This was part of 
            Computational Challenges and Optimization in Kinetic Plasma Physics
          
        
            
      An Adjoint Method for the Boltzmann Equation
                  
            Russ Caflisch, New York University
            
              Thursday, February 22, 2024
            
          
              
    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).