Adjoint computational methods for 2D inverse design of linear transport equations on unstructured grids

Morales-Hernandez M, Zuazua E (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Computational and Applied Mathematics Sociedade Brasileira de Matemática Aplicada e Computacional

Book Volume: 38

Article Number: 168

Journal Issue: 4

DOI: 10.1007/s40314-019-0935-0

Abstract

We address the problem of inverse design of linear hyperbolic transport equations in 2D heterogeneous media. We develop numerical algorithms based on gradient-adjoint methodologies on unstructured grids. While the flow equation is compulsorily solved by means of a second order upwind scheme so to guarantee sufficient accuracy, the necessity of using the same order of approximation when solving the sensitivity or adjoint equation is examined. Two test cases, including Doswell frontogenesis, are analysed. We show the convenience of using a low order method for the adjoint resolution, both in terms of accuracy and efficiency. An analytical explanation for this fact is also provided in the sense that, when employing higher order schemes for the adjoint problem, spurious high frequency numerical components slow down the convergence process.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

University of Deusto / Universidad de Deusto ES Spain (ES) Universidad de Zaragoza ES Spain (ES)

How to cite

APA:

Morales-Hernandez, M., & Zuazua, E. (2019). Adjoint computational methods for 2D inverse design of linear transport equations on unstructured grids. Computational and Applied Mathematics, 38(4). https://dx.doi.org/10.1007/s40314-019-0935-0

MLA:

Morales-Hernandez, M., and Enrique Zuazua. "Adjoint computational methods for 2D inverse design of linear transport equations on unstructured grids." Computational and Applied Mathematics 38.4 (2019).

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