Article
The Influence of Mesh Granularity on the Accuracy of FEM
Modelling of the Resonant State in a Microwave Chamber
Anna Ostaszewska-Li
˙
zewska
1,
* , Dominika Kopala
1
, Jakub Szałatkiewicz
2
, Roman Szewczyk
3
and Peter Råback
4
Citation: Ostaszewska-Li
˙
zewska, A.;
Kopala, D.; Szałatkiewicz, J.;
Szewczyk, R.; Råback, P. The
Influence of Mesh Granularity on the
Accuracy of FEM Modelling of the
Resonant State in a Microwave
Chamber. Appl. Sci. 2021, 11, 7932.
https://doi.org/10.3390/app11177932
Academic Editor: Arkadiusz Gola
Received: 11 August 2021
Accepted: 26 August 2021
Published: 27 August 2021
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4.0/).
1
Institute of Metrology and Biomedical Engineering, Faculty of Mechatronics, Warsaw University of
Technology, sw. A. Boboli 8, 02-525 Warsaw, Poland; dominika.kopala.stud@pw.edu.pl
2
Phoenix Surowce Sp z o.o., ul. Kasztanowa 18, 05-816 Michałowice Wie´s, Poland;
jakub.szalatkiewicz@gmail.com
3
Łukasiewicz Research Network—Industrial Research Institute for Automation and Measurements PIAP,
Al. Jerozolimskie 202, 02-486 Warsaw, Poland; roman.szewczyk@pw.edu.pl
4
CSC–IT Center for Science, P.O. Box 405, FI-02101 Espoo, Finland; peter.raback@csc.fi
* Correspondence: anna.lizewska@pw.edu.pl; Tel.: +48-790-016-546
Featured Application: Modelling and development of microwave resonant chambers for indus-
trial processes and laboratory tests equipment.
Abstract:
Microwave technology is widely used in different areas of advanced industry when energy
must be provided to water-containing and other materials. The main barrier in the development
of microwave devices is the possibility of efficient design by modelling a microwave system in
a resonant state. For technical systems, the finite element method is widely used. However, the
convergence process in the microwave finite element solver is sophisticated. The process itself and
the influence of mesh granularity on the accuracy of modelling of microwave chambers in resonant
states have not been investigated previously. The present paper aims to fill this gap. The resonance
conditions of a microwave chamber were tested from the point of view of spatial resolution of the
tetrahedral mesh used for open-source ELMER FEM software. The presented results experimentally
determine the limits of accuracy of the geometry of microwave resonant chamber finite element
method-based models. The determined values of microwave resonant chamber dimension tolerances
should be considered for both open-source and commercial software for microwave modelling.
Keywords:
microwave chamber; resonance conditions; finite element method; open source software;
ELMER FEM
1. Introduction
Microwaves are a form of electromagnetic radiation with wave frequencies (wave-
lengths) ranging from 300 MHz (
λ
= 1 m) up to 300 GHz (
λ
= 1 mm) [
1
]. Microwave technol-
ogy is nowadays present in numerous fields and is utilized in the radar and communication
industry [
2
], in laboratory measurements [
3
], in medical and scientific appliances [
4
], and
in the field of chemistry [
5
]. This article focuses on issues related to the use of microwaves
as an alternative method for heating and drying. Microwaves in this case are converted
into heat by interacting with dielectric dipolar materials.
The most common substance that can easily absorb microwave energy and can dis-
sipate it as heat is water [
6
] as it is presented in Figure 1. Additionally, some carbon-
based materials react like dielectric materials, as they contain freely moving delocalized
π-electrons [7–10].
Appl. Sci. 2021, 11, 7932. https://doi.org/10.3390/app11177932 https://www.mdpi.com/journal/applsci
