Time domain scattering and inverse scattering problems in a locally perturbed half-plane

References

• Zhang H, Zhang B. A novel integral equation for scattering by locally rough surfaces and application to the inverse problem. SIAM J. Appl. Math. 2013;73:1811–1829.
   Web of Science ®Google Scholar
• Colton D, Kress R. Inverse acoustic and electromagnetic scattering theory. 3rd ed. Berlin: Springer; 2013.
   Google Scholar
• Arens T. Why linear sampling works. Inverse Prob. 2004;20:163–173.
   Web of Science ®Google Scholar
• Sun Y, Guo Y, Ma F. The reciprocity gap functional method for the inverse scattering problem for cavities. Appl. Anal. 2016;95:1327–1346.
   Web of Science ®Google Scholar
• Chen Q, Haddar H, Lechleiter A, et al. A sampling method for inverse scattering in the time domain. Inverse Prob. 2010;26:85001–85017.
   Web of Science ®Google Scholar
• Guo Y, Monk P, Colton D. The linear sampling method for sparse small aperture data. Appl. Anal. 2015;95:1599–1615
   Web of Science ®Google Scholar
• Monk P, Selgas V. An inverse acoustic waveguide problem in the time domain. Inverse Prob. 2016;32:055001.
   Web of Science ®Google Scholar
• Guo Y, Hömberg D, Hu G, et al. A time domain sampling method for inverse acoustic scattering problems. J. Comput. Phys. 2016;314:647–660.
   Web of Science ®Google Scholar
• Ha-Duong T. On retarded potential boundary integral equations and their discretisation. Top. Comput. Wave Propag. 2003;31:301–336.
   Google Scholar
• Kress R, Tran T. Inverse scattering for a locally perturbed half-plane. Inverse Prob. 2000;16:1541–1559.
   Web of Science ®Google Scholar
• Feng L, Ma F. A sampling method for solving inverse scattering problems with a locally perturbed half plane. Northeastern Math. J. 2003;19:1–4.
   Google Scholar
• Dong H, Ma F. Reconstruction of the shape of object with near field measurements in a half-plane. Sci. China Ser. A: Math. 2008;51:1059–1070.
   Google Scholar
• Dong H, Ma F, Yuan X, et al. Inverse electromagnetic scattering for a locally perturbed perfectly conducting plate. Wave Motion. 2016;60:95–107.
   Web of Science ®Google Scholar
• Colton D, Kress R. Integral equation methods in scattering theory. New York (NY): John Wiley; 1983.
   Google Scholar
• Sayas FJ. Retarded potentials and time domain boundary integral equations: a road-map. Vol. 50, Springer Series in Computational Mathematics. Basel: Springer; 2016.
   Google Scholar
• Colton D, Kirsch A. A simple method for solving inverse scattering problems in the resonance region. Inverse Prob. 1996;12:383–393.
   Web of Science ®Google Scholar
• Cakoni F, Colton D, Monk P. The linear sampling method in inverse electromagnetic scattering. Philadelphia: SIAM Publications; 2011.
   Google Scholar
• Cakoni F, Colton D. A qualitative approach to inverse scattering theory. New York (NY): Springer; 2014.
   Google Scholar
• Guo Y, Monk P, Colton D. Toward a time domain approach to the linear sampling method. Inverse Prob. 2013;29:95016–95032.
   Web of Science ®Google Scholar
• Haddar H, Lechleiter A, Marmorat S. An improved time domain linear sampling method for Robin and Neumann obstacles. Appl. Anal. 2014;93:369–390.
   Web of Science ®Google Scholar
• Hsiao GC, Wendland WL. Boundary integral equations. Berlin: Springer; 2008.
   Google Scholar
• Kirsch A, Ritter S. A linear sampling method for inverse scattering from an open arc. Inverse Prob. 2000;16:89–105.
   Web of Science ®Google Scholar
• Cakoni F, Colton D. The linear sampling method for cracks. Inverse Prob. 2003;19:279–295.
   Web of Science ®Google Scholar
• Banjai L, Sauter S. Rapid solution of the wave equation in unbounded domains. SIAM J. Numer. Anal. 2008;47:227–249.
   Web of Science ®Google Scholar
• Lubich C. Convolution quadrature and discretized operational calculus I. Numerische Math. 1988;52:129–145.
   Web of Science ®Google Scholar
• Lubich C. Convolution quadrature and discretized operational calculus II. Numerische Math. 1988;52:413–425.
   Web of Science ®Google Scholar
• Lubich C. On the multistep time discretization of linear initial-boundary value problems and their boundary integral equations. Numerische Math. 1994;67:365–389.
   Web of Science ®Google Scholar
• Kress R. Linear integral equations. 2nd ed. New York (NY): Springer; 1999.
   Google Scholar
• Lehoucq R, Maschhoff K, Sorensen D. ARPACK software. Available from: http://www.caam.rice.edu/software/ARPACK/.
   Google Scholar