Computation of magnetization, exchange stiffness, anisotropy, and susceptibilities in large-scale systems using GPU-accelerated atomistic parallel Monte Carlo algorithms

This paper refers to Monte Carlo magnetic simulations for large-scale systems. We propose scaling rules to facilitate analysis of mesoscopic objects using a relatively small amount of system nodes. In our model, each node represents a volume defined by an enlargement factor. As a consequence of this approach, the parameters describing magnetic interactions on the atomic level should also be re-scaled, taking into account the detailed thermodynamic balance as well as energetic equivalence between the real and re-scaled systems. Accuracy and efficiency of the model have been depicted through analysis of the size effects of magnetic moment configuration for various characteristic objects. As shown, the proposed scaling rules, applied to the disorder-based cluster Monte Carlo algorithm, can be considered suitable tools for designing new magnetic materials and a way to include low-level or first principle calculations in finite element Monte Carlo magnetic simulations.

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Sensitivity study of a large-scale air pollution model by using high-performance computations and Monte Carlo algorithms

10.1063/1.4827224 ◽

2013 ◽

Author(s):

Tz. Ostromsky ◽

I. Dimov ◽

R. Georgieva ◽

P. Marinov ◽

Z. Zlatev

Keyword(s):

Air Pollution ◽

Monte Carlo ◽

High Performance ◽

Large Scale ◽

Sensitivity Study ◽

Monte Carlo Algorithms ◽

Air Pollution Model

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Extended stochastic gradient Markov chain Monte Carlo for large-scale Bayesian variable selection

Biometrika ◽

10.1093/biomet/asaa029 ◽

2020 ◽

Vol 107 (4) ◽

pp. 997-1004

Author(s):

Qifan Song ◽

Yan Sun ◽

Mao Ye ◽

Faming Liang

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Latent Variables ◽

Large Scale ◽

Bayesian Variable Selection ◽

Stochastic Gradient ◽

Monte Carlo Algorithm ◽

Monte Carlo Algorithms ◽

Fixed Dimension

Summary Stochastic gradient Markov chain Monte Carlo algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed dimension and the log-posterior density is differentiable with respect to the parameters. This paper proposes an extended stochastic gradient Markov chain Monte Carlo algorithm which, by introducing appropriate latent variables, can be applied to more general large-scale Bayesian computing problems, such as those involving dimension jumping and missing data. Numerical studies show that the proposed algorithm is highly scalable and much more efficient than traditional Markov chain Monte Carlo algorithms.

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Monte Carlo Algorithms for Moments of Transition Arrays

International Astronomical Union Colloquium ◽

10.1017/s0252921100107468 ◽

1988 ◽

Vol 102 ◽

pp. 79-81

Author(s):

A. Goldberg ◽

S.D. Bloom

Keyword(s):

Monte Carlo ◽

State Vector ◽

Basis Vector ◽

Collective State ◽

Dispersion Characteristics ◽

Dipole Strength ◽

The Third ◽

Monte Carlo Algorithms ◽

Third Moment ◽

Very High

AbstractClosed expressions for the first, second, and (in some cases) the third moment of atomic transition arrays now exist. Recently a method has been developed for getting to very high moments (up to the 12th and beyond) in cases where a “collective” state-vector (i.e. a state-vector containing the entire electric dipole strength) can be created from each eigenstate in the parent configuration. Both of these approaches give exact results. Herein we describe astatistical(or Monte Carlo) approach which requires onlyonerepresentative state-vector |RV> for the entire parent manifold to get estimates of transition moments of high order. The representation is achieved through the random amplitudes associated with each basis vector making up |RV>. This also gives rise to the dispersion characterizing the method, which has been applied to a system (in the M shell) with≈250,000 lines where we have calculated up to the 5th moment. It turns out that the dispersion in the moments decreases with the size of the manifold, making its application to very big systems statistically advantageous. A discussion of the method and these dispersion characteristics will be presented.

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