Parallel Fast Sweeping: Algorithms and Applications

Speaker: Miles Detrixhe, University of California Santa Barbara
October 20, 2016

Presentation

Abstract

The Fast Sweeping Method (FSM) is an efficient iterative finite-difference method for solving a range of nonlinear static (time-independent) Hamilton-Jacobi equations. The focus of this talk is the family of parallel FSMs which take advantage of modern high performance computing technology (HPC). In this talk I will discuss algorithms for uniform Cartesian meshes designed for both shared and distributed parallel systems. I will also present the graph theoretic approach for generalizing the parallel scheme to arbitrary grids including adaptive tree based and triangulated meshes. The jump from a serial algorithm to one that utilizes HPC has made possible the solution of problems that were previously intractable. During the talk I will demonstrate this with numerical results from a wide range of applications including optimal control, dynamic games, and seismic wave propagation.

Biography

Miles Detrixhe is a researcher in the University of California Santa Barbara's Department of Mechanical Engineering. He received a Bachelor’s degree from the University of Kansas in 2010. In 2013, Detrixhe worked at the Los Alamos National Laboratory to develop a numerical tool to interchange between a volume-of-fluid representation of a fluid and a level-set representation. He recently graduated with a Ph.D. from the University of California Santa Barbara's Department of Mechanical Engineering. There, he conducted original research on parallel fast sweeping algorithms and developed novel applications for the methods. A recent example is the mathematical formulation of isochrons of a dynamical system as the solution to a static Hamilton-Jacobi equation. Detrixhe's current research is on fast surface generation techniques for modeling biomolecules for electrostatic computations.

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