ScaFaCoS – A Scalable library of Fast Coulomb Solvers for particle Systems

The simulation of classical particle systems by means of molecular dynamics techniques requires the evaluation of potentials and forces between particles to explore the phase or configuration space of the system. The interactions can be classified into short-range and long-range contributions. While short-range potentials are evaluated very efficiently by means of neighbor list techniques, which reduce the computational complexity to O(N), the long range interactions must be evaluated over all particle pair contributions in the system. This increases the complexity to O(N2), limiting very often the tractable system size to a few thousand particles. In charged or polarized systems, the evaluation of Coulomb interactions between particles is the dominant part of the computation. To tame the quadratic computational complexity of the problem, a number of different methods with O(N) and O(N log(N)) have been developed over the past. Prominent examples are the linearly scaling fast multipole method and FFT-based methods, like P3M, which exhibit an N log(N) scaling but also tree methods, originally designed for strongly inhomogeneous gravitational problems as well as variants of the multigrid method. To integrate an efficient, yet accurate method into an existing simulation code is often a time consuming task, because of the level of implementation complexity. This is even more pronounced when considering scalability on parallel computers. Furthermore, different types of boundary conditions might be necessary to consider, which are not implemented in a standard way even in community codes. To tackle large particle systems, solvers of low computational complexity and good scalability have to be considered. In order to facilitate the integration of such high level implementations of Coulomb solvers into existing programs, the scalable library ScaFaCoS was developed [1], which contains various methods for treating long range interactions in complex particle systems under various boundary conditions, e.g., open boundaries or periodic boundaries in various cartesian directions [2]. Implemented algorithms comprise the fast multipole method, Barnes–Hut tree method, P3M, multigrid methods, and a newly developed Maxwell solver MEMD. Several methods allow full error control and the optimal adjustment of method parameters to reduce run time. An overview will be given about the methods, their accuracy and stability, as well as results for performance and scalability on parallel clusters. REFERENCES 1. http://www.scafacos.de 2. Arnold, A., Fahrenberger, F. Holm, Chr., Lenz, O., Bolten, M., Dachsel, H., Halver,. R., Kabadshow, I., Gähler, F., Heber, F., Iseringhausen, J., Hofmann, M., Pippig, M., Potts, D., Sutmann, G. Comparison of scalable fast methods for long-range interactions. Phys. Rev. E. 2013, 88, 063308

Multi-level load balancing for parallel particle simulations

Ideas from multi-level relaxation methods are combined with load balancing techniques to achieve a convergence acceleration for a homogeneous work load distribution over a given set of processors when the underlying work function is inhomogeneously distributed in space. The algorithm is based on an orthogonal recursive bisection ap- proach which is evaluated via a hierarchically refined coarse integration. The method only requires a minimal information transfer across processors during the tree traversal steps. It is described of how to partition the system of processors to geometrical space, when global information is needed for the spatial tesselation

A consistent boundary method for the material point method - using imge particles to reduce boundary artefacts

The material point method (MPM) is a continuum-based numerical method hich discretises the object as material points. It is particulary ell suited for and has shon great success in the community for large deformations. Even though it has been idely adopted, ther are still fundamental questions to be addressed. In MPM the material properties are carried on the material points and the dynamics is calculated on an overlaid grid. Afterwards the material points are integrated according to are applied on the grid values, such as setting the grid momentum to zero for grid nodes inside a fixed wall. These disort the stress multiple grid lengths into the object. Inthis papr e propose a novel consistent boundary method to reduce these artefacts. The method is based on image particles, an approach originally developed for electrotatic problems. This concept allos a consistent formulation for the momentum field on both the grid and particles. We demonstrate a way of optimization that makes the explicit construction of mirror particles unnecessary. The explicit boundary method and image particle method are then compared using numerical examples featuring stress induced by simple shear and body forces. These numerical examples sho a significant reduction of boundary artefacts using the image particle method

Free energy function of dislocation densities by large scale atomistic simulations

The energy of complex dislocation microstructures is a fundamental property of continuum plasticity on the nanoscale. The question how the energy depends on the characteristic of a dislocation network is still not fully answered, although various - and often contradicting - models have been proposed in the literature. In this talk, this question is addressed using large scale Molecular Dynamics simulations of nanoindentation, which have been conducted to gain insight into the relationship between dislocation microstructures and the associated free energy from an atomistic level. Several single crystalline samples of aluminum are indented using varying tip radii to study possible size effects. In the largest sample, a 24nm tip is used to indent into a volume of 150³nm³ that consists of about 2×108 atoms. Thus, these atomistic simulations are reaching a size that is comparable to experiments. Dislocation microstructures are directly identified from the atomistic data, providing the mean to measure both the total and geometrically necessary dislocation densities in the volume and further related them to the energy which is obtained from the simulations as well. Using this approach, an atomistically informed free energy function for dislocation densities is derived from nanomechanical simulations, without the need to account for theoretical or phenomenological arguments commonly used in modeling crystal plasticity. Furthermore, several size effects are clearly observed in the conducted series of simulations with varying tip radii and sample volumes. Whereas for small indenter tips only plastic deformation by dislocations is observed, twinning and subgrains formation additionally occur in the samples underneath the indenter tips having a radius of 16nm or higher. This mechanism is having a significant influence on the measured geometrically necessary dislocation densities

