A Mathematical Model of Asynchronous Data Flow in Parallel Computers

Dr. Cory Hauck
Oak Ridge National Laboratory

Oak Ridge, TN
November 7, 2019
Cory Hauck

Abstract: In the first part of this talk, we present a simple ordinary differential equation model of data flow through nodes in a computer processor network. Under an appropriate asymptotic scaling, this model approximates a partial differential equation which treats data as a continuum fluid and takes the form of a non-standard conservation law. From this conservation law, we derive a Hamilton-Jacobi equation for which the existence and uniqueness of solutions can be proven. We then present numerical results that demonstrate qualitative agreement between the discrete and continuum models, and we explore the effects of variations in the parameters of the computing environment. In the second part of the talk, we introduce an auxiliary variable, reformulate the continuum model as a PDE system, and define weak solutions. We then identify a special class of solutions which take the form of piecewise constants separated by fronts. Qualitative properties such as propagation speed and stalling are investigated, both theoretically and numerically.

Speaker’s Bio:  Cory Hauck received his Bachelor's degree in Physics and Mathematics from the University of South Carolina in 1997 and, shortly after graduating, took an engineering position at Doty Scientific, Inc. in Columbia, SC. In 1999, he attended graduate school at the University of Maryland, receiving a Master's Degree in Electrical and Computer Engineering in 2004 and a Ph.D. in Applied Mathematics in 2006. Before coming to Oak Ridge, he was a postdoctoral research associate with the Center for Nonlinear Studies at the Computational Physics and Methods group at Los Alamos. Cory's research to date has focused on computational aspects of kinetic theory and hyperbolic PDE.