Year: 2022
Author: Giorgio Bornia, Andrea Chierici, Saikanth Ratnavale
International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 2-3 : pp. 329–346
Abstract
In this work we propose and compare multiple approaches for the formulation of boundary optimal control problems constrained by PDEs. In particular, we define a property of balanced regularity that is not satisfied by traditional approaches. In order to instead guarantee this property, we consider the use of other regularization terms, one involving fractional Sobolev norms and the other one based on the introduction of lifting functions. As required by the fractional norm approach, we present a semi-analytical numerical implementation of the fractional Laplacian operator. All the proposed formulations are also considered in conjunction with constraints of inequality type on the control variable. Numerical results are reported to compare all the presented regularization techniques.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2022-IJNAM-20484
International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 2-3 : pp. 329–346
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Boundary optimal control regularization methods inequality constraints