SCATTERING BY CIRCULAR VOIDS WITH RIGID BOUNDARY: DIRECT AND INVERSE PROBLEMS FOR OPEN AND CLOSE DOMAINS


Abstract

Problems with the accuracy of calculations by the Boundary Element Method of acoustic and ultrasonic problems formulated in the frequency domain were presented in this paper. The inverse problem was formulated to identify the position and dimensions of the scattering object. A series of numerical experiments carried out with the help of the Boundary Elements Method proved the algorithm's robustness to noise and high precision in a wide frequency spectrum.


Keywords

acoustics-ultrasound wave propagation; BEM simulation; inverse problems; optimization methods

Abramowitz M., Stegun I. A.: Handbook of mathematical functions with formulas, graphs, and mathematical tables. John Wiley, New York 1973.

Athanasiadis C.: Scattering relations for point sources: Acoustic and electromagnetic waves. Journal of mathematical physics 43(11), 2002, 5683. DOI: https://doi.org/10.1063/1.1509089

Harwood A. R. G.: Numerical Evaluation of Acoustic Green’s Functions. PhD School of Mechanical, Aerospace & Civil Engineering, University of Manchester, Manchester 2014.

Kirkup S.: The Boundary Element Method in Acoustics: A Survey. Applied Sciences 9(8), 2019, 1642 [http://doi.org/10.3390/app9081642]. DOI: https://doi.org/10.3390/app9081642

Lynott G. M.: Efficient numerical evaluation of the scattering of acoustic and elastic waves by arrays of cylinders of arbitrary cross section. Thesis of Doctor of Philosophy. School of Natural Sciences, Department of Mathematics, University of Manchester, Manchester 2020.

Opieliński K. J., Pruchnicki P., Gudra T.: Ultrasonic Mammography with Circular Transducer Array. Archives of Acoustics 39(4), 2014, 559–568 [http://doi.org/10.2478/aoa-2014-0060]. DOI: https://doi.org/10.2478/aoa-2014-0060

Rymarczyk T.: Tomographic Imaging in Environmental, Industrial and Medical Applications. Innovatio Press Publishing Hause, Lublin 2019.

Rymarczyk T., Sikora J.: On precision acoustic wave calculation in a frequency domain. IAPGOS 2, 2022, 64–68 [http://doi.org/10.35784/iapgos.2966]. DOI: https://doi.org/10.35784/iapgos.2966

Sikora J.: Boundary Element Method for Impedance and Optical Tomography. Warsaw University of Technology Publishing Hause, Warsaw 2007.

https://www.comsol.com/acoustics-module

https://reference.wolfram.com/language/PDEModels/tutorial/Acoustics/AcousticsFrequencyDomain.html

Download

Published : 2022-12-30


Rymarczyk, T., & Sikora, J. (2022). SCATTERING BY CIRCULAR VOIDS WITH RIGID BOUNDARY: DIRECT AND INVERSE PROBLEMS FOR OPEN AND CLOSE DOMAINS. Informatyka, Automatyka, Pomiary W Gospodarce I Ochronie Środowiska, 12(4), 4-10. https://doi.org/10.35784/iapgos.3376

Tomasz Rymarczyk 
1 Research & Development Centre Netrix S.A., 2 WSEI University, Faculty of Transport and Informatics  Poland
http://orcid.org/0000-0002-3524-9151
Jan Sikora  sik59@wp.pl
1 Research & Development Centre Netrix S.A., 2 WSEI University, Faculty of Transport and Informatics  Poland
http://orcid.org/0000-0002-9492-5818