Table Of ContentLecture Notes
in Computational Science 89
and Engineering
Editors:
TimothyJ. Barth
MichaelGriebel
DavidE. Keyes
RistoM. Nieminen
DirkRoose
TamarSchlick
Forfurthervolumes:
http://www.springer.com/series/3527
(cid:127)
Michael Griebel Marc Alexander Schweitzer
(cid:2)
Editors
Meshfree Methods for Partial
Differential Equations VI
123
Editors
MichaelGriebel MarcAlexanderSchweitzer
Institutfu¨rNumerischeSimulation Institutfu¨rParalleleundVerteilteSysteme
Universita¨tBonn Universita¨tStuttgart
Bonn Stuttgart
Germany Germany
ISSN1439-7358
ISBN978-3-642-32978-4 ISBN978-3-642-32979-1(eBook)
DOI10.1007/978-3-642-32979-1
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2012951790
MathematicsSubjectClassification(2010):65N99,64M99,65M12,65Y99
(cid:2)c Springer-VerlagBerlinHeidelberg2013
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Preface
The Sixth International Workshop on Meshfree Methods for Partial Differential
EquationswasheldfromOctober4–6,2011,inBonn,Germany.Oneofthemajor
goalsofthisworkshopserieswastobringtogetherEuropean,AmericanandAsian
researchersworkinginthisexcitingfieldofinterdisciplinaryresearchona regular
basis.Tothisend,IvoBabusˇka,TedBelytschko,Jiun-ShyanChen,MichaelGriebel,
WingKamLiu,MarcAlexanderSchweitzerandHarryYserentantinvitedscientists
fromallovertheworldtoBonntostrengthenthemathematicalunderstandingand
analysisof meshfreediscretizations,butalso to promotethe exchangeofideas on
theirimplementationandapplication.
TheworkshopwasagainhostedbytheInstitutfu¨rNumerischeSimulationatthe
Rheinische Friedrich-Wilhelms-Universita¨tBonn with the financial supportof the
Sonderforschungsbereich 611 Singular Phenomena and Scaling in Mathematical
Models.Moreover,wewouldliketothankChristianRiegerwhocarriedmostofthe
loadasthelocalorganizerofthisworkshop.
This volume of LNCSE now comprises selected contributions of attendees of
the workshop. Their content ranges from applied mathematics to physics and
engineering which clearly indicates the maturity meshfree methods have reached
inrecentyears.Theyarebecomingmoreandmoremainstreaminmanyfieldsdue
totheirflexibilityandwideapplicability.
BonnandStuttgart,Germany MichaelGriebel
MarcAlexanderSchweitzer
v
(cid:127)
Contents
ESPResSo 3.1: Molecular Dynamics Software for
Coarse-GrainedModels......................................................... 1
AxelArnold,Olaf Lenz,StefanKesselheim, RudolfWeeber,
Florian Fahrenberger, Dominic Roehm, Peter Kosˇovan,
andChristianHolm
OntheRateofConvergenceoftheHamiltonianParticle-Mesh
Method ............................................................................ 25
Bob Peeters, Marcel Oliver, Onno Bokhove,
andVladimirMolchanov
Peridynamics:ANonlocalContinuumTheory............................... 45
EtienneEmmrich,RichardB.Lehoucq,andDimitriPuhst
ImmersedMolecularElectrokineticFiniteElementMethod
forNano-devicesinBiotechnologyandGeneDelivery....................... 67
WingKamLiu,AdrianM.Kopacz,Tae-RinLee,HansungKim,
andPaoloDecuzzi
CorrectedStabilizedNon-conformingNodalIntegrationin
MeshfreeMethods ............................................................... 75
MarcusRu¨ter,MichaelHillman,andJiun-ShyanChen
MultilevelPartitionofUnityMethodforEllipticProblems
withStronglyDiscontinuousCoefficients ..................................... 93
MarcAlexanderSchweitzer
