An adaptive wavelet collocation method for the optimal heat source problem
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 17 November 2021
Issue publication date: 16 May 2022
Abstract
Purpose
This paper aims to propose a new adaptive numerical method to find more accurate numerical solution for the heat source optimal control problem (OCP).
Design/methodology/approach
The main aim of this paper is to present an adaptive collocation approach based on the interpolating wavelets to solve an OCP for finding optimal heat source, in a two-dimensional domain. This problem arises when the domain is heated by microwaves or by electromagnetic induction.
Findings
This paper shows that combination of interpolating wavelet basis and finite difference method makes an accurate structure to design adaptive algorithm for such problems which usually have non-smooth solution.
Originality/value
The proposed numerical technique is flexible for different OCP governed by a partial differential equation with box constraint over the control or the state function.
Keywords
Acknowledgements
Mahmood Khaksar-e Oshagh was supported by Grant No. 96008495 from Iran National Science Foundation which is gratefully acknowledged. The authors would like to thank the anonymous reviewers for their careful reading and constructive comments to improve the quality of this work.
Citation
Khaksar-e Oshagh, M., Abbaszadeh, M., Babolian, E. and Pourbashash, H. (2022), "An adaptive wavelet collocation method for the optimal heat source problem", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 32 No. 7, pp. 2360-2382. https://doi.org/10.1108/HFF-04-2021-0284
Publisher
:Emerald Publishing Limited
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