ITLApplied  Computational Mathematics Division
ACMD Seminar Series
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Stochastic Methods in Electrostatics: Applications to Biological and Physical Science

Michael Mascagni
Florida State University, Department of Computer Science

Thursday, June 16, 2005 15:00-16:00,
NIST North (820), Room 145
Thursday, June 16, 2005 13:00-14:00,
Room 5000

Abstract: We present an overview of stochastic methods for the solution of elliptic partial differential equations (PDEs). In particular, we consider the solution of linear and nonlinear problems that arise in electrostatics computations in various applications. We discuss the "Walk On Spheres" (WOS), "Greens Function First-Passage" (GFFP), and "Simulation-Tabulation" (S-T) Monte Carlo methods for the computation of capacitance, charge density, and related problems in materials science and biophysics. In addition, we introduce the "Walk on the Boundary" method for rapid calculation of capacitance. We then present generalizations that permit direct computation of charge density. Finally, we consider the problem of the electrostatics of large molecules in aqueous solution. An implicit model of the solvent leads to consideration of the Poisson-Boltzmann equation (PBE) as a continuum electrostatic model. We present new Monte Carlo methods for the solution of the linear PBE based on WOS, GFFP, and other methods. In particular, we solve an elliptic PDE system with the Poisson equation inside the molecule of interest, the linear PBE outside, and matching Neumann boundary conditions on the molecular surface. We demonstrate the intrinsic advantages of these methods on an electrostatic internal energy computation with the use of new, efficient Monte Carlo approaches to the boundary conditions. This work is joint with Dr. Nikolai Simonov of Florida State University and the Siberian Branch of the Russian Academy of Sciences.

Speaker Bio: Professor Mascagni received his PhD in Mathematics in 1987 from the Courant Institute of Mathematical Sciences on the topic of negative feedback in neural networks. He joined Florida State University in 1999 after experience with both the National Institutes of Health and the Institute for Defense Analyses. His current research interests include computational science, mathematical biology, Monte Carlo methods, numerical analysis, parallel/distributed/grid computing, random number generation, and software engineering. He is a member of the Association for Computing Machinery (ACM), the Society for Industrial and Applied Mathematics (SIAM), and the International Association for Mathematics and Computers in Simulation (IMACS).

Presentation Slides: PDF

Contact: P. M. Ketcham

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