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An adaptive wavelet collocation method for the optimal heat source problem

Mahmood Khaksar-e Oshagh (Mosaheb Institute of Mathematics, Kharazmi University, Tehran, Iran)
Mostafa Abbaszadeh (Department of Mathematics and Computer Sciences, Amirkabir University of Technology, Tehran, Iran)
Esmail Babolian (Faculty of Mathematical Sciences and Computer‎, ‎Kharazmi University‎, Tehran, Iran)
Hossein Pourbashash (Department of Mathematics, University of Garmsar, Garmsar, Iran)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 17 November 2021

Issue publication date: 16 May 2022

61

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

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Emerald Publishing Limited

Copyright © 2021, Emerald Publishing Limited

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