A3 Book section, Chapters in research books
Optimal Heating of an Indoor Swimming Pool (2020)

Wolfmayr, M. (2020). Optimal Heating of an Indoor Swimming Pool. In E. Lindner, A. Micheletti, & C. Nunes (Eds.), Mathematical Modelling in Real Life Problems : Case Studies from ECMI-Modelling Weeks (pp. 87-101). Springer. Mathematics in Industry, 33. https://doi.org/10.1007/978-3-030-50388-8_7

JYU authors or editors

Publication details

All authors or editors: Wolfmayr, Monika

Parent publication: Mathematical Modelling in Real Life Problems : Case Studies from ECMI-Modelling Weeks

Parent publication editors: Lindner, Ewald; Micheletti, Alessandra; Nunes, Cláudia

ISBN: 978-3-030-50387-1

eISBN: 978-3-030-50388-8

Journal or series: Mathematics in Industry

ISSN: 1612-3956

eISSN: 2198-3283

Publication year: 2020

Number in series: 33

Pages range: 87-101

Number of pages in the book: 165

Publisher: Springer

Place of Publication: Cham

Publication country: Switzerland

Publication language: English

DOI: https://doi.org/10.1007/978-3-030-50388-8_7

Publication open access: Not open

Publication channel open access: 

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/75311

Abstract

This work presents the derivation of a model for the heating process of the air of a glass dome, where an indoor swimming pool is located in the bottom of the dome. The problem can be reduced from a three dimensional to a two dimensional one. The main goal is the formulation of a proper optimization problem for computing the optimal heating of the air after a given time. For that, the model of the heating process as a partial differential equation is formulated as well as the optimization problem subject to the time-dependent partial differential equation. This yields the optimal heating of the air under the glass dome such that the desired temperature distribution is attained after a given time. The discrete formulation of the optimization problem and a proper numerical method for it, the projected gradient method, are discussed. Finally, numerical experiments are presented which show the practical performance of the optimal control problem and its numerical solution method discussed.

Keywords: mathematical optimisation; partial differential equations; numerical analysis; finite element method; applied mathematics; mathematical models; heating systems

Free keywords: heat equation; PDE-constrained optimization; control constraints; projected gradient method; finite element method; implicit Euler method

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Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 1