N-body algorithms are the computational cornerstone for many problems in mathematical physics. In this talk, I will present (1) a brief history of N-body algorithms and their application to multiscale problems with an emphasis to fluid dynamics simulations; (2) give a brief overview of the most basic N-body algorithm, the Barnes-Hut method; and (3) conclude with applications of N-body algorithms to the simulation of Stokesian particulate flows.
Stokesian particulate flows are mixtures of a high viscosity Newtonian fluid and deformable capsules. Simulations of such flows require algorithms for infinite dimensional, highly stiff, nonlocal, and nonlinear dynamical systems. I will discuss some recent developments on numerical methods for such problems and I will report simulations with up to 260 million deformable capsules on the Oak Ridge National Laboratory's Cray XT5 "Jaguar" platform. The largest simulation amounts to 90 billion unknowns in space on 200,000 cores.
Prof. George Biros, The University of Texas at Austin
George Biros is the W. A. "Tex" Moncrief Chair in Simulation-Based Engineering Sciences in the Institute for Computational Engineering and Sciences and has Full Professor appointments with the departments of Mechanical Engineering and Computer Science at the University of Texas at Austin.
From 2008 to 2011, he was an Associate Professor in the School of Computational Science and Engineering at Georgia Tech and The Wallace H. Coulter Department of Biomedical Engineering at Georgia Tech and Emory University. From 2003 to 2008, he was an Assistant professor in Mechanical Engineering and Applied Mechanics, Bioengineering and Computer and Information Science at the University of Pennsylvania.
He received his BS in Mechanical Engineering from Aristotle University Greece (1995), his MS in Biomedical Engineering from Carnegie Mellon (1996), and his PhD in Computational Science and Engineering also from Carnegie Mellon (2000). He was a postdoctoral associate at the Courant Institute of Mathematical Sciences from 2000 to 2003.
Biros has research interests in Computational Science and Engineering. In particular, he works on numerical methods for integral and differential equations, parallel algorithms, and inverse problems. Applications include blood rheology, soft tissue mechanics, medical image analysis, electrophysiology, and forward and inverse scattering problems. Biros was among a team of researchers that won the IEEE/ACM SC03 and SC10 Gordon Bell Awards for special Achievement. His work has been further recognized for its importance with the IEEE/ACM SC03 best student paper (advisor), the IEEE/ACM SC02 best technical paper, and the IEEE/ACM SC07 best student paper finalist (advisor). In 2005, he received an Early Career Young Investigator Award from the U.S. Department of Energy. He serves as an Associate Editor for the SIAM Journal on Scientific Computing since January 2007 and as an Associate Editor for the ACM Transactions of Mathematical Software since 2011.
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