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Fast Ewald summation for free-space Stokes potentials
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0001-7425-8029
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
2017 (English)In: Research in the Mathematical Sciences, ISSN 2197-9847, Vol. 4, no 1Article in journal (Refereed) Published
Abstract [en]

We present a spectrally accurate method for the rapid evaluation of free-space Stokes potentials, i.e., sums involving a large number of free space Green’s functions. We consider sums involving stokeslets, stresslets and rotlets that appear in boundary integral methods and potential methods for solving Stokes equations. The method combines the framework of the Spectral Ewald method for periodic problems (Lindbo and Tornberg in J Comput Phys 229(23):8994–9010, 2010. doi: 10.1016/j.jcp.2010.08.026 ), with a very recent approach to solving the free-space harmonic and biharmonic equations using fast Fourier transforms (FFTs) on a uniform grid (Vico et al. in J Comput Phys 323:191–203, 2016. doi: 10.1016/j.jcp.2016.07.028 ). Convolution with a truncated Gaussian function is used to place point sources on a grid. With precomputation of a scalar grid quantity that does not depend on these sources, the amount of oversampling of the grids with Gaussians can be kept at a factor of two, the minimum for aperiodic convolutions by FFTs. The resulting algorithm has a computational complexity of $$O(N \log N)$$ O ( N log N ) for problems with N sources and targets. Comparison is made with a fast multipole method to show that the performance of the new method is competitive.

Place, publisher, year, edition, pages
Springer, 2017. Vol. 4, no 1
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-203922DOI: 10.1186/s40687-016-0092-7ISI: 000412664600001OAI: oai:DiVA.org:kth-203922DiVA: diva2:1083032
Funder
Göran Gustafsson Foundation for Research in Natural Sciences and MedicineSwedish Research Council, 2011-3178Swedish e‐Science Research Center
Note

QC 20170411

Available from: 2017-03-20 Created: 2017-03-20 Last updated: 2017-12-12Bibliographically 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. 58 p.
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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Tornberg, Anna-Karin

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