SOME MORE ON LOGARITHMIC SINGULARITY INTEGRATION IN BOUNDARY ELEMENT METOD
Tomasz Rymarczyk
1Research & Development Centre Netrix S.A., Lublin, Poland, 2University of Economics and Innovation in Lublin, Faculty of Transport and Informatics (Poland)
https://orcid.org/0000-0002-3524-9151
Jan Sikora
sik59@wp.pl1Research & Development Centre Netrix S.A., Lublin, Poland, 2University of Economics and Innovation in Lublin, Faculty of Transport and Informatics (Poland)
https://orcid.org/0000-0002-9492-5818
Abstract
The accuracy of calculations of integrals with logarithmic singularities for two methods, namely the method of ignoring singularities and the method of subtraction (consisting in separating the singular part from the remaining non-singular), are presented in this paper. Only two-dimensional problems, like Dirichlet's problems, as well as acoustic problems formulated in the frequency domain are considered. Problems related to the accuracy of calculations are discussed and the influence of frequency, as well as the influence of the geometry of the analysed area on the accuracy of calculations, are indicated. When we talk about the influence of geometry, we mean not only discretization, but also the configuration of the area, such as the sharp edges of the boundary line, assuming the use of the classic, without any modifications, Boundary Element Method.
Keywords:
singular integral calculating, ignoring singularity method, singularity subtraction technique, acoustic wave propagation, Boundary Element Method (BEM)References
Aliabadi M. H.: The Boundary Element Method, Volume 2, Applications in Solids and Structures. John Wiley & Sons, LTD, 2002.
Google Scholar
Harwood A. R. G.: Numerical Evaluation of Acoustic Green’s Functions. PhD School of Mechanical, Aerospace & Civil Engineering, University of Manchester, 2014.
Google Scholar
Kirkup S.: The Boundary Element Method in Acoustics: A Survey. Appl. Sci. 9, 2019, 1642.
DOI: https://doi.org/10.3390/app9081642
Google Scholar
Rymarczyk T.: Tomographic Imaging in Environmental, Industrial and Medical Applications. Innovatio Press Publishing Hause 2019.
Google Scholar
Sikora J.: Boundary Element Method for Impedance and Optical Tomography. Warsaw University of Technology Publishing Hause, Warsaw 2007.
Google Scholar
Smith R. N. L.: Direct Gauss quadrature formulae for logarithmic singularities on isoparametric elements. Engineering Analysis with Boundary Elements 24, 2000, 161–167.
DOI: https://doi.org/10.1016/S0955-7997(99)00054-5
Google Scholar
[https://www.comsol.com/acoustics-module] (available: 10.01.2024).
Google Scholar
[https://reference.wolfram.com/language/PDEModels/tutorial/Acoustics/AcousticsFrequencyDomain.html] (available: 10.01.2024).
Google Scholar
Gaussian Quadrature Weights and Abscissae [po-max.github.io] (available: 10.01.2024).
Google Scholar
Authors
Tomasz Rymarczyk1Research & Development Centre Netrix S.A., Lublin, Poland, 2University of Economics and Innovation in Lublin, Faculty of Transport and Informatics Poland
https://orcid.org/0000-0002-3524-9151
Authors
Jan Sikorasik59@wp.pl
1Research & Development Centre Netrix S.A., Lublin, Poland, 2University of Economics and Innovation in Lublin, Faculty of Transport and Informatics Poland
https://orcid.org/0000-0002-9492-5818
Statistics
Abstract views: 283PDF downloads: 166
Most read articles by the same author(s)
- Grzegorz Kłosowski, Tomasz Rymarczyk, USING NEURAL NETWORKS AND DEEP LEARNING ALGORITHMS IN ELECTRICAL IMPEDANCE TOMOGRAPHY , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 7 No. 3 (2017)
- Tomasz Rymarczyk, Tomasz Cieplak, Grzegorz Kłosowski, Paweł Rymarczyk, DESIGN OF DATA ANALYSIS SYSTEMS FOR BUSINESS PROCESS AUTOMATION , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 8 No. 3 (2018)
- Tomasz Rymarczyk, Michał Gołąbek, Piotr Lesiak, Andrzej Marciniak, Mirosław Guzik, CONSTRUCTION OF AN ULTRASONIC TOMOGRAPH FOR ANALYSIS OF TECHNOLOGICAL PROCESSES IN THE FIELD OF REFLECTION AND TRANSMISSION WAVES , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 9 No. 4 (2019)
- Tomasz Rymarczyk, Grzegorz Kłosowski, THE USE OF ARTIFICIAL INTELLIGENCE IN AUTOMATED IN-HOUSE LOGISTICS CENTRES , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 8 No. 1 (2018)
- Tomasz Rymarczyk, Bartek Przysucha, Marcin Kowalski, Piotr Bednarczuk, ANALYSIS OF DATA FROM MEASURING SENSORS FOR PREDICTION IN PRODUCTION PROCESS CONTROL SYSTEMS , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 9 No. 4 (2019)
- Tomasz Rymarczyk, Krzysztof Polakowski, Jan Sikora, A NEW CONCEPT OF DISCRETIZATION MODEL FOR IMAGING IMPROVING IN ULTRASOUND TRANSMISSION TOMOGRAPHY , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 9 No. 4 (2019)
- Konrad Niderla, Tomasz Rymarczyk, Jan Sikora, MANUFACTURING PLANNING AND CONTROL SYSTEM USING TOMOGRAPHIC SENSORS , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 8 No. 3 (2018)
- Tomasz Rymarczyk, Jan Sikora, SINGULAR INTEGRATION IN BOUNDARY ELEMENT METHOD FOR HELMHOLTZ EQUATION FORMULATED IN FREQUENCY DOMAIN , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 11 No. 4 (2021)
- Grzegorz Kłosowski, Tomasz Rymarczyk, APPLICATION OF CONVOLUTIONAL NEURAL NETWORKS IN WALL MOISTURE IDENTIFICATION BY EIT METHOD , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 12 No. 1 (2022)
- Tomasz Rymarczyk, Grzegorz Kłosowski, SUPPLY CHAIN RISK MANAGEMENT BY MONTE CARLO METHOD , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 7 No. 4 (2017)