Adjoint computational methods for 2D inverse design of linear transport equations on unstructured grids
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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.
KeywordsLinear transport Inverse design Sensitivity First and second order schemes Gradient descent method Adjoint
Mathematics Subject Classification35L04 49M04 93B00
This work was done while the first author was a postdoctoral fellow of the team of the Advanced Grant NUMERIWAVES/FP7-246775 of the European Research Council. The second author was partially supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement NO: 694126-DyCon), the Grant MTM2017-92996-C2-1-R COSNET of MINECO (Spain), the ELKARTEK project KK-2018/00083 ROAD2DC of the Basque Government, the Air Force Office of Scientific Research under Award NO: FA9550-18-1-0242, the Marie Curie Training Action “ConFlex” SEP-210412102 and the ICON project of the French ANR.
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