APPLICATION OF FINITE DIFFERENCE METHOD FOR MEASUREMENT SIMULATION IN ULTRASOUND TRANSMISSION TOMOGRAPHY

Antunes dos Santos Júnior, A. (2012). Ultrasonic Waves. BoD – Books on Demand.
DOI: https://doi.org/10.5772/1411   Google Scholar

Asadzadeh, M. (2020). An introduction to the finite element method for differential equations. John Wiley & Sons.
DOI: https://doi.org/10.1002/9781119671688   Google Scholar

Benito, J., García, A., Gavete, L., Negreanu, M., Ureña, F., & Vargas, A. (2020). Solving a fully parabolic chemotaxis system with periodic asymptotic behavior using generalized finite difference method. Applied Numerical Mathematics, 157, 356–371. https://doi.org/10.1016/j.apnum.2020.06.011
DOI: https://doi.org/10.1016/j.apnum.2020.06.011   Google Scholar

Bilbao, S. (2013). Modeling of complex geometries and boundary conditions in finite difference/Finite volume time domain room acoustics simulation. IEEE Transactions on Audio, Speech, and Language Processing, 21(7), 1524–1533. https://doi.org/10.1109/tasl.2013.2256897
DOI: https://doi.org/10.1109/TASL.2013.2256897   Google Scholar

Botteldooren, D. (1994). Acoustical finite-difference time-domain simulation in a quasi-Cartesian grid. Journal of the Acoustical Society of America, 95, 2313–2319.
DOI: https://doi.org/10.1121/1.409866   Google Scholar

Chiba, O., Kashiwa, T., Shimoda, H., Kagami, S., & Fukai, I. (1993). Analysis of sound fields in threedimensional space by the time-dependent finite-difference method based on the leapfrog algorithm. Journal Acoustical Society of Japan, 49, 551–562.
  Google Scholar

Degroot‐Hedlin, C. D. (2008). Finite difference time domain synthesis of infrasound propagation through an absorbing atmosphere. The Journal of the Acoustical Society of America, 123(5), 3839–3839. https://doi.org/10.1121/1.2935641
DOI: https://doi.org/10.1121/1.2935641   Google Scholar

Forsythe, G. E., & Wasow, W. R. (1960). Finite-difference methods for partial differential equations. John Wiley & Sons.
  Google Scholar

Ishimaru, A. (2017). Electromagnetic wave propagation, radiation, and scattering: From fundamentals to applications. John Wiley & Sons.
DOI: https://doi.org/10.1002/9781119079699   Google Scholar

Kania, K., Maj, M., Rymarczyk, T., Adamkiewicz, P., & Gołąbek, M. (2020). Image reconstruction in ultrasound transmission tomography using the Fermat’s principle. Przegląd Elektrotechniczny, 1(1), 188–191. https://doi.org/10.15199/48.2020.01.41
DOI: https://doi.org/10.15199/48.2020.01.41   Google Scholar

Kania, K., Rymarczyk, T., Maj, M., & Gołąbek, M. (2019). 2019 applications of electromagnetics in modern engineering and medicine (PTZE). IEEE. https://doi.org/10.23919/PTZE.2019.8781687
DOI: https://doi.org/10.23919/PTZE.2019.8781687   Google Scholar

Kania, K., Rymarczyk, T., Maj, M., Gołąbek, M., Adamkiewicz, P., & Sikora, J. (2019). 2019 international interdisciplinary PhD workshop (IIPhDW). IEEE. https://doi.org/10.1109/IIPHDW.2019.8755416
DOI: https://doi.org/10.1109/IIPHDW.2019.8755416   Google Scholar

Knabner, P., & Angermann, L. (2021). Numerical methods for elliptic and parabolic partial differential equations: With contributions by Andreas Rupp. Springer Nature.
DOI: https://doi.org/10.1007/978-3-030-79385-2   Google Scholar

Kumar, A. (2004). Isotropic finite-differences. Journal of Computational Physics, 201(1), 109–118. https://doi.org/10.1016/j.jcp.2004.05.005
DOI: https://doi.org/10.1016/j.jcp.2004.05.005   Google Scholar

Li, W., Li, S., Shao, X., & Li, Z. (2019). Proceedings of the 6th conference on sound and music technology (CSMT): Revised selected papers. Springer.
DOI: https://doi.org/10.1007/978-981-13-8707-4   Google Scholar

Liu, Y., & Sen, M. K. (2009). A new time-space domain high-order finite-difference method for the acoustic wave equation. Journal of Computational Physics, 228(23), 8779–8806. https://doi.org/10.1016/j.jcp.2009.08.027
DOI: https://doi.org/10.1016/j.jcp.2009.08.027   Google Scholar

Liu, Y., Ding, L., & Sen, M. K. (2011). Comparisons between the hybrid ABC and the PML method for 2D high‐order finite‐difference acoustic modeling. SEG Technical Program Expanded Abstracts 2011. https://doi.org/10.1190/1.3627807
DOI: https://doi.org/10.1190/1.3627807   Google Scholar

Mickens, R. E. (1994). Nonstandard finite difference models of differential equations. World Scientific. Polakowski, K. A., Rymarczyk, T., & Sikora, J. (2020). Obrazowanie ultradźwiękowe: Wybrane algorytmy obrazowania. Oficyna Wydawnicza Politechniki Warszawskiej.
DOI: https://doi.org/10.1142/2081   Google Scholar

Polakowski, K., & Sikora, J. (2016). Podstawy matematyczne obrazowania ultradźwiękowego. Politechnika Lubelska.
  Google Scholar

Sullivan, D., & Young, J. (2001). Far-field time-domain calculation from aperture radiators using the FDTD method. IEEE Transactions on Antennas and Propagation, 49(3), 464–469. https://doi.org/10.1109/8.918622
DOI: https://doi.org/10.1109/8.918622   Google Scholar

Svensson, U. P., Fred, R. I., & Vanderkooy, J. (1999). An analytic secondary source model of edge diffraction impulse responses. The Journal of the Acoustical Society of America, 106(5), 2331–2344. https://doi.org/10.1121/1.428071
DOI: https://doi.org/10.1121/1.428071   Google Scholar

Thomas, J. (2013). Numerical partial differential equations: Finite difference methods. Springer Science & Business Media.
  Google Scholar

Thomée, V. (2001). From finite differences to finite elements a short history of numerical analysis of partial differential equations. Partial Differential Equations, 2001, 1–54. https://doi.org/10.1016/b978-0-444-50616-0.50004-x
DOI: https://doi.org/10.1016/B978-0-444-50616-0.50004-X   Google Scholar