Numerical methods for molecular dynamics. Progress report
This report summarizes our research progress to date on the use of multigrid methods for three-dimensional elliptic partial differential equations, with particular emphasis on application to the Poisson-Boltzmann equation of molecular biophysics. This research is motivated by the need for fast and accurate numerical solution techniques for three-dimensional 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 three-dimensional 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 multi-level principles, for the solutions of the Poisson-Boltzmann 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 Poisson-Boltzmann 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.
- Research Organization:
- Univ. of Illinois at Urbana-Champaign, IL (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- FG02-91ER25099
- OSTI ID:
- 10135540
- Report Number(s):
- DOE/ER/25099-1; ON: DE92010934
- Resource Relation:
- Other Information: PBD: [1991]
- Country of Publication:
- United States
- Language:
- English
Similar Records
Fast Computational Algorithms for Partial Differential Equations and Uncertainty Quantifications
Reduced Order Modeling for Prediction and Control of Large-Scale Systems.
Related Subjects
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
PARTIAL DIFFERENTIAL EQUATIONS
NUMERICAL SOLUTION
MOLECULES
DYNAMICS
PROGRESS REPORT
BIOPHYSICS
EQUATIONS OF MOTION
BOLTZMANN EQUATION
ITERATIVE METHODS
664000
990200
ATOMIC AND MOLECULAR PHYSICS
MATHEMATICS AND COMPUTERS