Numerical methods for molecular dynamics
Abstract
This report summarizes our research progress to date on the use of multigrid methods for threedimensional elliptic partial differential equations, with particular emphasis on application to the PoissonBoltzmann equation of molecular biophysics. This research is motivated by the need for fast and accurate numerical solution techniques for threedimensional problems arising in physics and engineering. In many applications these problems must be solved repeatedly, and the extremely large number of discrete unknowns required to accurately approximate solutions to partial differential equations in threedimensional regions necessitates the use of efficient solution methods. This situation makes clear the importance of developing methods which are of optimal order (or nearly so), meaning that the number of operations required to solve the discrete problem is on the order of the number of discrete unknowns. Multigrid methods are generally regarded as being in this class of methods, and are in fact provably optimal order for an increasingly large class of problems. The fundamental goal of this research is to develop a fast and accurate numerical technique, based on multilevel principles, for the solutions of the PoissonBoltzmann equation of molecular biophysics and similar equations occurring in other applications. An outline of the report is as follows. Wemore »
 Authors:
 Publication Date:
 Research Org.:
 Illinois Univ., Urbana, IL (United States)
 Sponsoring Org.:
 USDOE; USDOE, Washington, DC (United States)
 OSTI Identifier:
 5436878
 Report Number(s):
 DOE/ER/250991
ON: DE92010934
 DOE Contract Number:
 FG0291ER25099
 Resource Type:
 Technical Report
 Country of Publication:
 United States
 Language:
 English
 Subject:
 74 ATOMIC AND MOLECULAR PHYSICS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; MOLECULES; DYNAMICS; PARTIAL DIFFERENTIAL EQUATIONS; NUMERICAL SOLUTION; BIOPHYSICS; BOLTZMANN EQUATION; EQUATIONS OF MOTION; ITERATIVE METHODS; PROGRESS REPORT; DIFFERENTIAL EQUATIONS; DOCUMENT TYPES; EQUATIONS; MECHANICS; 664000*  Atomic & Molecular Physics (1992); 990200  Mathematics & Computers
Citation Formats
Skeel, R.D.. Numerical methods for molecular dynamics. United States: N. p., 1991.
Web. doi:10.2172/5436878.
Skeel, R.D.. Numerical methods for molecular dynamics. United States. doi:10.2172/5436878.
Skeel, R.D.. Tue .
"Numerical methods for molecular dynamics". United States.
doi:10.2172/5436878. https://www.osti.gov/servlets/purl/5436878.
@article{osti_5436878,
title = {Numerical methods for molecular dynamics},
author = {Skeel, R.D.},
abstractNote = {This report summarizes our research progress to date on the use of multigrid methods for threedimensional elliptic partial differential equations, with particular emphasis on application to the PoissonBoltzmann equation of molecular biophysics. This research is motivated by the need for fast and accurate numerical solution techniques for threedimensional problems arising in physics and engineering. In many applications these problems must be solved repeatedly, and the extremely large number of discrete unknowns required to accurately approximate solutions to partial differential equations in threedimensional regions necessitates the use of efficient solution methods. This situation makes clear the importance of developing methods which are of optimal order (or nearly so), meaning that the number of operations required to solve the discrete problem is on the order of the number of discrete unknowns. Multigrid methods are generally regarded as being in this class of methods, and are in fact provably optimal order for an increasingly large class of problems. The fundamental goal of this research is to develop a fast and accurate numerical technique, based on multilevel principles, for the solutions of the PoissonBoltzmann equation of molecular biophysics and similar equations occurring in other applications. An outline of the report is as follows. We first present some background material, followed by a survey of the literature on the use of multigrid methods for solving problems similar to the PoissonBoltzmann equation. A short description of the software we have developed so far is then given, and numerical results are discussed. Finally, our research plans for the coming year are presented.},
doi = {10.2172/5436878},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue Jan 01 00:00:00 EST 1991},
month = {Tue Jan 01 00:00:00 EST 1991}
}

This report summarizes our research progress to date on the use of multigrid methods for threedimensional elliptic partial differential equations, with particular emphasis on application to the PoissonBoltzmann equation of molecular biophysics. This research is motivated by the need for fast and accurate numerical solution techniques for threedimensional problems arising in physics and engineering. In many applications these problems must be solved repeatedly, and the extremely large number of discrete unknowns required to accurately approximate solutions to partial differential equations in threedimensional regions necessitates the use of efficient solution methods. This situation makes clear the importance of developing methods whichmore »

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A numerical study of hybrid optimization methods for the molecular conformation problems
An important area of research in computational biochemistry is the design of molecules for specific applications. The design of these molecules depends on the accurate determination of their threedimensional structure or conformation. Under the assumption that molecules will settle into a configuration for which their energy is at a minimum, this design problem can be formulated as a global optimization problem. The solution of the molecular conformation problem can then be obtained, at least in principle, through any number of optimization algorithms. Unfortunately, it can easily be shown that there exist a large number of local minima for most moleculesmore »