Paramatrized intrusive POD-based reduced-order models applied to advection–diffusion–reaction problems

P. Solán-Fustero; J. L. Gracia; A. Navas-Montilla; Pilar García-Navarro; P. Solán-Fustero; J. L. Gracia; A. Navas-Montilla; Pilar García-Navarro

doi:10.3934/mbe.2025066

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 7: 1825-1860. doi: 10.3934/mbe.2025066

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Paramatrized intrusive POD-based reduced-order models applied to advection–diffusion–reaction problems

1.
I3A and Fluid Mechanics Department, University of Zaragoza, Spain
2.
IUMA and Applied Mathematics Department, University of Zaragoza, Spain

Received: 16 April 2025 Revised: 22 May 2025 Accepted: 27 May 2025 Published: 05 June 2025

Parametrized problems involve high computational costs when looking for the proper values of their input parameters and solved with classical schemes. Reduced-order models (ROMs) based on the proper orthogonal decomposition act as alternative numerical schemes that speed up computational times while maintaining the accuracy of the solutions. They can be used to obtain solutions in a less expensive way for different values of the input parameters. The samples that compose the training set determine some computational limits on the solution that can be computed by the ROM. It is highly interesting to study what can be done to overcome these limits. In this article, the possibilities to obtain solutions to parametrized problems are explored and illustrated with several numerical cases using the two–dimensional (2D) advection–diffusion–reaction equation and the 2D wildfire propagation model.
- reduced-order modeling,
- POD methods,
- parametrized problems,
- computational resources,
- advection–diffusion–reaction equations
Citation: P. Solán-Fustero, J. L. Gracia, A. Navas-Montilla, Pilar García-Navarro. Paramatrized intrusive POD-based reduced-order models applied to advection–diffusion–reaction problems[J]. Mathematical Biosciences and Engineering, 2025, 22(7): 1825-1860. doi: 10.3934/mbe.2025066

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Abstract

Parametrized problems involve high computational costs when looking for the proper values of their input parameters and solved with classical schemes. Reduced-order models (ROMs) based on the proper orthogonal decomposition act as alternative numerical schemes that speed up computational times while maintaining the accuracy of the solutions. They can be used to obtain solutions in a less expensive way for different values of the input parameters. The samples that compose the training set determine some computational limits on the solution that can be computed by the ROM. It is highly interesting to study what can be done to overcome these limits. In this article, the possibilities to obtain solutions to parametrized problems are explored and illustrated with several numerical cases using the two–dimensional (2D) advection–diffusion–reaction equation and the 2D wildfire propagation model.

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