Parallel Brownian dynamics simulations with the message-passing and PGAS programming models

This is a post-peer-review, pre-copyedit version of an article published in Computer Physics Communications. The final authenticated version is available online at: https://doi.org/10.1016/j.cpc.2012.12.015[Abstract] The simulation of particle dynamics is among the most important mechanisms to study the behavior of molecules in a medium under specific conditions of temperature and density. Several models can be used to compute efficiently the forces that act on each particle, and also the interactions between them. This work presents the design and implementation of a parallel simulation code for the Brownian motion of particles in a fluid. Two different parallelization approaches have been followed: (1) using traditional distributed memory message-passing programming with MPI, and (2) using the Partitioned Global Address Space (PGAS) programming model, oriented towards hybrid shared/distributed memory systems, with the Unified Parallel C (UPC) language. Different techniques for domain decomposition and work distribution are analyzed in terms of efficiency and programmability, in order to select the most suitable strategy. Performance results on a supercomputer using up to 2048 cores are also presented for both MPI and UPC codes.Ministerio de Ciencia e Innovación ; TIN2010-16735Xunta de Galicia; ref. 2010/

Multi-level load balancing for parallel particle simulations

Ideas from multi-level relaxation methods are combined with load balancing techniques to achieve a convergence acceleration for a homogeneous work load distribution over a given set of processors when the underlying work function is inhomogeneously distributed in space. The algorithm is based on an orthogonal recursive bisection ap- proach which is evaluated via a hierarchically refined coarse integration. The method only requires a minimal information transfer across processors during the tree traversal steps. It is described of how to partition the system of processors to geometrical space, when global information is needed for the spatial tesselation

Green's function enriched Poisson Solver for Electrostatics in Many-Particle Systems

A highly accurate method is presented for the construction of the charge density for the solution of the Poissonequation in particle simulations. The method is based on an operator adjusted source term which can be shown to produceexact results up to numerical precision in the case of a large support of the charge distribution, therefore compensating thediscretization error of finite difference schemes. This is achieved by balancing an exact representation of the known Green’sfunction of regularized electrostatic problem with a discretized representation of the Laplace operator. It is shown that theexact calculation of the potential is possible independent of the order of the finite difference scheme but the computationalefficiency for higher order methods is found to be superior due to a faster convergence to the exact result as a function of thecharge support

Mesoscopic Particle Methods for Solvent Effects in MD Simulations and Parallel Computing

Mesoscale simulations of hydrodynamic media have attracted great interest during the last years in order to bridge the gap between microscopic simulations on the atomistic level on the one side and macroscopic calculations on the continuum level on the other side. Various methods have been proposed which all have in common that they solve the Navier-Stokes equations in different types of discretisation, e.g. Lattice-Boltzmann simulations on a spatial grid. Grid-free methods are mainly based on the concept of particles and include methods like Dissipative Particle Dynamics (DPD), Smooth Particle Hydrodynamics (SPH) or Multi-Particle Collision Dynamics (MPC). In the latter approach, pseudo-particles are considered to carry both hydrodynamic information and thermal noise. With a small set of parameters (particle density, scattering angle, mean free path of a particle) it is possible to reproduce hydrodynamic behaviour. In particular, the regime of small Reynolds numbers has been investigated in detail, e.g. Poiseuille flow, shear flow, vortices or hydrodynamic long time tails, to name a few. In the present talk some recent developments in Multi-Particle Collision Dynamics are presented, including a scalable implementation (MP2C) for massively parallel computers. The method enables a coupling between molecular dynamics simulations and a mesoscopic solvent, taking into account hydrodynamic interactions between solutes. For dilute systems of solutes, load balancing issues are discussed. Furthermore, an implementation of a local thermostat is presented which takes into account statistical fluctuations in energy distributions of small set of particles and therefore enables a locall temperature control of systems under non-equilibrium conditions. A theoretical description enables the proper treatment of a thermostat into dynamical quantities, like dynamic structure factors. Large scale parallel applications are shown for semi-dilute polymer solutions in shear flow as well as flow simulations in stochastic geometries. Furthermore, first results of a hybrid coupling between a mesoscopic and atomistic description of a solvent is presented, which allows for an adaptive description of solvent properties