TY - GEN
T1 - Different approaches for Dirichlet and Neumann boundary optimal control
AU - Bornia, Giorgio
AU - Ratnavale, Saikanth
N1 - Publisher Copyright:
© 2018 Author(s).
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/7/10
Y1 - 2018/7/10
N2 - In this paper we consider different methods for formulating boundary optimal control problems of either Dirichlet or Neumann type. On one hand, standard approaches typically have the drawback of searching for the optimal controls in proper sub-spaces of natural trace spaces. Therefore, we consider alternative formulations with lifting functions that have several advantages. First of all, boundary controls can be determined on natural trace spaces, without additional regularity as required by standard approaches. This also leads to numerical discretizations that have the same rate of convergence for the unknowns defined on the domain and for those on the boundary. A potential drawback of the method consists in the use of control functions defined over the problem domain instead of on its boundary, thus increasing the number of degrees of freedom of the problem. This drawback can be compensated by using lifting functions with restricted support, whose boundary contains the control boundary under interest. Numerical results solving the optimality systems in an all-at-once approach show that it is possible to use restricted functions which do not substantially change the minimum value of the target functional with respect to the case of lifting functions with non-restricted support.
AB - In this paper we consider different methods for formulating boundary optimal control problems of either Dirichlet or Neumann type. On one hand, standard approaches typically have the drawback of searching for the optimal controls in proper sub-spaces of natural trace spaces. Therefore, we consider alternative formulations with lifting functions that have several advantages. First of all, boundary controls can be determined on natural trace spaces, without additional regularity as required by standard approaches. This also leads to numerical discretizations that have the same rate of convergence for the unknowns defined on the domain and for those on the boundary. A potential drawback of the method consists in the use of control functions defined over the problem domain instead of on its boundary, thus increasing the number of degrees of freedom of the problem. This drawback can be compensated by using lifting functions with restricted support, whose boundary contains the control boundary under interest. Numerical results solving the optimality systems in an all-at-once approach show that it is possible to use restricted functions which do not substantially change the minimum value of the target functional with respect to the case of lifting functions with non-restricted support.
UR - http://www.scopus.com/inward/record.url?scp=85049971181&partnerID=8YFLogxK
U2 - 10.1063/1.5043899
DO - 10.1063/1.5043899
M3 - Conference contribution
AN - SCOPUS:85049971181
T3 - AIP Conference Proceedings
BT - International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017
A2 - Tsitouras, Charalambos
A2 - Simos, Theodore
A2 - Simos, Theodore
A2 - Simos, Theodore
A2 - Simos, Theodore
A2 - Simos, Theodore
PB - American Institute of Physics Inc.
Y2 - 25 September 2017 through 30 September 2017
ER -