Abstract
This paper is concerned with the analysis of the time domain acoustic scattering from locally perturbed flat substrates. For this three dimensional scattering problem with unbounded scatterer, boundary integral equation is directly established on the boundary of the unbounded scatterer without application of the symmetric continuation. The well-posedness of the time domain boundary integral equation is proved.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Colton, D., Kress, R.: Inverse Acoustic and Electromagnetic Scattering Theory, 3rd edn. Springer, Berlin (2013)
Sun, Y., Guo, Y., Ma, F.: The reciprocity gap functional method for the inverse scattering problem for cavities. Appl. Anal. 95, 1327–1346 (2016)
Guo, Y., Monk, P., Colton, D.: The linear sampling method for sparse small aperture data. Appl. Anal. 95(8), 1599–1615 (2016)
Guo, Y., Hömberg, D., Hu, G., Li, J., Liu, H.: A time domain sampling method for inverse acoustic scattering problems. J. Comput. Phys. 314, 647–660 (2016)
Feng, L., Ma, F.: A sampling method for solving inverse scattering problems with a locally perturbed half plane. Northeast. Math. J. 19, 1–4 (2003)
Dong, H., Ma, F.: Reconstruction of the shape of object with near field measurements in a half-plane. Sci. China, Ser. A Math. 51, 1059–1070 (2008)
Chen, B., Ma, F., Guo, Y.: Time domain scattering and inverse scattering problems in a locally perturbed half-plane. Appl. Anal. 96(8), 1303–1325 (2016)
Colton, D., Kress, R.: Integral Equation Methods in Scattering Theory. Wiley, New York (1983)
Banjai, L., Sauter, S.: Rapid solution of the wave equation in unbounded domains. SIAM J. Numer. Anal. 47, 227–249 (2008)
Chen, Q., Haddar, H., Lechleiter, A., Monk, P.: A sampling method for inverse scattering in the time domain. Inverse Prob. 26, 85001–85017 (2010)
Sayas, F.J.: Retarded Potentials and Time Domain Boundary Integral Equations: A Road-Map. Springer Series in Computational Mathematics, vol. 50. Springer, Basel (2016)
Hsiao, G.C., Wendland, W.L.: Boundary Integral Equations. Springer, Berlin (2008)
Acknowledgements
The work of Bo Chen was supported by the National Natural Science Foundation of China (NSFC) grants 11371172 and 11671170 and the Scientific Research Foundation of Civil Aviation University of China (No. 2017QD04S). The work of Minghui Liu was supported by the NSFC Grant 11626230 and the Fundamental Research Funds for the Central Universities Grant 2016JKF01101. The work of Fuquan Zhang was supported by the Scientific Research Foundation of Minjiang University (No. MYK17021).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Chen, B., Zhang, F., Xu, L., Liu, M. (2018). Time Domain Acoustic Scattering from Locally Perturbed Flat Substrates. In: Pan, JS., Wu, TY., Zhao, Y., Jain, L. (eds) Advances in Smart Vehicular Technology, Transportation, Communication and Applications. VTCA 2017. Smart Innovation, Systems and Technologies, vol 86. Springer, Cham. https://doi.org/10.1007/978-3-319-70730-3_35
Download citation
DOI: https://doi.org/10.1007/978-3-319-70730-3_35
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-70729-7
Online ISBN: 978-3-319-70730-3
eBook Packages: EngineeringEngineering (R0)