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A fast multipole method for evaluating exponential integral type kernels
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0002-4290-1670
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We present a fast multipole method for evaluation of sums with exponential  integral type kernels. These sums appear while solving free space Poisson problems in two dimensions and in the derivation of 1d-periodic Ewald sums. The presented method uses recurrence relations to derive multipole expansions for computing interactions between particles and far clusters.

Keyword [en]
Fast multipole method, Exponential integral, recurrence relation, Spectral Ewald
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-219774OAI: oai:DiVA.org:kth-219774DiVA, id: diva2:1165209
Funder
Swedish e‐Science Research CenterSwedish Research Council for Environment, Agricultural Sciences and Spatial Planning, 2011-3178
Note

QC 20171213

Available from: 2017-12-12 Created: 2017-12-12 Last updated: 2017-12-13Bibliographically approved
In thesis
1. Fast methods for electrostatic calculations in molecular dynamics simulations
Open this publication in new window or tab >>Fast methods for electrostatic calculations in molecular dynamics simulations
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis deals with fast and efficient methods for electrostatic calculations with application in molecular dynamics simulations. The electrostatic calculations are often the most expensive part of MD simulations of charged particles. Therefore, fast and efficient algorithms are required to accelerate these calculations. In this thesis, two types of methods have been considered: FFT-based methods and fast multipole methods (FMM).

The major part of this thesis deals with fast N.log(N) and spectrally accurate methods for accelerating the computation of pairwise interactions with arbitrary periodicity. These methods are based on the Ewald decomposition and have been previously introduced for triply and doubly periodic problems under the name of Spectral Ewald (SE) method. We extend the method for problems with singly periodic boundary conditions, in which one of three dimensions is periodic. By introducing an adaptive fast Fourier transform, we reduce the cost of upsampling in the non periodic directions and show that the total cost of computation is comparable with the triply periodic counterpart. Using an FFT-based technique for solving free-space harmonic problems, we are able to unify the treatment of zero and nonzero Fourier modes for the doubly and singly periodic problems. Applying the same technique, we extend the SE method for cases with free-space boundary conditions, i.e. without any periodicity.

This thesis is also concerned with the fast multipole method (FMM) for electrostatic calculations. The FMM is very efficient for parallel processing but it introduces irregularities in the electrostatic potential and force, which can cause an energy drift in MD simulations. In this part of the thesis we introduce a regularized version of the FMM, useful for MD simulations, which approximately conserves energy over a long time period and even for low accuracy requirements. The method introduces a smooth transition over the boundary of boxes in the FMM tree and therefore it removes the discontinuity at the error level inherent in the FMM.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2018. p. 58
Series
TRITA-MAT-A ; 2018:02
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-219775 (URN)978-91-7729-640-9 (ISBN)
Public defence
2018-01-26, F3, Lindstedtsvägen 26, Stockholm, 10:00 (English)
Opponent
Supervisors
Funder
Swedish e‐Science Research Center
Note

QC 20171213

Available from: 2017-12-13 Created: 2017-12-12 Last updated: 2017-12-13Bibliographically approved

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Saffar Shamshirgar, DavoodTornberg, Anna-Karin

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