A coarse-grained model for polymers

A new model for polymers is presented. REVLD (Rigid, Excluded Volume, Langevin Dynamics) is similar to the coarse-grained, bead spring model for linear chains except that the inter-bead distance is rigidly constrained instead of using an inter-bead potential to encapsulate the connectivity. Static and dynamic results support that REVLD accurately reproduces the single-chain behavior of real polymers known from experiment, theory, and published data from existing models. Additionally, a time step can be used that is at least comparable to simulations using a FENE potential without introducing any computational overhead for accessing longer time scale modes. REVLD, and more simply the idea of using constraints in Cartesian coordinates for large simulations, was made computationally viable through the recent development of the algorithm MILC SHAKE. We expect it to improve established techniques and aid in the development of new models of import to large scale simulations that were not practicable before.     

Non-Markovian melting: a novel procedure to generate initial liquid like phases for small molecules for use in computer simulation studies

Computer simulations of liquid phases require an initial configuration from which to begin. The preparation of such an initial configuration or ‘snapshot’ often involves the melting of a solid phase. This melting is usually undertaken by heating the system at low pressure, followed by a lengthy re-compression and cooling once the melt has formed. This note looks at a novel technique to produce a liquid phase from a perfect crystal using a standard Monte Carlo simulation code.     

The truncated polynomial expansion Monte Carlo method for fermion systems coupled to classical fields: a model independent implementation

A software library is presented for the polynomial expansion method (PEM) of the density of states (DOS) introduced in [Y. Motome, N. Furukawa, J. Phys. Soc. Japan 68 (1999) 3853; N. Furukawa, Y. Motome, H. Nakata, Comput. Phys. Comm. 142 (2001) 410]. The library provides all necessary functions for the use of the PEM and its truncated version (TPEM) in a model independent way. The PEM/TPEM replaces the exact diagonalization of the one electron sector in models for fermions coupled to classical fields. The computational cost of the algorithm is O(N)—with N the number of lattice sites—for the TPEM [N. Furukawa, Y. Motome, J. Phys. Soc. Japan 73 (2004) 1482] which should be contrasted with the computational cost of the diagonalization technique that scales as O(N⁴). The method is applied for the first time to a double exchange model with finite Hund coupling and also to diluted spin-fermion models.

Program summary

Title of library:TPEMCatalogue identifier: ADVKProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVKProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandNo. of lines in distributed program, including test data, etc.: 1707No. of bytes in distributed program, including test data, etc.: 13 644Distribution format:tar.gzOperating system:Linux, UNIXNumber of files:4 plus 1 test programProgramming language used:CComputer:PCNature of the physical problem:The study of correlated electrons coupled to classical fields appears in the treatment of many materials of much current interest in condensed matter theory, e.g., manganites, diluted magnetic semiconductors and high temperature superconductors among others.Method of solution: Typically an exact diagonalization of the electronic sector is performed in this type of models for each configuration of classical fields, which are integrated using a classical Monte Carlo algorithm. A polynomial expansion of the density of states is able to replace the exact diagonalization, decreasing the computational complexity of the problem from O(N⁴) to O(N) and allowing for the study of larger lattices and more complex and realistic systems.     

Pathfinder: A parallel search algorithm for concerted atomistic events

An algorithm has been designed to search for the escape paths with the lowest activation barriers when starting from a local minimum-energy configuration of a many-atom system. The pathfinder algorithm combines: (1) a steered eigenvector-following method that guides a constrained escape from the convex region and subsequently climbs to a transition state tangentially to the eigenvector corresponding to the lowest negative Hessian eigenvalue; (2) discrete abstraction of the atomic configuration to systematically enumerate concerted events as linear combinations of atomistic events; (3) evolutionary control of the population dynamics of low activation-barrier events; and (4) hybrid task + spatial decompositions to implement massive search for complex events on parallel computers. The program exhibits good scalability on parallel computers and has been used to study concerted bond-breaking events in the fracture of alumina.     

Fast Fourier Transform simulation techniques for Coulomb gases

An improved approach to updating the electric field in simulations of Coulomb gases using the local lattice technique introduced by Maggs and Rossetto [A.C. Maggs, V. Rossetto, Phys. Rev. Lett. 88 (2002) 196402] is described and tested. Using the Fast Fourier Transform (FFT) an independent configuration of electric fields subject to Gauss' law constraint can be generated in a single update step. This FFT based method is shown to outperform previous approaches to updating the electric field in the simulation of a basic test problem in electrostatics of strongly correlated systems.     

Reduction of the self-forces in Monte Carlo simulations of semiconductor devices on unstructured meshes

When using an unstructured mesh for device geometry, the ensemble Monte Carlo simulations of semiconductor devices may be affected by unwanted self-forces resulting from the particle-mesh coupling. We report on the progress in minimisation of the self-forces on arbitrary meshes by showing that they can be greatly reduced on a finite element mesh with proper interpolation functions. The developed methodology is included into a self-consistent finite element 3D Monte Carlo device simulator. Minimising of the self-forces using the proper interpolation functions is tested by simulating the electron transport in a 10 nm gate length, 6.1 nm body thick, double gate metal-oxide-semiconductor field-effect transistor (MOSFET). We demonstrate the reduction in the self-force and illustrate the practical distinction by showing I-V characteristics for the device.     

