Automatic Generation of FFT for Translations of Multipole Expansions in                 Spherical Harmonics

Kurzak, Jakub; Mirković, Dragan; Pettitt, B. Montgomery; Johnsson, S. Lennart

doi:10.1177/1094342008090915

Cited by 3 publications

(3 citation statements)

References 24 publications

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“…120 One of the most recent enhancements of the FMM method is given by the automatic generation of highly optimized FFTs (that incorporate knowledge of symmetries in the input arrays) for translations of multipole expansions in spherical harmonics. 125 Also, a very interesting recent development is the extension of an adaptive tree code and the FMM to charge densities with high angular momentum. 126 This is an ( ) method aimed at classical molecular simulations with stochastic boundaries that may include polarizable force fields and/or QM/MM potentials, and shows a lot of promise for the more sophisticated force fields under present development.…”

Section: Methods For Computing the Long-range Electrostatic Interacmentioning

confidence: 99%

“…A comprehensive and insightful review of the method is given by Kurzak and Pettitt . One of the most recent enhancements of the FMM method is given by the automatic generation of highly optimized FFTs (that incorporate knowledge of symmetries in the input arrays) for translations of multipole expansions in spherical harmonics . Also, a very interesting recent development is the extension of an adaptive tree code and the FMM to charge densities with high angular momentum .…”

Section: Methods For Computing the Long-range Electrostatic Interactionsmentioning

confidence: 99%

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Classical Electrostatics for Biomolecular Simulations

et al. 2013

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CONTENTS 1. Introduction 779 1.1. Electrostatic Problem 780 2. Methods for Computing the Long-Range Electrostatic Interactions 781 2.1. Ewald Summations 782 2.2. Particle−Mesh Methods That Use Fourier Transforms 784 2.3. Particle−Mesh Methods in Real Space 784 2.4. Fast Multipole Methods 786 2.5. Local Methods 786 2.6. Truncation Methods 787 2.6.1. Reaction Field Methods 789 2.7. Charge-Group Methods 789 2.8. Treatments and Artifacts of Boundary Conditions 790 3. Accurate Representation of the Electronic Charge 791 3.1. Charge Assignment Schemes 791 3.2. Point Multipoles 792 3.3. Continuous Representations of Molecular Charge Density 793 3.4. Polarization 795 3.5. Charge Transfer 797 3.6. Polarizable Force fields 798 4. Electrostatics in Multiscale Modeling 800 4.1. Long-Range Electrostatics in QM/MM 800 4.2. Continuous Functions in QM/MM 801 4.3. Electrostatics in Coarse-Grained Models 802 5. Other Developments 804 6. Summary and Perspective 805 Author Information 806 Corresponding Author 806 Notes 806 Biographies 806 Acknowledgments 806 References 806

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Section: Methods For Computing the Long-range Electrostatic Interacmentioning

confidence: 99%

Section: Methods For Computing the Long-range Electrostatic Interactionsmentioning

confidence: 99%

Classical Electrostatics for Biomolecular Simulations

et al. 2013

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“…Existing frameworks are PHiPAC [10] and ATLAS [11] for dense linear algebra, OSKI [12] for sparse linear algebra, FFTW [13] for fast Fourier transform, and SPIRAL [14] for digital signal processing. In the field of particle simulations, automatic tuning is used in [15] for the generation of FFT codes for multipole-tolocal translations in spherical harmonics. In [16], an FMM implementation is tuned for multi-core processors.…”

Section: Related Workmentioning

confidence: 99%

Automatic Tuning of the Fast Multipole Method Based on Integrated Performance Prediction

Dachsel

Hofmann

Lang

et al. 2012

2012 IEEE 14th International Conference on High Performance Computing and Communication &Amp; 2012 IEEE 9th International Confe

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The Fast Multipole Method (FMM) is an efficient, widely used method for the solution of N-body problems. One of the main data structures is a hierarchical tree data structure describing the separation into near-field and farfield particle interactions. This article presents a method for automatic tuning of the FMM by selecting the optimal FMM tree depth based on an integrated performance prediction of the FMM computations. The prediction method exploits benchmarking of significant parts of the FMM implementation to adapt the tuning to the specific hardware system being used. Furthermore, a separate analysis phase at runtime is used to predict the computational load caused by the specific particle system to be computed. The tuning method was integrated into an FMM implementation. Performance results show that a reliable determination of the tree depth is achieved, thus leading to minimal execution times of the FMM algorithm.

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A Two-Step Surface Reconstruction Method Using Signed Marching Cubes

2022

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In this paper, we explore a new approach, a two-step surface reconstruction method to extract the target isosurface from a given implicit function efficiently. Our main contribution is that we improve the surface reconstruction process by accelerating the speed of evaluation using signed marching cubes. The basic strategy is to filter the invalid voxels that do not intersect with the target isosurface in a low-cost manner, and to evaluate the valid voxels that intersect with the target isosurface accurately. The improved signed marching cubes method consists of a rough evaluation step and an exact evaluation step. The coarse evaluation step evaluates the points of all voxels using the fast multipole method with a lower order. After the rough evaluation step, the voxels that intersect with the target isosurface are screened out. Then, the exact evaluation step evaluates the points of filtered voxels using the fast multipole method with a higher order. The experimental results show that, compared with the traditional marching cubes method, the improved reconstruction method reduces the amounts of calculation for invalid voxels that do not intersect with the target isosurfaces, which is useful to improve the efficiency of surface reconstruction.

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Automatic Generation of FFT for Translations of Multipole Expansions in Spherical Harmonics

Cited by 3 publications

References 24 publications

Classical Electrostatics for Biomolecular Simulations

Classical Electrostatics for Biomolecular Simulations

Automatic Tuning of the Fast Multipole Method Based on Integrated Performance Prediction

A Two-Step Surface Reconstruction Method Using Signed Marching Cubes

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