Brown Analysis Seminar
Applied Mathematics Colloquium
Brown University, Providence, RI 02912 | |
Abstract: It has been called the most significant mathematical result of the 20th Century and yet it appears to be irrelevant to most mathematicians.
Scientific Computing Seminar
Abstract: Most of previous work in inverse scattering has been carried out in two dimensions assuming a homogeneous background medium. The use of a homogeneous background and a two-dimensional approximation simplifies computations significantly. Although in some cases the two-dimensional approximation is appropriate and the background is indeed homogeneous, there are many problems for which the two-dimension and homogeneous medium approximations are inappropriate. For example, when one is interested in sensing subsurface targets, one often has to deal with a half-space medium (air-ground) and the sensors are incompatible with a two-dimensional approximation. This talk will present our research results on a complete three-dimensional inverse problem. In this study, we model the transmitter as a loop antenna, with separate bistatic loops used for detection. The simulated measured data is generated via a rigorous volumetric method-of-moments (MoM) and complex white Gaussian noise is added to the data. We employ the extend-Born method as forward solver to accelerate inversion. The inversion is performed via the iterative extend-Born method with simple Tikhonov regularization. Our results show the efficiency of these algorithms in three-dimensional inverse scattering problem.
PDE Seminar
Department of Mathematics Colloquium
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