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On the Optimal Control of a Linear Peridynamics Model

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Abstract

We study a non-local optimal control problem involving a linear, bond-based peridynamics model. In addition to existence and uniqueness of solutions to our problem, we investigate their behavior as the horizon parameter \(\delta \), which controls the degree of nonlocality, approaches zero. We then study a finite element-based discretization of this problem, its convergence, and the so-called asymptotic compatibility as the discretization parameter h and the horizon parameter \(\delta \) tend to zero simultaneously.

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Acknowledgements

TM is supported by NSF grants DMS-1910180 and DMS-2206252. AJS and JMS have been supported by NSF grant DMS-2111228.

Funding

Tadele Mengesha is supported by National Science Foundation grants DMS-1910180 and DMS-2206252. Abner J. Salgado and Joshua M. Siktar have been supported by National Science Foundation grant DMS-2111228.

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  1. Department of Mathematics, University of Tennessee, Knoxville, TN, 37996, USA

    Tadele Mengesha, Abner J. Salgado & Joshua M. Siktar

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  1. Tadele Mengesha
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  2. Abner J. Salgado
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  3. Joshua M. Siktar
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Correspondence to Abner J. Salgado.

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Mengesha, T., Salgado, A.J. & Siktar, J.M. On the Optimal Control of a Linear Peridynamics Model. Appl Math Optim 88, 70 (2023). https://doi.org/10.1007/s00245-023-10045-x

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