Title: Optimization for the Boltzmann Equation
Abstract: We present an adjoint method for optimization of the Boltzmann equation for rarefied gas dynamics. The adjoint method is derived using a “discretize then optimize” approach. Discretization (in time and velocity) is via the Direct Simulation Monte Carlo (DSMC) method, and adjoint equations are derived from an augmented Lagrangian. For general collision models, DSMC requires the use of a rejection sampling step, which involves discontinuities that lead to a new term, involving a “score function”. This is joint work with Yunan Yang (Cornell) and Denis Silantyev (U Colorado, Colorado Springs).