A decomposition scheme for acoustic obstacle scattering in a multilayered medium

References

• Colton , D and Kress , R . 1983 . Integral Equation Methods in Scattering Theory , New York : John Wiley & Sons .
   Google Scholar
• Colton , D and Kress , R . 1998 . Inverse Acoustic and Electromagnetic Scattering Theory, , 2nd , Berlin : Springer-Verlag .
   Google Scholar
• Nédélec , JC . 2001 . Acoustic and Electromagnetic Equations , New York : Springer-Verlag .
   Google Scholar
• Potthast , R . 2001 . Point Sources and Multipoles in Inverse Scattering Theory , London : Chapman & Hall/CRC .
   Google Scholar
• Martin , PA . 2006 . Multiple Scattering , Cambridge : Cambridge University Press .
   Google Scholar
• Balabane , M . 2004 . Boundary decomposition for Helmholtz and Maxwell equations. 1: Disjoint sub-scatterers . Asymptotic Anal. , 38 : 1 – 10 .
   Web of Science ®Google Scholar
• Ganesh , M and Hawkins , SC . 2008 . Simulation of acoustic scattering by multiple obstacles in three dimension . ANZIAM J. , 50 : C31 – C45 .
   Web of Science ®Google Scholar
• Grote , MJ and Kirsch , C . 2004 . Dirichlet-to-Neumann boundary conditions for multiple scattering problems . J. Comput. Phys. , 201 : 630 – 650 .
   Web of Science ®Google Scholar
• Grote , MJ and Kirsch , C . 2007 . Nonreflecting boundary conditions for time dependent multiple scattering . J. Comput. Phys. , 221 : 41 – 62 .
   Web of Science ®Google Scholar
• Hassen , FB , Liu , JJ and Potthast , R . 2007 . On source analysis by wave splitting with applications in inverse scattering of multiple obstacles . J. Comput. Math. , 25 ( 3 ) : 266 – 281 .
   Google Scholar
• Potthast , R , Fazi , FM and Nelson , PA . 2010 . Source splitting via the point sources method . Inverse Probl. , 26 ( 4 ) : 045002
   Google Scholar
• Cheng , J , Liu , JJ , Nakamura , G and Wang , SZ . 2009 . Recovery of multiple obstacles by probe method . Quart. Appl. Math. , 67 ( 2 ) : 221 – 247 .
   Web of Science ®Google Scholar
• Liu , JJ , Nakamura , G and Sini , M . 2007 . Reconstruction of the shape and surface impedance from acoustic scattering data for arbitrary cylinder . SIAM J. Appl. Math. , 67 ( 4 ) : 1124 – 1146 .
   Web of Science ®Google Scholar
• Liu , JJ and Sini , M . 2009 . On the accuracy of the numerical detection of complex obstacles from far field data using the probe method . SIAM J. Sci. Comput. , 31 ( 4 ) : 2665 – 2687 .
   Web of Science ®Google Scholar
• Cai , LW . 2004 . Multiple scattering in single scattering . J. Acoustic. Soc. Am. , 115 : 986 – 995 .
   Web of Science ®Google Scholar
• Cai , LW and Sánchez-Dehasa , J . 2008 . Acoustic scattering by radially stratified scatterers . J. Acoust. Soc. Am. , 124 : 2715 – 2726 .
   PubMed Web of Science ®Google Scholar
• Huang , K , Solna , K and Zhao , H . 2010 . Generalized Foldy–Lax formulation . J. Comput. Phys. , 229 : 4544 – 4553 .
   Web of Science ®Google Scholar
• Huang , K and Li , PJ . 2010 . A two-scale multiple scattering problem . Multiscale Model. Simul. , 8 ( 4 ) : 1511 – 1534 .
   Google Scholar
• Kress , R , Yaman , F , Yapar , A and Akduman , I . 2009 . Inverse scattering for an impedance cylinder buried in a dielectric cylinder . Inverse Probl. Sci. Eng. , 17 ( 4 ) : 473 – 488 .
   Web of Science ®Google Scholar
• Liu , XD and Zhang , B . 2010 . Direct and inverse scattering problem in a piecewise homogeneous medium . SIAM J. Appl. Math. , 70 ( 8 ) : 3105 – 3120 .
   Google Scholar
• Kress , R and Roach , GF . 1978 . Transmission problems for the Helmholtz equation . J. Math. Phys. , 19 ( 6 ) : 1433 – 1437 .
   Google Scholar
• Bérenger , JP . 1994 . A perfectly matched layer for the absorption of electromagnetic waves . J. Comput. Phys. , 114 ( 2 ) : 185 – 200 .
   Web of Science ®Google Scholar
• Engquist , B and Majda , A . 1977 . Absorbing boundary conditions for the numerical simulation of waves . Math. Comput. , 31 ( 139 ) : 629 – 651 .
   Web of Science ®Google Scholar
• Grote , MJ and Keller , JB . 1995 . On nonreflecting boundary conditions . J. Comput. Phys. , 122 ( 2 ) : 231 – 243 .
   Google Scholar
• Rapún , ML and Sayas , FJ . 2008 . Mixed boundary integral methods for Helmholtz transmission problems . J. Comput. Appl. Math. , 214 : 238 – 258 .
   Web of Science ®Google Scholar
• Zinn , A . 1989 . A numerical method for Transmission problems for the Helmholtz equation . Computing , 41 : 267 – 274 .
   Web of Science ®Google Scholar