Large-scale simulations on multiple Graphics Processing Units (GPUs) for the direct simulation Monte Carlo method

In this study, the application of the two-dimensional direct simulation Monte Carlo (DSMC) method using an MPI-CUDA parallelization paradigm on Graphics Processing Units (GPUs) clusters is presented. An all-device (i.e. GPU) computational approach is adopted where the entire computation is performed on the GPU device, leaving the CPU idle during all stages of the computation, including particle moving, indexing, particle collisions and state sampling. Communication between the GPU and host is only performed to enable multiple-GPU computation. Results show that the computational expense can be reduced by 15 and 185 times when using a single GPU and 16 GPUs respectively when compared to a single core of an Intel Xeon X5670 CPU. The demonstrated parallel efficiency is 75% when using 16 GPUs as compared to a single GPU for simulations using 30 million simulated particles. Finally, several very large-scale simulations in the near-continuum regime are employed to demonstrate the excellent capability of the current parallel DSMC method.     

Particle-in-cell charged-particle simulations, plus Monte Carlocollisions with neutral atoms, PIC-MCC

Many-particle charged-particle plasma simulations using spatial meshes for the electromagnetic field solutions, particle-in-cell (PIC) merged with Monte Carlo collision (MCC) calculations, are coming into wide use for application to partially ionized gases. The author emphasizes the development of PIC computer experiments since the 1950s starting with one-dimensional (1-D) charged-sheet models, the addition of the mesh, and fast direct Poisson equation solvers for 2-D and 3-D. Details are provided for adding the collisions between the charged particles and neutral atoms. The result is many-particle simulations with many of the features met in low-temperature collision plasmas; for example, with applications to plasma-assisted materials processing, but also related to warmer plasmas at the edges of magnetized fusion plasmas     

Beyond direct simulation Monte Carlo (DSMC) modelling of collision environments

ABSTRACT

Direct simulation Monte Carlo (DSMC) models have been successfully adopted and adapted to describe gas flows in a wide range of environments since the method was first introduced by Bird in the 1960s. We propose a new approach to modelling collisions between gas-phase particles in this work – operating in a similar way to the DSMC model, but with one key difference. Particles move in a mean field, generated by all previously propagated particles, which removes the requirement that all particles be propagated simultaneously. This yields a significant reduction in computation effort and lends itself to applications for which DSMC becomes intractable, such as when a species of interest is only a minor component of a large gas mixture.     

Monte Carlo simulation of supercooled liquids using a self-consistent local temperature

We combine Creutz energy conservation with Kawasaki spin exchange to simulate the microcanonical dynamics of a system of interacting particles. Relaxation occurs via Glauber spin-flip activation using a self-consistent temperature. Heterogeneity in the dynamics comes from finite-size constraints on the spin exchange that yield a distribution of correlated regions. The simulation produces a high-frequency response that can be identified with the boson peak, and a lower-frequency peak that contains non-Debye relaxation and non-Arrhenius activation, similar to the primary response of supercooled liquids.     

Monte Carlo simulations for two-dimensional quantum systems

The Trotter-Suzuki transformation has been used to obtain the classical representation ford-dimensional lattice systems with boson and fermion degrees of freedom. A Monte Carlo algorithm for the equivalent (d+1)-dimensional classical system is presented. Numerical results are shown for the Heisenberg-spin-glass, the XY model and the spinless fermion lattice gas in two dimensions.     

Monte Carlo simulations for the two-dimensional O(3) non-linear sigma model

We report on the results of Monte Carlo simulations for the two-dimensional O(3) non-linear sigma model. The estimates based on the combined use of the renormalization group and of the high temperature expansion are found to be in agreement with our “data”. We present good experimental evidence for the absence of any phase transition, as expected on theoretical grounds.     

A high-order Monte Carlo algorithm for the direct simulation of Boltzmann equation

A high-order algorithm of the direct simulation Monte Carlo (DSMC) method, H-DSMC, has been developed to simulate rarefied flow regimes. The mth order Taylor series expansion has been employed to obtain a more generalized form of the time discretization for the collision part of Boltzmann equation. In the purposed algorithm, the higher order collision terms are introduced as well as higher order terms in the time step of the probabilistic coefficients. These newly implemented higher order terms improve the accuracy and efficiency of the solution and enhance the convergence rate quite significantly. Comparison between results of the classic DSMC method and the H-DSMC method shows the promising performance of the introduced technique.     

Monte Carlo molecular dynamics simulations for two-dimensional magnets

A combined Monte Carlo molecular dynamics simulation technique is used to study thedynamic structure factor on a square lattice for isotropic Heisenberg and planar classical ferromagnetic spin Hamiltonians.     

Parallel cluster labeling for large-scale Monte Carlo simulations

We present an optimized version of a cluster labeling algorithm previously introduced by the authors. This algorithm is well suited for large-scale Monte Carlo simulations of spin models using cluster dynamics on parallel computers with large numbers of processors. The algorithm divides physical space into rectangular cells which are assigned to processors and combines a serial local labeling procedure with a relaxation process across nearest-neighbor processors. By controlling overhead and reducing inter-processor communication this method attains good computational speed-up and efficiency. Large systems of up to 65536² spins have been simulated at updating speeds of 11 nanosecs/site (90.7 × 10⁶ spin updates/sec) using state-of-the-art supercomputers. In the second part of the article we use the cluster algorithm to study the relaxation of magnetization and energy on large Ising models using Swendsen-Wang dynamics. We found evidence that exponential and power law factors are present in the relaxation process as has been proposed by Hackl et al. The variation of the power-law exponent λ_M taken at face value indicates that the value of Z_M falls in the interval 0.31–0.49 for the time interval analysed and appears to vanish asymptotically.     