A scalable parallel algorithm for large-scale reactive force-field molecular dynamics simulations

A scalable parallel algorithm has been designed to perform multimillion-atom molecular dynamics (MD) simulations, in which first principles-based reactive force fields (ReaxFF) describe chemical reactions. Environment-dependent bond orders associated with atomic pairs and their derivatives are reused extensively with the aid of linked-list cells to minimize the computation associated with atomic n-tuple interactions (n?4 explicitly and ?6 due to chain-rule differentiation). These n-tuple computations are made modular, so that they can be reconfigured effectively with a multiple time-step integrator to further reduce the computation time. Atomic charges are updated dynamically with an electronegativity equalization method, by iteratively minimizing the electrostatic energy with the charge-neutrality constraint. The ReaxFF-MD simulation algorithm has been implemented on parallel computers based on a spatial decomposition scheme combined with distributed n-tuple data structures. The measured parallel efficiency of the parallel ReaxFF-MD algorithm is 0.998 on 131,072 IBM BlueGene/L processors for a 1.01 billion-atom RDX system.     

Large scale fractal aggregates using the tunable dimension cluster-cluster aggregation

The tunable dimension cluster-cluster aggregation (tdCCA) [R. Thouy, R. Jullien, J. Phys. A: Math. Gen. 27 (1994) 2953] provides a computational model for creating fractal aggregates with a tunable fractal dimension. A straightforward implementation of this model requires a computational effort scaling with O(N_total⁴) of the number of particles N_total. By applying two minor changes to the algorithm the computational effort can be reduced to O(N_total²) and allows an efficient parallel implementation of the tdCCA. On a modern parallel computer a fractal aggregate of one million particles has been built in less than 24 h.     

Partitioning 3D space for parallel many-particle simulations

In a common approach for parallel processing applied to simulations of many-particle systems with short-ranged interactions and uniform density, the cubic simulation box is partitioned into domains of equal shape and size, each of which is assigned to one processor. We compare the commonly used simple-cubic (SC) domain shape to domain shapes chosen as the Voronoi cells of BCC, FCC, and HCP sphere packings. The latter three are found to result in superior partitionings with respect to communication overhead. Scaling of the domain shape is used to extend the range of applicability of these partitionings to a large set of processor numbers. The higher efficiency with BCC and FCC partitionings is demonstrated in simulations of the sillium model for amorphous silicon.     

Optimization techniques for parallel force-decomposition algorithm in molecular dynamic simulations

The efficiency and scalability of traditional parallel force-decomposition (FD) algorithms are not good because of high communication cost which is introduced when skew-symmetric character of force matrix is applied. This paper proposed a new parallel algorithm called UTFBD (Under Triangle Force Block Decomposition), which is based on a new efficient force matrix decomposition strategy. This strategy decomposes only the under triangle force matrix and greatly reduces parallel communication cost, e.g., the communication cost of UTFBD algorithm is only one third of Taylor's FD algorithm. UTFBD algorithm is implemented on Cluster system and applied to solve a physical nucleation problem with 500,000 particles. Numerical results are analyzed and compared among three algorithms, namely, FRI, Taylor's FD and UTFBD. The efficiency of UTFBD on 105 processors is 41.3%, and the efficiencies of FRI and Taylor's FD on 100 processors are 4.3 and 35.2%, respectively. In another words, the efficiency of UTFBD on about 100 processors is 37.0 and 6.1% higher than that of FRI and Taylor's FD, respectively. Results show that UTFBD can increase the efficiency of parallel MD (Molecular Dynamics) simulation to a higher degree and has a better scalability.     

Exploiting symmetries for exponential error reduction in path integral Monte Carlo

The path integral of a quantum system with an exact symmetry can be written as a sum of functional integrals each giving the contribution from quantum states with definite symmetry properties. We propose a strategy to compute each of them, normalized to the one with vacuum quantum numbers, by a Monte Carlo procedure whose cost increases power-like with the time extent of the lattice. This is achieved thanks to a multi-level integration scheme, inspired by the transfer matrix formalism, which exploits the symmetry and the locality in time of the underlying statistical system. As a result the cost of computing the lowest energy level in a given channel, its multiplicity and its matrix elements is exponentially reduced with respect to the standard path-integral Monte Carlo. We test the strategy with a one-dimensional harmonic oscillator, by computing the ratio of the parity odd over the parity even functional integrals and the two-point correlation function. The cost of the simulations scales as expected. In particular the effort for computing the lowest energy eigenvalue in the parity odd sector grows linearly with the time extent. At a fixed CPU time, the statistical error on the two-point correlation function is exponentially reduced with respect to the standard Monte Carlo procedure, and at large time distances it is lowered by many orders of magnitude.