Adjoint DSMC for nonlinear Boltzmann equation constrained optimization

Caflisch, Russel; Silantyev, Denis; Yang, Yunan

doi:10.1016/j.jcp.2021.110404

Adjoint DSMC for nonlinear Boltzmann equation constrained optimization

Journal Article · Tue May 04 00:00:00 EDT 2021 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2021.110404· OSTI ID:1849936

^[1]; ^[2]; Yang, Yunan ^[2]

New York Univ. (NYU), NY (United States); OSTI
New York Univ. (NYU), NY (United States)

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. Here, several numerical examples are presented to demonstrate their accuracy and efficiency.

View Accepted Manuscript (DOE)

Research Organization:: New York Univ. (NYU), NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC); National Science Foundation (NSF)

Grant/Contract Number:: FG02-86ER53223

OSTI ID:: 1849936

Alternate ID(s):: OSTI ID: 1782909
OSTI ID: 23203758

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 439; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
Boltzmann equation
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Adjoint DSMC for nonlinear Boltzmann equation constrained optimization

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