Benchmark calculations for Monte Carlo simulations of electrontransport

Benchmark calculations have been performed for electron transport coefficients with an aim to produce a body of data required to verify the codes used in plasma modeling. The present code for the time resolved Monte Carlo simulation (MCS) was shown to represent properly DC transport coefficients in a purely electric field, in crossed electric and magnetic fields, and in the presence of nonconservative collisions, ionization, and attachment. In addition, we have suggested tests of the time dependent solutions. Relaxation of the initial transport coefficient may serve as an accurate test of the code as well as the input data for some fluid codes. In this paper, we show only one example, but several different sets of conditions and cross sections should be used as well. Finally, we propose application of the quasi-steady state results in RF fields. As an example we suggest calculation of the components of diffusion tensor showing anomalous longitudinal diffusion and calculations made with nonconservative collisions (ionization in this case). We also check the application of approximate formulas to determine drift velocity on the basis of total collision frequency and to determine a diffusion coefficient by using the Einstein relation. Other tests required to verify the transport data calculations are discussed as well     

Monte Carlo simulations of luminescence processes under quasi-equilibrium (QE) conditions

Previous researchers have carried out Monte Carlo simulations of thermoluminescence (TL) phenomena by considering the allowed transitions of charge carriers between the conduction band, electron traps and recombination centers. Such simulations have demonstrated successfully the effect of trap clustering on the kinetics of charge carriers in a solid, and showed that trap clustering can significantly change the observed luminescence properties. While such Monte Carlo simulations have been carried out for TL, there has been no such trap clustering studies for optically stimulated luminescence phenomena (OSL). This paper presents a simplified method of carrying out Monte Carlo simulations for TL and linearly modulated optically stimulated luminescence (LM-OSL) phenomena, based on the General One Trap (GOT) model, which is a special case of the one trap one recombination center model (OTOR) when quasi-equilibrium conditions (QE) hold. The simulated results show that the presence of small clusters consisting of a few traps in a solid can lead to multiple peaks in both the TL and LM-OSL signals. The effects of retrapping and degree of trap filling are simulated for such multi-peak luminescence signals, and insight is obtained into the mechanism producing these peaks. The method presented in this paper can be easily generalized for other types of luminescence solids in which the recombination probability varies with time.     

A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation

Bird's direct simulation Monte Carlo method for the Boltzmann equation is considered. The limit (as the number of particles tends to infinity) of the random empirical measures associated with the Bird algorithm is shown to be a deterministic measure-valued function satisfying an equation close (in a certain sense) to the Boltzmann equation. A Markov jump process is introduced, which is related to Bird's collision simulation procedure via a random time transformation. Convergence is established for the Markov process and the random time transformation. These results, together with some general properties concerning the convergence of random measures, make it possible to characterize the limiting behavior of the Bird algorithm.     

Supercooled superfluids in Monte Carlo simulations

We perform path integral Monte Carlo simulations to study the imaginary time dynamics of metastable supercooled superfluid states and nearly superglassy states of a one component fluid of spinless bosons square wells. Our study shows that the identity of the particles and the exchange symmetry is crucial for the frustration necessary to obtain metastable states in the quantum regime. Whereas the simulation time has to be chosen to determine whether we are in a metastable state or not, the imaginary time dynamics tells us if we are or not close to an arrested glassy state.     

Monte Carlo simulations of sexual reproduction

Modifying the Redfield model of sexual reproduction and the Penna model of biological aging, we compare reproduction with and without recombination in age-structured populations. In constrast to Redfield and in agreement with Bernardes we find sexual reproduction to be preferred to asexual one. In particular, the presence of old but still reproducing males helps the survival of younger females beyond their reproductive age.     

Monte Carlo simulation for ultra-small MOS devices

This paper discusses advanced needs of Monte Carlo simulation approaches for MOS silicon devices scaled below 0.1 μ m channel length. For predictive simulation over a wide range of biases, it is necessary to provide the Monte Carlo procedure with tuning capabilities to adjust the mobility through calibration of the interface roughness scattering. This is accomplished by introducing a semi-empirical procedure with a physical elastic scattering rate and an inelastic rate with tunable strength. To resolve the role of hot carriers in relation to oxide interface damage, it is also important to realize fully bipolar MOS simulation, so that one can analyze the transport of impact-ionization generated carriers and secondary ionization. As the devices become quite small, three-dimensional simulation can be not only feasible, but also necessary to resolve the granularity of doping profiles and the complete carrier–carrier and carrier–ion interactions. Issues of device Monte Carlo implementation on parallel environments are discussed, and a practical approach for resolving the short-range forces of the charge–charge interaction in three dimensionals is described. Several examples and preliminary results are presented to illustrate the various issues.     

Monte Carlo simulation for radiative kaon decays

For high precision measurements of K decays, the presence of radiated photons cannot be neglected. The Monte Carlo simulations must include the radiative corrections in order to compute the correct event counting and for efficiency calculations. In this paper, a method for simulating such decays is briefly described. Arrival of the final proofs: 24 November 2005