DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Michael Mascagni, Florida State University/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 on high-performance architectures and algorithmic resilience.

**Time:** Friday, April 17, 2015, 1:30-2:30 p.m.

**Place:** Exploratory Hall, Room 4106

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491