345 research outputs found
GPU accelerated Monte Carlo simulation of Brownian motors dynamics with CUDA
This work presents an updated and extended guide on methods of a proper
acceleration of the Monte Carlo integration of stochastic differential
equations with the commonly available NVIDIA Graphics Processing Units using
the CUDA programming environment. We outline the general aspects of the
scientific computing on graphics cards and demonstrate them with two models of
a well known phenomenon of the noise induced transport of Brownian motors in
periodic structures. As a source of fluctuations in the considered systems we
selected the three most commonly occurring noises: the Gaussian white noise,
the white Poissonian noise and the dichotomous process also known as a random
telegraph signal. The detailed discussion on various aspects of the applied
numerical schemes is also presented. The measured speedup can be of the
astonishing order of about 3000 when compared to a typical CPU. This number
significantly expands the range of problems solvable by use of stochastic
simulations, allowing even an interactive research in some cases.Comment: 21 pages, 5 figures; Comput. Phys. Commun., accepted, 201
GPU-accelerated simulation of colloidal suspensions with direct hydrodynamic interactions
Solvent-mediated hydrodynamic interactions between colloidal particles can
significantly alter their dynamics. We discuss the implementation of Stokesian
dynamics in leading approximation for streaming processors as provided by the
compute unified device architecture (CUDA) of recent graphics processors
(GPUs). Thereby, the simulation of explicit solvent particles is avoided and
hydrodynamic interactions can easily be accounted for in already available,
highly accelerated molecular dynamics simulations. Special emphasis is put on
efficient memory access and numerical stability. The algorithm is applied to
the periodic sedimentation of a cluster of four suspended particles. Finally,
we investigate the runtime performance of generic memory access patterns of
complexity for various GPU algorithms relying on either hardware cache
or shared memory.Comment: to appear in a special issue of Eur. Phys. J. Special Topics on
"Computer Simulations on GPUs
Multi-Architecture Monte-Carlo (MC) Simulation of Soft Coarse-Grained Polymeric Materials: SOft coarse grained Monte-carlo Acceleration (SOMA)
Multi-component polymer systems are important for the development of new
materials because of their ability to phase-separate or self-assemble into
nano-structures. The Single-Chain-in-Mean-Field (SCMF) algorithm in conjunction
with a soft, coarse-grained polymer model is an established technique to
investigate these soft-matter systems. Here we present an im- plementation of
this method: SOft coarse grained Monte-carlo Accelera- tion (SOMA). It is
suitable to simulate large system sizes with up to billions of particles, yet
versatile enough to study properties of different kinds of molecular
architectures and interactions. We achieve efficiency of the simulations
commissioning accelerators like GPUs on both workstations as well as
supercomputers. The implementa- tion remains flexible and maintainable because
of the implementation of the scientific programming language enhanced by
OpenACC pragmas for the accelerators. We present implementation details and
features of the program package, investigate the scalability of our
implementation SOMA, and discuss two applications, which cover system sizes
that are difficult to reach with other, common particle-based simulation
methods
CUDA simulations of active dumbbell suspensions
We describe and analyze CUDA simulations of hydrodynamic interactions in
active dumbbell suspensions. GPU-based parallel computing enables us not only
to study the time-resolved collective dynamics of up to a several hundred
active dumbbell swimmers but also to test the accuracy of effective
time-averaged models. Our numerical results suggest that the stroke-averaged
model yields a relatively accurate description down to distances of only a few
times the dumbbell's length. This is remarkable in view of the fact that the
stroke-averaged model is based on a far-field expansion. Thus, our analysis
confirms that stroke-averaged far-field equations of motion may provide a
useful starting point for the derivation of hydrodynamic field equations.Comment: 16 pages, 4 figure
Strong scaling of general-purpose molecular dynamics simulations on GPUs
We describe a highly optimized implementation of MPI domain decomposition in
a GPU-enabled, general-purpose molecular dynamics code, HOOMD-blue (Anderson
and Glotzer, arXiv:1308.5587). Our approach is inspired by a traditional
CPU-based code, LAMMPS (Plimpton, J. Comp. Phys. 117, 1995), but is implemented
within a code that was designed for execution on GPUs from the start (Anderson
et al., J. Comp. Phys. 227, 2008). The software supports short-ranged pair
force and bond force fields and achieves optimal GPU performance using an
autotuning algorithm. We are able to demonstrate equivalent or superior scaling
on up to 3,375 GPUs in Lennard-Jones and dissipative particle dynamics (DPD)
simulations of up to 108 million particles. GPUDirect RDMA capabilities in
recent GPU generations provide better performance in full double precision
calculations. For a representative polymer physics application, HOOMD-blue 1.0
provides an effective GPU vs. CPU node speed-up of 12.5x.Comment: 30 pages, 14 figure
Direct numerical simulation of complex viscoelastic flows via fast lattice-Boltzmann solution of the Fokker–Planck equation
Micro–macro simulations of polymeric solutions rely on the coupling between macroscopic conservation equations for the fluid flow and stochastic differential equations for kinetic viscoelastic models at the microscopic scale. In the present work we introduce a novel micro–macro numerical approach, where the macroscopic equations are solved by a finite-volume method and the microscopic equation by a lattice-Boltzmann one. The kinetic model is given by molecular analogy with a finitely extensible non-linear elastic (FENE) dumbbell and is deterministically solved through an equivalent Fokker–Planck equation. The key features of the proposed approach are: (i) a proper scaling and coupling between the micro lattice-Boltzmann solution and the macro finite-volume one; (ii) a fast microscopic solver thanks to an implementation for Graphic Processing Unit (GPU) and the local adaptivity of the lattice-Boltzmann mesh; (iii) an operator-splitting algorithm for the convection of the macroscopic viscoelastic stresses instead of the whole probability density of the dumbbell configuration. This latter feature allows the application of the proposed method to non-homogeneous flow conditions with low memory-storage requirements. The model optimization is achieved through an extensive analysis of the lattice-Boltzmann solution, which finally provides control on the numerical error and on the computational time. The resulting micro–macro model is validated against the benchmark problem of a viscoelastic flow past a confined cylinder and the results obtained confirm the validity of the approach
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