374 research outputs found
Near-field imaging of scattering obstacles with the factorization method
In this paper we establish a factorization method for recovering the location and shape of an acoustic bounded obstacle with using the near-field data, corresponding to infinitely many incident point sources. The obstacle is allowed to be an impenetrable scatterer of sound-soft, sound-hard or impedance type or a penetrable scatterer. An outgoing-to-incoming operator is constructed for facilitating the factorization of the near-field operator, which can be easily implemented numerically. Numerical examples are presented to demonstrate the feasibility and effectiveness of our inversion algorithm, including the case where limited aperture near-field data are available only
Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems
In this paper, we propose and study the uniaxial perfectly matched layer
(PML) method for three-dimensional time-domain electromagnetic scattering
problems, which has a great advantage over the spherical one in dealing with
problems involving anisotropic scatterers. The truncated uniaxial PML problem
is proved to be well-posed and stable, based on the Laplace transform technique
and the energy method. Moreover, the -norm and -norm error
estimates in time are given between the solutions of the original scattering
problem and the truncated PML problem, leading to the exponential convergence
of the time-domain uniaxial PML method in terms of the thickness and absorbing
parameters of the PML layer. The proof depends on the error analysis between
the EtM operators for the original scattering problem and the truncated PML
problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3)
(2020), 1918-1940).Comment: 23 pages, 1 figure. arXiv admin note: text overlap with
arXiv:1907.0890
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