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Spectrally accurate fast summation for periodic Stokes potentials
KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
2010 (engelsk)Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 229, nr 23, s. 8994-9010Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

A spectrally accurate method for the fast evaluation of N-particle sums of the periodic Stokeslet is presented. Two different decomposition methods, leading to one sum in real space and one in reciprocal space, are considered. An FFT based method is applied to the reciprocal part of the sum, invoking the equivalence of multiplications in reciprocal space to convolutions in real space, thus using convolutions with a Gaussian function to place the point sources on a grid. Due to the spectral accuracy of the method, the grid size needed is low and also in practice, for a fixed domain size, independent of N. The leading cost, which is linear in N, arises from the to-grid and from-grid operations. Combining this FFT based method for the reciprocal sum with the direct evaluation of the real space sum, a spectrally accurate algorithm with a total complexity of 0(N log N) is obtained. This has been shown numerically as the system is scaled up at constant density. (C) 2010 Elsevier Inc. All rights reserved.

sted, utgiver, år, opplag, sider
2010. Vol. 229, nr 23, s. 8994-9010
Emneord [en]
Viscous flow, Stokes equations, Potential theory, Ewald summation, FFT, Spectral accuracy
HSV kategori
Identifikatorer
URN: urn:nbn:se:kth:diva-26264DOI: 10.1016/j.jcp.2010.08.026ISI: 000283405700019Scopus ID: 2-s2.0-77956947285OAI: oai:DiVA.org:kth-26264DiVA, id: diva2:387717
Merknad
QC 20110114Tilgjengelig fra: 2011-01-14 Laget: 2010-11-21 Sist oppdatert: 2017-12-11bibliografisk kontrollert
Inngår i avhandling
1. Spectral Accuracy in Fast Ewald Methods and Topics in Fluid Interface Simulation
Åpne denne publikasjonen i ny fane eller vindu >>Spectral Accuracy in Fast Ewald Methods and Topics in Fluid Interface Simulation
2011 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

  This work contains two separate but related parts: one on spectrally  accurate and fast Ewald methods for electrostatics and viscous flow,  and one on micro- and complex fluid interface problems.  In Part I we are concerned with fast and spectrally accurate methods  to compute sums of slowly decaying potentials over periodic  lattices. We consider two PDEs: Laplace (electrostatics, the Coulomb  potential) and Stokes (viscous flow, the ``Stokeslet''  potential). Moreover, we consider both full and planar periodicity,  the latter meaning that periodicity applies in two dimensions and  the third is ``free''. These are major simulation tasks in current  molecular dynamics simulations and in many areas of computational  fluid mechanics involving e.g. particle suspensions.   For each of the four combinations of PDE and periodic structure, we  give spectrally accurate and O(N log N) fast methods based on  Ewald's or Ewald-like decompositions of the underlying potential  sums. In the plane-periodic cases we derive the decompositions in a  manner that lets us develop fast methods. Associated error estimates  are developed as needed throughout. All four methods can be placed  in the P3M/PME (Particle Mesh Ewald) family. We argue that they  have certain novel and attractive features: first, they are spectral  accurate; secondly, they use the minimal amount of memory possible  within the PME family; third, each has a clear and reliable view of  numerical errors, such that parameters can be chosen  wisely. Analytical and numerical results are given to support these  propositions. We benchmark accuracy and performance versus an  established (S)PME method.  Part II deals with free boundary problems, specifically numerical  methods for multiphase flow. We give an interface tracking method  based on a domain-decomposition idea that lets us split the  interface into overlapping patches. Each patch is discretized on a  uniform grid, and accurate and efficient numerical methods are given  for the equations that govern interface transport. We demonstrate  that the method is accurate and how it's used in immersed boundary,  and interface, Navier-Stokes methods, as well as in a boundary  integral Stokes setting.  Finally, we consider a problem in complex fluidics where there is a  concentration of surfactants \emph{on} the interface and the  interface itself is in contact with a solid boundary (the contact  line problem). We argue that the domain-decomposition framework is  attractive for formulating and treating complex models  (e.g. involving PDEs on a dynamic interface) and proceed with  developing various aspects of such a method.

sted, utgiver, år, opplag, sider
Stockholm: KTH Royal Institute of Technology, 2011. s. xv, 104
Serie
Trita-CSC-A, ISSN 1653-5723 ; 2011:19
HSV kategori
Identifikatorer
urn:nbn:se:kth:diva-48805 (URN)978-91-7501-195-0 (ISBN)
Disputas
2011-12-16, Salongen, KTHB, Osquars backe 25, Stockholm, 10:00 (engelsk)
Opponent
Veileder
Forskningsfinansiär
Swedish e‐Science Research Center
Merknad
QC 20111125Tilgjengelig fra: 2011-11-25 Laget: 2011-11-23 Sist oppdatert: 2012-05-24bibliografisk kontrollert

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