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June 20, 2026Acta NumericaOpen Access

Nonlinear model reduction for transport-dominated problems

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Authors

JHJan S. HesthavenBPBenjamin PeherstorferBUBenjamin Unger

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Overview

Survey explores nonlinear model reduction techniques for transport-dominated phenomena, suggesting efficiency in problem-solving.

Key Points

  • The aim is to evaluate nonlinear model reduction methods effective in transport-dominated contexts.
  • Categorizes techniques into transformation-based methods, online adaptive techniques, and combined formulations.
  • Focuses on three elements: nonlinear parametrizations, reduced dynamics, and online solvers.
  • Surveys existing approaches for tackling wave-like phenomena and coherent structures.
  • Identifies key elements for effective nonlinear model reduction in transport-dominated problems.
  • Demonstrates that linear approximations are inefficient in certain regimes.
  • Provides a comprehensive overview of the categorization of approaches.

Cite This Study

Hesthaven et al. (2026) studied this question.

synapsesocial.com/papers/6a362f3bdb0793dc1a536bc7https://doi.org/10.1017/s0962492926100294
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