Prof. Michael Mascagni, Florida State University
Location
Mathematics/Psychology : 104
Date & Time
October 17, 2014, 12:00 pm – 1:00 pm
Description
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.
Tags: