Author: George Biros - Georgia Tech.

Title: Parallel algorithms for boundary value problems


George Biros is an associate professor with joint appointment to the Georgia Tech College of Computing’s Computational Science and Engineering division and the Wallace H. Coulter Department of Biomedical Engineering. Prior to joining Georgia Tech, he was an assistant professor in Mechanical Engineering and Applied Mechanics, Bioengineering, and Computer and Information Science at the University of Pennsylvania, and earned his master’s and doctorate from Carnegie Mellon University. He joined Penn in 2003 after serving as a postdoctoral associate at the Courant Institute of Mathematical Sciences at New York University.


Boundary value problems are ubiquitous in computational science and engineering. I will discuss two classes of problems: multigrid for stencil-based non-uniform discretizations on bounded regular geometries, and integral equation solvers for exterior problems in complex geometries. I will discuss the basic algorithmic components of the proposed methodologies and give an overview of the challenges associated with scaling them to large number of cores. I will give details for a common component, an octree data structure. In particular, I will explain the construction, coarsening/refining, and balancing of octrees. I will present scalability results on up to 32,000 cores.