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dc.contributor.advisorDevanayagam, Palaniappanen_US
dc.contributor.advisorSarin, Viveken_US
dc.creatorKannan, Kasthuri Srinivasanen_US
dc.date.accessioned2010-01-15T00:09:39Zen_US
dc.date.accessioned2010-01-16T01:05:16Z
dc.date.available2010-01-15T00:09:39Zen_US
dc.date.available2010-01-16T01:05:16Z
dc.date.created2008-08en_US
dc.date.issued2009-05-15en_US
dc.identifier.urihttp://hdl.handle.net/1969.1/ETD-TAMU-2911
dc.description.abstractN-body problems encompass a variety of fields such as electrostatics, molecularbiology and astrophysics. If there are N particles in the system, the brute force algorithmfor these problems based on particle-particle interaction takes O(N2), whichis clearly expensive for large values of N. There have been some approximation algorithmslike the Barnes-Hut Method and the Fast Multipole Method (FMM) proposedfor these problems to reduce the complexity. However, the applicability of these algorithmsare limited to operators with analytic multipole expansions or restricted tosimulations involving low accuracy. The shortcoming of N-body treecodes are moreevident for particles in motion where the movement of the particles are not consideredwhen evaluating the potential. If the displacement of the particles are small, thenupdating the multipole coefficients for all the nodes in the tree may not be requiredfor computing the potential to a reasonable accuracy. This study focuses on some ofthe limitations of the existing approximation schemes and presents new algorithmsthat can be used for N-body simulations to efficiently compute potentials and forces.In the case of electrostatics, existing algorithms use Cartesian coordinates to evaluatethe potentials of the form r−, where 1. The use of such coordinates toseparate the variables results in cumbersome expressions and does not exploit the inherent spherical symmetry found in these kernels. For such potentials, we providea new multipole expansion series and construct a method which is asymptoticallysuperior than the current treecodes. The advantage of this expansion series is furtherdemonstrated by an algorithm that can compute the forces to the desired accuracy.For particles in motion, we introduce a new method in which we retain the multipolecoefficients when performing multipole updates (to the parent nodes) at every timestep. This results in considerable savings in time while maintaining the accuracy. Wefurther illustrate the efficiency of our algorithms through numerical experiments.en_US
dc.format.mediumelectronicen_US
dc.format.mimetypeapplication/pdfen_US
dc.language.isoen_USen_US
dc.subjectTreecodeen_US
dc.subjectBarnes-Huten_US
dc.titleTreecodes for Potential and Force Approximationsen_US
dc.typeBooken
dc.typeThesisen
thesis.degree.departmentComputer Scienceen_US
thesis.degree.disciplineComputer Scienceen_US
thesis.degree.grantorTexas A&M Universityen_US
thesis.degree.nameDoctor of Philosophyen_US
thesis.degree.levelDoctoralen_US
dc.contributor.committeeMemberAmato, Nancyen_US
dc.contributor.committeeMemberNelson, Paulen_US
dc.type.genreElectronic Dissertationen_US
dc.type.materialtexten_US
dc.format.digitalOriginborn digitalen_US


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