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.
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