Regularizing the fast multipole method for use in molecular simulation

Shamshirgar, Davoud Saffar; Yokota, Rio; Tornberg, Anna‐Karin; Hess, Berk

doi:10.1063/1.5122859

Cited by 13 publications

(7 citation statements)

References 14 publications

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“…Whereas with double precision and a large enough Verlet buffer, the total drift can be reduced to <10 –7 kJ/mol/ps per atom for both PME and FMM (see Figure 11 in Kohnke et al), typical mixed-precision MD settings yield drifts of (5–8) × 10 –5 kJ/mol/ps per atom. Regularizing the FMM could help to meet the energy conservation requirements of MD simulation at even lower p , as shown by Shamshirgar et al…”

Section: Resultsmentioning

confidence: 97%

See 1 more Smart Citation

A GPU-Accelerated Fast Multipole Method for GROMACS: Performance and Accuracy

Kohnke

Kutzner

Grubmüller

2020

J. Chem. Theory Comput.

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An important and computationally demanding part of molecular dynamics simulations is the calculation of long-range electrostatic interactions. Today, the prevalent method to compute these interactions is particle mesh Ewald (PME). The PME implementation in the GROMACS molecular dynamics package is extremely fast on individual GPU nodes. However, for large scale multinode parallel simulations, PME becomes the main scaling bottleneck as it requires all-to-all communication between the nodes; as a consequence, the number of exchanged messages scales quadratically with the number of involved nodes in that communication step. To enable efficient and scalable biomolecular simulations on future exascale supercomputers, clearly a method with a better scaling property is required. The fast multipole method (FMM) is such a method. As a first step on the path to exascale, we have implemented a performance-optimized, highly efficient GPU FMM and integrated it into GROMACS as an alternative to PME. For a fair performance comparison between FMM and PME, we first assessed the accuracies of the methods for various sets of input parameters. With parameters yielding similar accuracies for both methods, we determined the performance of GROMACS with FMM and compared it to PME for exemplary benchmark systems. We found that FMM with a multipole order of 8 yields electrostatic forces that are as accurate as PME with standard parameters. Further, for typical mixed-precision simulation settings, FMM does not lead to an increased energy drift with multipole orders of 8 or larger. Whereas an ≈50 000 atom simulation system with our FMM reaches only about a third of the performance with PME, for systems with large dimensions and inhomogeneous particle distribution, e.g., aerosol systems with water droplets floating in a vacuum, FMM substantially outperforms PME already on a single node.

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Section: Resultsmentioning

confidence: 97%

“…As almost all energy errors are ≥10 −6 for single precision, they were omitted from the graph for the "maximal" parameter set (brown). FMM could help to meet the energy conservation requirements of MD simulation at even lower p, as shown by Shamshirgar et al 59 3.4. Performance of GPU FMM in GROMACS.…”

Section: Energy Conservation With Fmmmentioning

confidence: 92%

A GPU-Accelerated Fast Multipole Method for GROMACS: Performance and Accuracy

Kohnke

Kutzner

Grubmüller

2020

J. Chem. Theory Comput.

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“…When it comes to algorithms, we expect PME to remain the long-range interaction method of choice at low scale, but the limitations of the 3D FFT many-to-many communication for strong scaling requires a new approach. With recent extensions to the fast multipole method 51 , we expect it to become the algorithm of choice for the largest parallel runs. Future technological improvements, including faster interconnects and closer onchip integration as well as advances in both traditional 3,52 and coarse-grained reconfigurable architectures 53 could allow getting closer to this performance target.…”

Section: Discussionmentioning

confidence: 99%

Heterogeneous Parallelization and Acceleration of Molecular Dynamics Simulations in GROMACS

Páll,

Zhmurov,

Bauer

et al. 2020

Preprint

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The introduction of accelerator devices such as graphics processing units (GPUs) has had profound impact on molecular dynamics simulations and has enabled order-of-magnitude performance advances using commodity hardware. To fully reap these benefits, it has been necessary to reformulate some of the most fundamental algorithms, including the Verlet list, pair searching and cut-offs. Here, we present the heterogeneous parallelization and acceleration design of molecular dynamics implemented in the GROMACS codebase over the last decade. The setup involves a general cluster-based approach to pair lists and non-bonded pair interactions that utilizes both GPUs and CPU SIMD acceleration efficiently, including the ability to load-balance tasks between CPUs and GPUs. The algorithm work efficiency is tuned for each type of hardware, and to use accelerators more efficiently we introduce dual pair lists with rolling pruning updates. Combined with new direct GPU-GPU communication as well as GPU integration, this enables excellent performance from single GPU simulations through strong scaling across multiple GPUs and efficient multi-node parallelization.

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“…Hybrid BD-MC schemes require computing both forces and energy. Each of the many linear-scaling methods available to compute these quantities (for varying geometries and boundary conditions) falls into one of two categories: fast multipole methods [1][2][3], and variants of particle-(particle-particle)-mesh (P3M) methods, including pre-corrected FFT and spectral Ewald (SE) methods [4][5][6][7][8][9]. Our focus in this work is on the latter type of method, which tends to be more efficient than the former for homogeneous charge distributions.…”

Section: Introductionmentioning

confidence: 99%

A fast spectral method for electrostatics in doubly-periodic slit channels

Maxian,

Peláez,

Greengard

et al. 2021

Preprint

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We develop a fast method for computing the electrostatic energy and forces for a collection of charges in doubly-periodic slabs with jumps in the dielectric permittivity at the slab boundaries. Our method achieves spectral accuracy by using Ewald splitting to replace the original Poisson equation for nearly-singular sources with a smooth far-field Poisson equation, combined with a localized near-field correction.Unlike existing spectral Ewald methods, which make use of the Fourier transform in the aperiodic direction, we recast the problem as a two-point boundary value problem in the aperiodic direction for each transverse Fourier mode, for which exact analytic boundary conditions are available. We solve each of these boundary value problems using a fast, well-conditioned Chebyshev method. In the presence of dielectric jumps, combining Ewald splitting with the classical method of images results in smoothed charge distributions which overlap the dielectric boundaries themselves.We show how to preserve high order accuracy in this case through the use of a harmonic correction which involves solving a simple Laplace equation with smooth boundary data. We implement our method on Graphical Processing Units, and combine our doubly-periodic Poisson solver with Brownian Dynamics to study the equilibrium structure of double layers in binary electrolytes confined by dielectric boundaries. Consistent with prior studies, we find strong charge depletion near the interfaces due to repulsive interactions with image charges, which points to the need for incorporating polarization effects in understanding confined electrolytes, both theoretically and computationally.

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Regularizing the fast multipole method for use in molecular simulation

Cited by 13 publications

References 14 publications

A GPU-Accelerated Fast Multipole Method for GROMACS: Performance and Accuracy

A GPU-Accelerated Fast Multipole Method for GROMACS: Performance and Accuracy

Heterogeneous Parallelization and Acceleration of Molecular Dynamics Simulations in GROMACS

A fast spectral method for electrostatics in doubly-periodic slit channels

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