Multilevel Evaluation of Coulomb Lattice Sums of Charge Systems

Suwan, Iyad; Brandt, Achi; Ilyin, Valery

doi:10.3844/jmssp.2012.361.372

Cited by 3 publications

(2 citation statements)

References 55 publications

(50 reference statements)

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“…A small number of researchers have addressed the problem from the perspective of learning and adaptation, even though considerable attention has been paid to the resource allocation problem in Grid computing (Senthilnathan and Purusothaman, 2012;Suwan et al, 2012b). At the same time, the possibility of effectively solving the resource allocation problems using groups of autonomous learning agents has been proved by Multi-Agent Systems (MAS) and distributed AI communities.…”

Section: Jcsmentioning

confidence: 99%

A Fuzzy Based Mechanism for Allocation of Grid Resources

Poonguzhali¹,

Shanmugavel

2013

Journal of Computer Science

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One of the main challenges in Grid computing is efficient allocation of resources (CPU-hours, network bandwidth) to the tasks submitted by users. In our previous work a technique to allocate resources in a grid environment using predicted data has been proposed. We propose utilization of the predicted data the resources were classified into three types; they are permanent resources, semi-permanent and sporadic resources. These types of resources may become available for a time that is either higher than the dwelling time or lower than the dwelling time in a grid environment. As the nature features are not known in such classification and then allocation mechanism, the performance cannot be increased further. In order to avoid such problem, in this study, a prediction model and an allocation factor are introduced. These parameters are determined for the sporadic type and semi-permanent type of resources and they are used in the fuzzy-based resource allocation mechanism. The incorporation of these parameters in the resource allocation leads to a remarkable resource utilization rate and makespan. This can be observed from the simulation and comparative results. From the results, it can be said that the proposed resource allocation mechanism has proved the performance in a dynamic environment

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Section: Jcsmentioning

confidence: 99%

A Fuzzy Based Mechanism for Allocation of Grid Resources

Poonguzhali¹,

Shanmugavel

2013

Journal of Computer Science

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“…The multilevel summation method was introduced for integral transforms in 1990. 3 It was later applied to particle monopoles and dipoles in 2D, 12 C 1 kernels for particles in 3D, 13 eigenvalues, 14 generalized Born potentials, 15 interseismic stress interactions, 16 Madelung constants of ionic crystals, 17 and dispersion interactions. 18 The MSM has been shown to have good parallel scalability compared to PME, 19 it is an option in the molecular simulators NAMD 4 and LAMMPS, 20 and it has been used for a GPU implementation of the electrostatic potential calculation 21 in the molecular visualization and analysis program VMD.…”

Section: Introductionmentioning

confidence: 99%

Multilevel summation with B-spline interpolation for pairwise interactions in molecular dynamics simulations

Hardy

Wolff

Xia

et al. 2016

The Journal of Chemical Physics

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The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients. This article explores the use of B-splines to increase the accuracy of the multilevel summation method (for nonperiodic boundaries) without incurring additional computation other than a preprocessing step (whose cost also scales linearly). To obtain accurate results efficiently involves technical difficulties, which are overcome by a novel preprocessing algorithm. Numerical experiments demonstrate that the resulting method offers substantial improvements in accuracy and that its performance is competitive with an implementation of the fast multipole method in general and markedly better for Hamiltonian formulations of molecular dynamics. The improvement is great enough to establish multilevel summation as a serious contender for calculating pairwise interactions in molecular dynamics simulations. In particular, the method appears to be uniquely capable for molecular dynamics in two situations, nonperiodic boundary conditions and massively parallel computation, where the fast Fourier transform employed in the particle-mesh Ewald method falls short.

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Extension and evaluation of the multilevel summation method for fast long-range electrostatics calculations

Moore

2014

The Journal of Chemical Physics

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Several extensions and improvements have been made to the multilevel summation method (MSM) of computing long-range electrostatic interactions. These include pressure calculation, an improved error estimator, faster direct part calculation, extension to non-orthogonal (triclinic) systems, and parallelization using the domain decomposition method. MSM also allows fully non-periodic long-range electrostatics calculations which are not possible using traditional Ewald-based methods. In spite of these significant improvements to the MSM algorithm, the particle-particle particle-mesh (PPPM) method was still found to be faster for the periodic systems we tested on a single processor. However, the fast Fourier transforms (FFTs) that PPPM relies on represent a major scaling bottleneck for the method when running on many cores (because the many-to-many communication pattern of the FFT becomes expensive) and MSM scales better than PPPM when using a large core count for two test problems on Sandia's Redsky machine. This FFT bottleneck can be reduced by running PPPM on only a subset of the total processors. MSM is most competitive for relatively low accuracy calculations. On Sandia's Chama machine, however, PPPM is found to scale better than MSM for all core counts that we tested. These results suggest that PPPM is usually more efficient than MSM for typical problems running on current high performance computers. However, further improvements to MSM algorithm could increase its competitiveness for calculation of long-range electrostatic interactions.

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Multilevel Evaluation of Coulomb Lattice Sums of Charge Systems

Cited by 3 publications

References 55 publications

A Fuzzy Based Mechanism for Allocation of Grid Resources

A Fuzzy Based Mechanism for Allocation of Grid Resources

Multilevel summation with B-spline interpolation for pairwise interactions in molecular dynamics simulations

Extension and evaluation of the multilevel summation method for fast long-range electrostatics calculations

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