Monte Carlo Methods: Algorithms and Implications for High-Performance Computing

Name:    Prof. Michael Mascagni                 
Address: Department of Computer Science and
         Department of Mathematics and
	 Department of Scientific Computing and
         Graduate Program in Molecular Biophysics	
         Florida State University
         Tallahassee, FL  32306-4530  USA
         AND
         Information Technology Laboratory
         Applied and Computational Mathematics Division
         100 Bureau Drive M/S 8910
         National Institute of Standards and Technology (NIST)
         Gaithersburg, MD  20899-8910  USA

Offices: 498 Dirac Science Library/207A Love Building (FSU) Building 225/Room B154 (NIST)
Phone:   +1.850.644.3290 (FSU) +1.301.975.2051 (NIST)
FAX:     +1.850.644.0058
e-mail:  mascagni@fsu.edu (FSU) mascagni@nist.gov (NIST)

Title: Monte Carlo Methods and Partial Differential Equations: Algorithms and Implications for High-Performance Computing

Abstract:
We give a brief overview of the history of the Monte Carlo method for the numerical solution of partial differential equations (PDEs) focusing on the Feynman-Kac formula for the probabilistic representation of the solution of the PDEs. We then take the example of solving the linearized Poisson-Boltzmann equation to compare and contrast standard deterministic numerical approaches with the Monte Carlo method. Monte Carlo methods have always been popular due to the ease of finding computational work that can be done in parallel. We look at how to extract parallelism from Monte Carlo methods, and some newer ideas based on Monte Carlo domain decomposition that extract even more parallelism. In light of this, we look at the implications of using Monte Carlo to on high-performance architectures and algorithmic resilience.