Multilevel Summation for the Fast Evaluation of Forces for the Simulation of Biomolecules

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Hardy, David Joseph

Contributors dc:contributor

• Skeel, Robert D.

• Computer Science

Language dc:language

eng

Identifier

(MiAaPQ)AAI3223608

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/81713