Abstract
The primary objective of this work is to develop a computational framework for the inverse problem of identifying variable parameters appearing non-linearly in a variational problem. We propose a new first-order adjoint method and two new second-order adjoint methods. All the derivative formulas are given in continuous as well as discrete setting. Detailed numerical examples are given to show the feasibility of the proposed framework.
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Acknowledgements
Baasansuren Jadamba’s work is supported by RIT’s COS FEAD grant for 2016-2017. Akhtar Khan is supported by a grant from the Simons Foundation (\(\#\)210443) and RIT’s COS FEAD grant for 2016-2017. Miguel Sama’s work is partially supported by Ministerio de Economa y Competitividad (Spain), project MTM2015-68103-P.
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Cho, M., Jadamba, B., Kahler, R., Khan, A.A., Sama, M. (2017). First-Order and Second-Order Adjoint Methods for the Inverse Problem of Identifying Non-linear Parameters in PDEs. In: Manchanda, P., Lozi, R., Siddiqi, A. (eds) Industrial Mathematics and Complex Systems. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-10-3758-0_9
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DOI: https://doi.org/10.1007/978-981-10-3758-0_9
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