Multilevel Summation for the Fast Evaluation of Forces for the Simulation of Biomolecules
Hardy, David Joseph
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https://hdl.handle.net/2142/81713
Description
Title
Multilevel Summation for the Fast Evaluation of Forces for the Simulation of Biomolecules
Author(s)
Hardy, David Joseph
Issue Date
2006
Doctoral Committee Chair(s)
Skeel, Robert D.
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Computer Science
Language
eng
Abstract
This thesis provides the most thorough investigation to date of the multilevel summation method and its use for computing electrostatic interactions. The mathematical and algorithmic details are presented along with a precise operation count. The approximation error from the method is analyzed, with error bounds formulated in terms of the fundamental method parameters. The cost and error analyses enable the determination of optimal method parameters for a desired error tolerance. Various interpolation schemes for the approximation are considered, and several alternative approaches to smoothing the electrostatic potential are examined. The use of the method with different boundary conditions is discussed, and it is shown that the application of multilevel summation to the periodic potential yields a finite sum, with the truncation expressed as bounded approximation error. The performance of multilevel summation is demonstrated to be superior to other commonly used fast methods for electrostatics, while providing comparable accuracy. The method is also shown to produce stable dynamics for cheaper, lower accuracy approximation.
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