Adjoint DSMC for nonlinear Boltzmann equation constrained optimization

doi:10.1016/j.jcp.2021.110404

2021-08-01

Russel E. Caflisch

Denis A. Silantyev

Yunan Yang *

DOI：10.1016/j.jcp.2021.110404

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摘要

En 中文

Applications for kinetic equations such as optimal design and inverse problems often involve finding unknown parameters through gradient-based optimization algorithms. Based on the adjoint-state method, we derive two different frameworks for approximating the gradient of an objective functional constrained by the nonlinear Boltzmann equation. While the forward problem can be solved by the DSMC method, it is difficult to efficiently solve the high-dimensional continuous adjoint equation obtained by the optimize-then-discretize approach. This challenge motivates us to propose an adjoint DSMC method following the discretize-then-optimize approach for Boltzmann-constrained optimization. We also analyze the properties of the two frameworks and their connections. Several numerical examples are presented to demonstrate their accuracy and efficiency. (C) 2021 Elsevier Inc. All rights reserved.

Keyword:

Boltzmann equation

Direct simulation Monte Carlo methods

DSMC

Optimization

Adjoint-state method

Linear Boltzmann equation

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期刊

Journal of Computational Physics

IF:

3.8

论文数:

1.6W

被引数:

7.4W

机构

New York University

学者数:

4.4W

论文数: 3.9W

被引数: 5.8W

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