Events
DMS Applied Mathematics Seminar |
| Time: Apr 26, 2019 (02:00 PM) |
| Location: Parker Hall 328 |
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Details: Speaker: Prof. Dinh-Liem Nguyen, Kansas State University Title: Solving nonlinear inverse scattering problems with little a priori information
Abstract. The goal of inverse scattering problems is, broadly speaking, to determine information about an object from measurements of the field scattered by that object. These inverse problems arise in a wide range of applications, including non-destructive evaluations, detection of explosives, medical imaging, radar imaging, and geophysical prospecting. Inverse scattering problems are, in general, highly nonlinear and ill-posed problems, causing substantial challenges in studying their numerical solution. Optimization-based methods are the most widely studied approach among the numerical methods for solving these inverse problems. However, these methods suffer from the fact that they may converge to a local minimum of the cost function, which is not the true solution to the inverse problem. In addition, they require strong a priori information about the true solution which is not always available in some practical applications.
In this talk, after a short introduction to inverse scattering problems, we will discuss our recent results in developing two different numerical methods for solving these problems, without using any detailed a priori information of the solution. The first method is to solve a coefficient inverse problem for the Helmholtz equation and the second one is to solve a shape inverse problem for Maxwell's equations.
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