Title: Optimization of the Boltzmann Equation

Abstract: The kinetics of rarefied gases and plasmas are described by the Boltzmann equation and numerically approximated by the Direct Simulation Monte Carlo (DSMC) method. We present an optimization method for DSMC, derived from an augmented Lagrangian. After a forward (in time) solution of DSMC, adjoint variables are found by a backwards solver. They are equal to velocity derivatives of an objective function, which can then be optimized. This is joint work with Yunan Yang (Cornell) and Denis Silantyev (U Colorado, Colorado Springs).

Bio: Russel Caflisch is an applied mathematician whose research is on analysis and numerical methods for physical sciences. He is known for analysis of the fluid dynamic limit in kinetic theory and of vortex sheets in incompressible flow, for mathematical modeling of epitaxial growth, and for development of Monte Carlo methods for kinetic theory and finance. He is currently director of the Courant Institute of Mathematical Sciences at New York University and was director of the Institute for Pure and Applied Mathematics (IPAM) at UCLA 2008-2017. He is a fellow of the Society for Industrial and Applied Mathematics, the American Mathematical Society, and the American Academy of Arts and Sciences, and is a member of the National Academy of Sciences.