HOLMES:ConvergentMeshfreeApproximationSchemesof
ArbitraryOrderandSmoothness.............................................. 111
Agust´ın Bompadre, Luigi E. Perotti, Christian J. Cyron,
andMichaelOrtiz
vii
viii Contents
A Meshfree Splitting Method for Soliton Dynamics in
NonlinearSchro¨dingerEquations.............................................. 127
MarcoCaliari,AlexanderOstermann,andStefanRainer
AMeshlessDiscretizationMethodforMarkovStateModels
AppliedtoExplicitWaterPeptideFoldingSimulations ..................... 141
KonstantinFackeldey,AlexanderBujotzek,andMarcusWeber
Kernel-BasedCollocationMethodsVersusGalerkinFinite
Element Methods for ApproximatingElliptic Stochastic
PartialDifferentialEquations .................................................. 155
GregoryE.FasshauerandQiYe
AMeshfreeMethodfortheAnalysisofPlanarFlowsof
InviscidFluids.................................................................... 171
VasilyN.Govorukhin
SomeRegularizedVersionsoftheMethodofFundamentalSolutions..... 181
CsabaGa´spa´r
ACharacteristicParticleMethodforTrafficFlowSimulations
onHighwayNetworks ........................................................... 199
YossiFarjounandBenjaminSeibold
MeshfreeModelinginLaminatedComposites................................ 221
DanielC.Simkins,Jr.,NathanCollier,andJosephB.Alford
ESPResSo 3.1: Molecular Dynamics Software
for Coarse-Grained Models
AxelArnold,OlafLenz,StefanKesselheim,RudolfWeeber,
FlorianFahrenberger,DominicRoehm,PeterKosˇovan,andChristianHolm
Abstract ESPRESSO is a package for Molecular Dynamics (MD) simulationsof
coarse-grained models. We present the most recent version 3.1 of our software,
highlighting some recent algorithmic extensions to version 1.0 presented in a
previous paper (Limbach et al. Comput Phys Commun 174:704–727, 2006). A
major strength of our package is the multitude of implemented methods for
calculating Coulomb and dipolar interactions in periodic and partially periodic
geometries. Here we present some more recent additions which include methods
forsystemswithdielectriccontraststhatfrequentlyoccurincoarse-grainedmodels
ofchargedsystemswithimplicitwatermodels,andanalternative,completelylocal
electrostaticsolverthatisbasedontheelectrodynamicequations.Wealsodescribe
ourapproachtorigidbodydynamicsthatusesMDparticleswithfixedrelativeposi-
tions.ESPRESSOnowgainedtheabilitytoaddbondsduringtheintegration,which
allows to study e.g. agglomeration.For hydrodynamicinteractions, a thermalized
lattice Boltzmann solver has been built into ESPRESSO, which can be coupled
to the MD particles. This computationally expensive algorithm can be greatly
accelerated by using Graphics Processing Units. For the analysis of time series
spanningmanyordersofmagnitudeintimescales,weimplementedahierarchical
genericcorrelationalgorithmforuser-configurableobservables.
Keywords Moleculardynamics (cid:129) Coarse- graining (cid:129) Lattice-Boltzmann
A.Arnold((cid:2))(cid:2)O.Lenz(cid:2)S.Kesselheim(cid:2)R.Weeber(cid:2)F.Fahrenberger(cid:2)D.Roehm(cid:2)P.Kosˇovan(cid:2)
C.Holm
InstituteforComputationalPhysics,Universita¨tStuttgart,Allmandring3,70569Stuttgart,
Germany
e-mail:[email protected]
M.GriebelandM.A.Schweitzer(eds.),MeshfreeMethodsforPartialDifferential 1
EquationsVI,LectureNotesinComputationalScienceandEngineering89,
DOI10.1007/978-3-642-32979-1 1,©Springer-VerlagBerlinHeidelberg2013
