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An Adjoint Method for the Nonlinear Boltzmann Equation

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FKTW05 - Frontiers in numerical analysis of kinetic equations

We present an adjoint method for the spatially homogeneous, nonlinear Boltzmann equation, based on the “discretize then optimize” approach. The discretization (in time and velocity) is the DSMC method, and adjoint equations are derived from an augmented Lagrangian. After a forward (in time) solution of DSMC , the adjoint variables are found by a backwards solution. The adjoint variable is equal to a velocity derivative of an objective function. Numerical tests show that this gives accurate velocity derivatives and can be used in optimization for solutions of the Boltzmann equation. This is joint work with Yunan Yang and Denis Silantyev.

This talk is part of the Isaac Newton Institute Seminar Series series.

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